TimeSeries.ipynb

{"nbformat_minor": 1, "cells": [{"source": "# Applications of Data Science\n\n# Lab 1\n\n# Exploring Time Series Data\n\n## Overview\n\nTime series models are used in a wide range of applications, particularly for forecasting. \n\nThis notebook contains lab material to familarize yourself with key aspects of time series analysis. You will perform analyses on a time series of California dairy data. Specifically, you will explore the structure of the time series and forecast the monthly production of fresh milk in the state of California. \n\nThis exploration is performed in two steps:\n\n- Explore the characteristics of the time series data.\n- Decompose the time series of monthly milk production into trend, seasonal components, and remainder components. \n- Apply time series models to the remainder component of the time series.\n- Forecast the production of monthly milk production for a 12 month period. \n\n## What you will need\n\nTo complete this lab, you will need the following:\n\n- A web browser and Internet connection \n- An Azure Machine Learning workspace\n- The lab files for this lab\n\n**Note** To set up the required environment for the lab, follow the instructions in the [Setup guide](https://aka.ms/edx-dat203.3x-setup). \n", "cell_type": "markdown", "metadata": {}}, {"source": "# to avoid problems with loaing and installig R packages, this lab was executed on a local machine 'anaconda distribution', than uploaded to AzureML ", "cell_type": "markdown", "metadata": {}}, {"source": "## Load and Examine the Data\n\nAs a first step, ensure that you have uploaded the **cadairydata.csv** file as a new dataset in your Azure Machine Learning workspace, and then execute the code below to load the data set into a dataframe.", "cell_type": "markdown", "metadata": {}}, {"source": "to.POSIXct <- function(year, monthNumber){\n  ## Function to create a POSIXct time series \n  ## object from a year.month format\n  \n  ## Create a character vector from the numeric input\n  dateStr <- paste(as.character(year), \"-\",\n                   as.character(monthNumber), \"-\",\n                   \"01\", sep = \"\")\n  ## Return the POSIXct time series object\n  as.POSIXct( strptime(dateStr, \"%Y-%m-%d\"))\n}\n\norder.month <- function(x){\n  ## Function to make Month column an ordered factor.\n  x <- substr(x, 1, 3) ## Use just the first three letters\n  factor(x, levels = c(\"Jan\", \"Feb\", \"Mar\", \"Apr\", \"May\", \"Jun\",\"Jul\", \"Aug\", \"Sep\", \"Oct\", \"Nov\", \"Dec\"),\n         ordered = TRUE)\n}\n\nread.dairy <- function(dataSet = 'cadairydata.csv'){\n  ##library(\"AzureML\")\n  #ws <- workspace()\n\n  df <- read.csv('cadairydata.csv')\n\n    #download.datasets(ws, dataSet)\n  df$dateTime <- to.POSIXct(df$Year, df$Month.Number)\n\n  dropCols <- c(\"X\",\"Year.Month\", \"Month.Number\")\n\n  df$Month <- order.month(df$Month)\n\n  df[ , !(names(df) %in% dropCols)]\n\n}\n\ndairy <- read.dairy()", "execution_count": 2, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": []}, {"source": "", "execution_count": null, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": []}, {"source": "The code you just executed performs the following steps:\n\n- The data is read from a dataset in your Azure Machine Learning subscription.\n- A new column, of type POSIXct, is created. POSIXct is a flexible R data-time class. The **strtime** function formats a text string for conversion to the date-time class. \n- The **Month** column is converted to an ordered R factor class. \n- Some unnecessary columns are removed from the data frame.\n\nNext, execute the code below and examine the head of the data frame.", "cell_type": "markdown", "metadata": {}}, {"source": "head(dairy)", "execution_count": 3, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"data": {"text/latex": "\\begin{tabular}{r|lllllll}\n Year & Month & Cotagecheese.Prod & Icecream.Prod & Milk.Prod & N.CA.Fat.Price & dateTime\\\\\n\\hline\n\t 1995       & Jan        & 4.370      & 51.595     & 2.112      & 0.9803     & 1995-01-01\\\\\n\t 1995       & Feb        & 3.695      & 56.086     & 1.932      & 0.8924     & 1995-02-01\\\\\n\t 1995       & Mar        & 4.538      & 68.453     & 2.162      & 0.8924     & 1995-03-01\\\\\n\t 1995       & Apr        & 4.280      & 65.722     & 2.130      & 0.8967     & 1995-04-01\\\\\n\t 1995       & May        & 4.470      & 73.730     & 2.227      & 0.8967     & 1995-05-01\\\\\n\t 1995       & Jun        & 4.238      & 77.994     & 2.124      & 0.9160     & 1995-06-01\\\\\n\\end{tabular}\n", "text/plain": "  Year Month Cotagecheese.Prod Icecream.Prod Milk.Prod N.CA.Fat.Price\n1 1995 Jan   4.370             51.595        2.112     0.9803        \n2 1995 Feb   3.695             56.086        1.932     0.8924        \n3 1995 Mar   4.538             68.453        2.162     0.8924        \n4 1995 Apr   4.280             65.722        2.130     0.8967        \n5 1995 May   4.470             73.730        2.227     0.8967        \n6 1995 Jun   4.238             77.994        2.124     0.9160        \n  dateTime  \n1 1995-01-01\n2 1995-02-01\n3 1995-03-01\n4 1995-04-01\n5 1995-05-01\n6 1995-06-01", "text/html": "<table>\n<thead><tr><th scope=col>Year<\/th><th scope=col>Month<\/th><th scope=col>Cotagecheese.Prod<\/th><th scope=col>Icecream.Prod<\/th><th scope=col>Milk.Prod<\/th><th scope=col>N.CA.Fat.Price<\/th><th scope=col>dateTime<\/th><\/tr><\/thead>\n<tbody>\n\t<tr><td>1995      <\/td><td>Jan       <\/td><td>4.370     <\/td><td>51.595    <\/td><td>2.112     <\/td><td>0.9803    <\/td><td>1995-01-01<\/td><\/tr>\n\t<tr><td>1995      <\/td><td>Feb       <\/td><td>3.695     <\/td><td>56.086    <\/td><td>1.932     <\/td><td>0.8924    <\/td><td>1995-02-01<\/td><\/tr>\n\t<tr><td>1995      <\/td><td>Mar       <\/td><td>4.538     <\/td><td>68.453    <\/td><td>2.162     <\/td><td>0.8924    <\/td><td>1995-03-01<\/td><\/tr>\n\t<tr><td>1995      <\/td><td>Apr       <\/td><td>4.280     <\/td><td>65.722    <\/td><td>2.130     <\/td><td>0.8967    <\/td><td>1995-04-01<\/td><\/tr>\n\t<tr><td>1995      <\/td><td>May       <\/td><td>4.470     <\/td><td>73.730    <\/td><td>2.227     <\/td><td>0.8967    <\/td><td>1995-05-01<\/td><\/tr>\n\t<tr><td>1995      <\/td><td>Jun       <\/td><td>4.238     <\/td><td>77.994    <\/td><td>2.124     <\/td><td>0.9160    <\/td><td>1995-06-01<\/td><\/tr>\n<\/tbody>\n<\/table>\n", "text/markdown": "\nYear | Month | Cotagecheese.Prod | Icecream.Prod | Milk.Prod | N.CA.Fat.Price | dateTime | \n|---|---|---|---|---|---|\n| 1995       | Jan        | 4.370      | 51.595     | 2.112      | 0.9803     | 1995-01-01 | \n| 1995       | Feb        | 3.695      | 56.086     | 1.932      | 0.8924     | 1995-02-01 | \n| 1995       | Mar        | 4.538      | 68.453     | 2.162      | 0.8924     | 1995-03-01 | \n| 1995       | Apr        | 4.280      | 65.722     | 2.130      | 0.8967     | 1995-04-01 | \n| 1995       | May        | 4.470      | 73.730     | 2.227      | 0.8967     | 1995-05-01 | \n| 1995       | Jun        | 4.238      | 77.994     | 2.124      | 0.9160     | 1995-06-01 | \n\n\n"}, "output_type": "display_data", "metadata": {}}]}, {"source": "The data frame inlcudes **Year**, **Month**, and the **dateTime** column with calendar information. Other columns show the production of dairy products and a benchmark price for milk fat.\n\nNext, examine the class of the **dateTime** column. ", "cell_type": "markdown", "metadata": {}}, {"source": "class(dairy$dateTime)", "execution_count": 4, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"text/latex": "\\begin{enumerate*}\n\\item 'POSIXct'\n\\item 'POSIXt'\n\\end{enumerate*}\n", "text/plain": "[1] \"POSIXct\" \"POSIXt\" ", "text/html": "<ol class=list-inline>\n\t<li>'POSIXct'<\/li>\n\t<li>'POSIXt'<\/li>\n<\/ol>\n", "text/markdown": "1. 'POSIXct'\n2. 'POSIXt'\n\n\n"}, "output_type": "display_data", "metadata": {}}]}, {"source": "As expected, this column is of class **POSIXct**, which inherits from the R **POSIXt** class. \n\nNow, examine the first 20 values of the **dateTime** column.", "cell_type": "markdown", "metadata": {}}, {"source": "dairy$dateTime[1:20]", "execution_count": 5, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"text/plain": " [1] \"1995-01-01 WET\" \"1995-02-01 WET\" \"1995-03-01 WET\" \"1995-04-01 WET\"\n [5] \"1995-05-01 WET\" \"1995-06-01 WET\" \"1995-07-01 WET\" \"1995-08-01 WET\"\n [9] \"1995-09-01 WET\" \"1995-10-01 WET\" \"1995-11-01 WET\" \"1995-12-01 WET\"\n[13] \"1996-01-01 WET\" \"1996-02-01 WET\" \"1996-03-01 WET\" \"1996-04-01 WET\"\n[17] \"1996-05-01 WET\" \"1996-06-01 WET\" \"1996-07-01 WET\" \"1996-08-01 WET\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Note that these values inlcude the day and a time zone.\n\nYou can perform both arithmetic and logical operations on POSIXct objects. As an example, select the last 12 months of dairy data by executing the next code cell. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy[dairy$dateTime > '2012-12-01',]", "execution_count": 6, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"text/latex": "\\begin{tabular}{r|lllllll}\n  & Year & Month & Cotagecheese.Prod & Icecream.Prod & Milk.Prod & N.CA.Fat.Price & dateTime\\\\\n\\hline\n\tNA &   NA   & NA     &    NA  &     NA &    NA  &     NA & NA    \\\\\n\tNA.1 &   NA   & NA     &    NA  &     NA &    NA  &     NA & NA    \\\\\n\t217 & 2013       & Jan        & 2.282      & 62.612     & 3.462      & 1.7744     & 2013-01-01\\\\\n\t218 & 2013       & Feb        & 1.941      & 66.274     & 3.231      & 1.6224     & 2013-02-01\\\\\n\t219 & 2013       & Mar        & 2.150      & 75.770     & 3.676      & 1.6968     & 2013-03-01\\\\\n\t220 & 2013       & Apr        & 2.217      & 76.396     & 3.622      & 1.7444     & 2013-04-01\\\\\n\t221 & 2013       & May        & 2.341      & 80.899     & 3.720      & 1.8552     & 2013-05-01\\\\\n\t222 & 2013       & Jun        & 2.694      & 92.091     & 3.489      & 1.8314     & 2013-06-01\\\\\n\t223 & 2013       & Jul        & 2.433      & 84.026     & 3.373      & 1.6923     & 2013-07-01\\\\\n\t224 & 2013       & Aug        & 2.169      & 78.382     & 3.400      & 1.6273     & 2013-08-01\\\\\n\t225 & 2013       & Sep        & 2.193      & 74.871     & 3.197      & 1.5519     & 2013-09-01\\\\\n\t226 & 2013       & Oct        & 2.284      & 70.011     & 3.338      & 1.5566     & 2013-10-01\\\\\n\t227 & 2013       & Nov        & 1.865      & 61.394     & 3.275      & 1.7537     & 2013-11-01\\\\\n\t228 & 2013       & Dec        & 2.345      & 53.653     & 3.473      & 1.6747     & 2013-12-01\\\\\n\\end{tabular}\n", "text/plain": "     Year Month Cotagecheese.Prod Icecream.Prod Milk.Prod N.CA.Fat.Price\nNA     NA NA       NA                 NA           NA         NA        \nNA.1   NA NA       NA                 NA           NA         NA        \n217  2013 Jan   2.282             62.612        3.462     1.7744        \n218  2013 Feb   1.941             66.274        3.231     1.6224        \n219  2013 Mar   2.150             75.770        3.676     1.6968        \n220  2013 Apr   2.217             76.396        3.622     1.7444        \n221  2013 May   2.341             80.899        3.720     1.8552        \n222  2013 Jun   2.694             92.091        3.489     1.8314        \n223  2013 Jul   2.433             84.026        3.373     1.6923        \n224  2013 Aug   2.169             78.382        3.400     1.6273        \n225  2013 Sep   2.193             74.871        3.197     1.5519        \n226  2013 Oct   2.284             70.011        3.338     1.5566        \n227  2013 Nov   1.865             61.394        3.275     1.7537        \n228  2013 Dec   2.345             53.653        3.473     1.6747        \n     dateTime  \nNA   <NA>      \nNA.1 <NA>      \n217  2013-01-01\n218  2013-02-01\n219  2013-03-01\n220  2013-04-01\n221  2013-05-01\n222  2013-06-01\n223  2013-07-01\n224  2013-08-01\n225  2013-09-01\n226  2013-10-01\n227  2013-11-01\n228  2013-12-01", "text/html": "<table>\n<thead><tr><th><\/th><th scope=col>Year<\/th><th scope=col>Month<\/th><th scope=col>Cotagecheese.Prod<\/th><th scope=col>Icecream.Prod<\/th><th scope=col>Milk.Prod<\/th><th scope=col>N.CA.Fat.Price<\/th><th scope=col>dateTime<\/th><\/tr><\/thead>\n<tbody>\n\t<tr><th scope=row>NA<\/th><td>  NA  <\/td><td>NA    <\/td><td>   NA <\/td><td>    NA<\/td><td>   NA <\/td><td>    NA<\/td><td>NA    <\/td><\/tr>\n\t<tr><th scope=row>NA.1<\/th><td>  NA  <\/td><td>NA    <\/td><td>   NA <\/td><td>    NA<\/td><td>   NA <\/td><td>    NA<\/td><td>NA    <\/td><\/tr>\n\t<tr><th scope=row>217<\/th><td>2013      <\/td><td>Jan       <\/td><td>2.282     <\/td><td>62.612    <\/td><td>3.462     <\/td><td>1.7744    <\/td><td>2013-01-01<\/td><\/tr>\n\t<tr><th scope=row>218<\/th><td>2013      <\/td><td>Feb       <\/td><td>1.941     <\/td><td>66.274    <\/td><td>3.231     <\/td><td>1.6224    <\/td><td>2013-02-01<\/td><\/tr>\n\t<tr><th scope=row>219<\/th><td>2013      <\/td><td>Mar       <\/td><td>2.150     <\/td><td>75.770    <\/td><td>3.676     <\/td><td>1.6968    <\/td><td>2013-03-01<\/td><\/tr>\n\t<tr><th scope=row>220<\/th><td>2013      <\/td><td>Apr       <\/td><td>2.217     <\/td><td>76.396    <\/td><td>3.622     <\/td><td>1.7444    <\/td><td>2013-04-01<\/td><\/tr>\n\t<tr><th scope=row>221<\/th><td>2013      <\/td><td>May       <\/td><td>2.341     <\/td><td>80.899    <\/td><td>3.720     <\/td><td>1.8552    <\/td><td>2013-05-01<\/td><\/tr>\n\t<tr><th scope=row>222<\/th><td>2013      <\/td><td>Jun       <\/td><td>2.694     <\/td><td>92.091    <\/td><td>3.489     <\/td><td>1.8314    <\/td><td>2013-06-01<\/td><\/tr>\n\t<tr><th scope=row>223<\/th><td>2013      <\/td><td>Jul       <\/td><td>2.433     <\/td><td>84.026    <\/td><td>3.373     <\/td><td>1.6923    <\/td><td>2013-07-01<\/td><\/tr>\n\t<tr><th scope=row>224<\/th><td>2013      <\/td><td>Aug       <\/td><td>2.169     <\/td><td>78.382    <\/td><td>3.400     <\/td><td>1.6273    <\/td><td>2013-08-01<\/td><\/tr>\n\t<tr><th scope=row>225<\/th><td>2013      <\/td><td>Sep       <\/td><td>2.193     <\/td><td>74.871    <\/td><td>3.197     <\/td><td>1.5519    <\/td><td>2013-09-01<\/td><\/tr>\n\t<tr><th scope=row>226<\/th><td>2013      <\/td><td>Oct       <\/td><td>2.284     <\/td><td>70.011    <\/td><td>3.338     <\/td><td>1.5566    <\/td><td>2013-10-01<\/td><\/tr>\n\t<tr><th scope=row>227<\/th><td>2013      <\/td><td>Nov       <\/td><td>1.865     <\/td><td>61.394    <\/td><td>3.275     <\/td><td>1.7537    <\/td><td>2013-11-01<\/td><\/tr>\n\t<tr><th scope=row>228<\/th><td>2013      <\/td><td>Dec       <\/td><td>2.345     <\/td><td>53.653    <\/td><td>3.473     <\/td><td>1.6747    <\/td><td>2013-12-01<\/td><\/tr>\n<\/tbody>\n<\/table>\n", "text/markdown": "\n| <!--/--> | Year | Month | Cotagecheese.Prod | Icecream.Prod | Milk.Prod | N.CA.Fat.Price | dateTime | \n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| NA |   NA   | NA     |    NA  |     NA |    NA  |     NA | NA     | \n| NA.1 |   NA   | NA     |    NA  |     NA |    NA  |     NA | NA     | \n| 217 | 2013       | Jan        | 2.282      | 62.612     | 3.462      | 1.7744     | 2013-01-01 | \n| 218 | 2013       | Feb        | 1.941      | 66.274     | 3.231      | 1.6224     | 2013-02-01 | \n| 219 | 2013       | Mar        | 2.150      | 75.770     | 3.676      | 1.6968     | 2013-03-01 | \n| 220 | 2013       | Apr        | 2.217      | 76.396     | 3.622      | 1.7444     | 2013-04-01 | \n| 221 | 2013       | May        | 2.341      | 80.899     | 3.720      | 1.8552     | 2013-05-01 | \n| 222 | 2013       | Jun        | 2.694      | 92.091     | 3.489      | 1.8314     | 2013-06-01 | \n| 223 | 2013       | Jul        | 2.433      | 84.026     | 3.373      | 1.6923     | 2013-07-01 | \n| 224 | 2013       | Aug        | 2.169      | 78.382     | 3.400      | 1.6273     | 2013-08-01 | \n| 225 | 2013       | Sep        | 2.193      | 74.871     | 3.197      | 1.5519     | 2013-09-01 | \n| 226 | 2013       | Oct        | 2.284      | 70.011     | 3.338      | 1.5566     | 2013-10-01 | \n| 227 | 2013       | Nov        | 1.865      | 61.394     | 3.275      | 1.7537     | 2013-11-01 | \n| 228 | 2013       | Dec        | 2.345      | 53.653     | 3.473      | 1.6747     | 2013-12-01 | \n\n\n"}, "output_type": "display_data", "metadata": {}}]}, {"source": "Try selecting some other subsets of these data using the **POSIXct** column. \n\n## Create a Time Series Plot\n\nNow that you have examined the data frame, you will create a time series plot of milk production. When creating a time series plot, the **POSIXct** column is used to create the time axis. \n\nThe plot is created using the **ggplot2** package. Execute the code in the cell below to create the time series plot of milk production. ", "cell_type": "markdown", "metadata": {}}, {"source": "library(repr)\noptions(repr.plot.width=8, repr.plot.height=8)\n\ndairy.plot <- function(df, col = 'Milk.Prod'){\n  require(ggplot2)\n  ggplot(df, aes_string('dateTime', col)) +\n    geom_line() +\n    ggtitle(paste('Time series of', col)) +\n    xlab('Time in years')\n}\ndairy.plot(dairy)", "execution_count": 7, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stderr", "output_type": "stream", "text": "Loading required package: ggplot2\nWarning message:\n\"Removed 2 rows containing missing values (geom_path).\""}, {"data": {}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8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\nrkJggg==", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "The production of milk is shown on the vertical scale and the date is on the horizontal scale. \n\nFor most of the time period shown, the production of milk increased year over year. However, there is a decline in milk production starting in 2009 as a results of the recession. Also, notice that this time series exhibits a strong seasonal component with an annual cycle. \n\n\n## Statistical Properties of the Time Series\n\nHaving examined the time series of milk production, you will now explore some statistical properties of the time series. \n\nAutocorrelation is a fundamental property of time series. The **Autocorrelation Function** or ACF provides information on the dependency of the time series values of previous values. Later in this lab, you will use the results of a ACF analysis to estimate the order of moving average processes.The **Partial autocorrelation Function** or PACF, measures the correlation of the time series with its own lag values. Later in this lab you will use an  PACF to estimate the order of an autoregressive process. \n\nExecute the code in the following cell and examine the ACF of the milk production time series. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf <- function(df, col = 'remainder', is.df =TRUE){\n  if(is.df) temp <- df[, col]\n  else temp <- df\n  temp = ts(temp, start = 1995, frequency = 12)\n  par(mfrow = c(2,1))\n  acf(temp, main = paste('ACF of', col))\n  pacf(temp, main = paste('PACF of', col))\n  par(mfrow = c(1,1))\n}\ndairy.acf(dairy, col = 'Milk.Prod')", "execution_count": 8, "cell_type": "code", "metadata": {"scrolled": false, "collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\njAADwggwIIwAA8IIMCDsP9nQpzUGpq7NAAAAAElFTkSuQmCC", "text/plain": "Plot with title \"PACF of Milk.Prod\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Note that the values of the ACF at the various lags decays only slowly. This indicates there is considerable serial correlation between the time series values at the various lags, mostly likely from the trend. \n\nPlotting a histogram provides information on the distribution of values of the time series. Execute the code in the cell below and examine the histogram.", "cell_type": "markdown", "metadata": {}}, {"source": "hist.ts = function(df, col = 'Milk.Prod', bins = 40){\n    temp = df[,col]\n    breaks = seq(min(temp), max(temp), length.out = (bins + 1))\n    hist(temp, breaks = breaks, main = paste('Distribution of ', col), xlab = col)\n}\nhist.ts(dairy)", "execution_count": 9, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nYAwCAxiDwADGIDCAMQgMYAwCAxjzD9k+Q+wk5Ae0AAAAAElFTkSuQmCC", "text/plain": "Plot with title \"Distribution of  Milk.Prod\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The histogram of the full milk production time series shows considerable dispursion. Again this behavior is likely the result of the trend. \n\n\n### Exercise: Plot Ice Cream Production\n\nIn this exercise you will use the **Icecream.Prod** column of the **diary** data frame. Create plots to answer the following questions. \n\n- Does icecream production have a noticable seasonal component? Can you characterize the trend of ice cream production greater over time as strong or weak? \n- Is the seasonal variation of icecream production noticable in the plot of ACF? Does the ACF plot indicate a strong trend component? \n\nIn the code cell below, use the **dairy.plot** and **dairy.acf** functions to create new plots showing the ice cream production and answer the questions above. \n", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.plot(dairy, 'Icecream.Prod')", "execution_count": 10, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stderr", "output_type": "stream", "text": "Warning message:\n\"Removed 2 rows containing missing values (geom_path).\""}, {"data": {}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8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", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "## Simple Moving Average Decomposition of the Time Series\n\nTime series are typically decomposed into three components: trend, seasonal, and the remainder, or residual. Trend can be modeled by several methods. You will start by decomposing the time series using a simple moving average model. \n\nThe code in the cell below uses moving window method to compute the average of the time series over specified span, or order of the operator. As the moving window operator moves over the data, the average of the values in the windows is calculated. Execute the cell to load the function.", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.ma <- function(df, col = 'Milk.Prod', order = 12){\n  temp = df[, col]\n  end = length(temp) - 1\n  out = rep(0, length(temp))\n  out[1] = temp[1]\n  for(i in 1:end){\n    if(i - order <= 1) j = 1 \n    else j = j + 1\n    out[i + 1] = sum(temp[j:i])/(i - j + 1)\n  }\n  out\n}", "execution_count": 11, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": []}, {"source": "Once the trend has been removed, the seasonal component must be modeled and removed. The function in the cell below computes the seasonal component as a function of the month of the year using a linear model. The **0** in the model formula supresses the intercept term. Since 12 monthly factors are used to model seasonal variation, the model would be over-determined if an intercept was included. \n\nExecute the code in the cell to load the function.", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.seasons <- function(df, col = 'Milk.Prod'){\n  df$y = df[, col]\n  fit = lm(y ~ 0 + Month, data = df)\n  predict(fit, newdata = df)\n}", "execution_count": 12, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": []}, {"source": "Using these functions you will now decompose the time series into its components. The function in the code cell below uses multiplicative decomposition of the time series. The model is transformed to a multiplicative model by taking the log of the time series values. The moving average is computed over a twelve month moving window. \n\nExecute the code in the cell below and examine the head of the resulting data frame. ", "cell_type": "markdown", "metadata": {}}, {"source": "decomp.dairy <- function(df,  col = 'Milk.Prod', multiplicative = TRUE, order = 12){\n  if(multiplicative) {\n    temp = log(df[, col])\n    df[, col] = temp\n  } else { \n    temp = df[, col] \n  }\n  trend = dairy.ma(df, col = col, order = order)\n  temp = temp - trend\n  df[, col] = temp\n  seasonal = dairy.seasons(df, col = col)\n  remainder = temp - seasonal\n  data.frame(trend = trend, seasonal = seasonal, remainder = remainder)\n}\ndecomp <- decomp.dairy(dairy, order = 12)\nhead(decomp)", "execution_count": 13, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"text/latex": "\\begin{tabular}{r|lll}\n trend & seasonal & remainder\\\\\n\\hline\n\t 0.7476354     &  0.02471208   & -2.471208e-02\\\\\n\t 0.7476354     & -0.04996016   & -3.911947e-02\\\\\n\t 0.7030956     &  0.06783954   &  9.862991e-05\\\\\n\t 0.7257416     &  0.03872409   & -8.343715e-03\\\\\n\t 0.7333367     &  0.06733682   & -1.813267e-05\\\\\n\t 0.7468004     &  0.01530435   & -8.803681e-03\\\\\n\\end{tabular}\n", "text/plain": "  trend     seasonal    remainder    \n1 0.7476354  0.02471208 -2.471208e-02\n2 0.7476354 -0.04996016 -3.911947e-02\n3 0.7030956  0.06783954  9.862991e-05\n4 0.7257416  0.03872409 -8.343715e-03\n5 0.7333367  0.06733682 -1.813267e-05\n6 0.7468004  0.01530435 -8.803681e-03", "text/html": "<table>\n<thead><tr><th scope=col>trend<\/th><th scope=col>seasonal<\/th><th scope=col>remainder<\/th><\/tr><\/thead>\n<tbody>\n\t<tr><td>0.7476354    <\/td><td> 0.02471208  <\/td><td>-2.471208e-02<\/td><\/tr>\n\t<tr><td>0.7476354    <\/td><td>-0.04996016  <\/td><td>-3.911947e-02<\/td><\/tr>\n\t<tr><td>0.7030956    <\/td><td> 0.06783954  <\/td><td> 9.862991e-05<\/td><\/tr>\n\t<tr><td>0.7257416    <\/td><td> 0.03872409  <\/td><td>-8.343715e-03<\/td><\/tr>\n\t<tr><td>0.7333367    <\/td><td> 0.06733682  <\/td><td>-1.813267e-05<\/td><\/tr>\n\t<tr><td>0.7468004    <\/td><td> 0.01530435  <\/td><td>-8.803681e-03<\/td><\/tr>\n<\/tbody>\n<\/table>\n", "text/markdown": "\ntrend | seasonal | remainder | \n|---|---|---|---|---|---|\n| 0.7476354     |  0.02471208   | -2.471208e-02 | \n| 0.7476354     | -0.04996016   | -3.911947e-02 | \n| 0.7030956     |  0.06783954   |  9.862991e-05 | \n| 0.7257416     |  0.03872409   | -8.343715e-03 | \n| 0.7333367     |  0.06733682   | -1.813267e-05 | \n| 0.7468004     |  0.01530435   | -8.803681e-03 | \n\n\n"}, "output_type": "display_data", "metadata": {}}]}, {"source": "The resulting data frame has three components for trend, seasonal, and remainder.\n\nThe code in the cell below creates visualizations of each of the three components of the decomposition of the time series using **ggplot2**. Run the code in the cell to visualize these components. \n\n(**Note**: If an error occurs stating that gridExtra can't be found, save the notebook, halt and close it, reopen it, run all the cells above this one, and then re-run the cell below - occasionally newly installed packages fail to load in a timely fashion) ", "cell_type": "markdown", "metadata": {}}, {"source": "decomp.plot <- function(df){\n  require(ggplot2)\n  #install.packages(\"gridExtra\", repos='http://cran.us.r-project.org')\n  require(gridExtra)\n  df$x = 1:nrow(df)\n  ycols = c('trend', 'seasonal', 'remainder')\n  p <- lapply(ycols, function(y){\n               ggplot(df, aes_string('x', y)) + \n                         geom_line() +\n                         ylab(y)\n            })\n  grid.arrange(p[[1]], p[[2]], p[[3]], nrow = 3)\n}\ndecomp.plot(decomp)", "execution_count": 18, "cell_type": "code", "metadata": {"scrolled": true, "collapsed": false}, "outputs": [{"name": "stderr", "output_type": "stream", "text": "Loading required package: gridExtra\nWarning message:\n\"package 'gridExtra' was built under R version 3.4.3\""}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8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\nRK5CYII=", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "install.packages(\"forecast\", repos='http://cran.r-project.org/',dependencies = TRUE)", "execution_count": 16, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stderr", "output_type": "stream", "text": "Installing package into 'C:/Users/009/Documents/R/win-library/3.4'\n(as 'lib' is unspecified)\n"}, {"name": "stdout", "output_type": "stream", "text": "package 'forecast' successfully unpacked and MD5 sums checked\n\nThe downloaded binary packages are in\n\tC:\\Users\\009\\AppData\\Local\\Temp\\Rtmp6VoaUF\\downloaded_packages\n"}]}, {"source": "You can see the trend and seasonal components clearly separated in the above plots. The remainder plot looks fairly random, as expected. But, is the remainder actually stationary?  To test for stationarity of the remainder, plot the ACF by executing the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf(decomp)", "execution_count": 19, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8\nfHyMjIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////UNI3wAAAACXBIWXMAABJ0\nAAASdAHeZh94AAAgAElEQVR4nO3d2YKiMAAF0UxAUVHg/792ZFFxa1lCyA11HsalVUCoQQHV\nVABkmbVHAMB0BAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDAC\nBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDAC\nBoQRMCCMgAFhBByozBiT9S6f94kxdndqL5me749xsMbsZ4/Jn4P48VcsjWc/UC9t7m652vP9\nr78CPtR/JeC48eyH6dS0ebpdTHvBXqqBASftbeci4JDx7IfpWuz1RXTaXbquf+2xrKrieO1l\nVw3MxktbBLwunv0gFddi6zVo0Vy6XC+156pLcqjPfcsm39evmvP2wsuNrheLpHlfXWbW2Ky4\n3+iYmOT6yvxoTXpub3uqX7In7U26h6lP8uv/K/turV7srUmO94G8PGY3JCyNgIN0Xfse6vew\n2e3S8fnvXwK+vdLuVtLPL7DrJJuVemHbP93eTbf3KrLHlfdX7OeqH3D2eA1fndvzaffX18dM\nHi8fsCQCDtI1h7Iq69VwLb2tiu8+B3zf0lUX/Cng9m21vW0Pe1xbX3q0f32hnpbN/xu9l+uP\nN937bgz7b8I/POapwvIIOER5u/66Btm8Gn7P1Tznc7+Xub5TLuutz/n73UybZZdnuW8Ta6+t\n31snl+akqu6v3dtLj4Dt9VH37cVTeym37cVPjwkfCDhEXbl5uwocGvD+9ko7a9eS7wHn3YOX\n7eVu/Xp+Onm+R9UPuL572V68/d+S3y8+P2Y++znAIAQcoPtrZ9t2MTBg01VUbwIz73cz98ju\nr5qrfp5V/y7FKUvNa8DV4/R+w/vF58dkBewJAQfo2OuzXqe+79B9T/rpym8B30578X8M+JR8\nvcWvgD8MGAvimQ5Q0ushqQZvhe6vge37jW4X7YeXyc8n9VEkyf54GR7wx8eEBzzT4TmbvnNz\nxW0/8PmP/cC7n++BbzfL3659OkmeNp59DPj2IKfni89DwvJ4psOTPXbBHNtdwfcjseoNzF+P\nxPq9Fbo5PbUHVJ/aLd2fAu4u/LUGPrZboU/2vs5+f0x4wDMdnt42oG6bb9nb62q/H4n1OGJ6\nX73f6H7x/mDPh2k8TtLmv43bLqKPAX/bD/xhWzaWxDMdnFP/I0S7dm1c3ttM+oc3vrrdqr3/\nt4Dz7lZZ79qnk9treNv0+Dng7ja77uKnx4QHPNPBSfvvJ/PbIYn53tZblj4f5vy4eX2r78dC\nd+fK7Poud5f3r30+ueyv9e4vxe2Qrv7db6fF9TZp/1jot8eEBzzTgDACBoQRMCCMgAFhBAwI\nI2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwI\nI2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwI\nI2BAGAEDwggYEEbAgDACBoQRMCBsesDnw87UdtnZ4fgAGGFqwGViHlKnowRgqKkBZ8aeLs25\nIrcmczdCAIabGrA1l/v5i7FuRgbAOFMDNubbhQ83BTDEhBDH36UxYg3Mhm5gEI8BX98D50Vz\n7ud7YAIGBvEYcJX2VvxJucgggG3xGXB1zpr9wHZ3+LEfmICBQbwGHNIggBgQMCCMgAFhawX8\nYz+wi0EA8Qsn4OF7p8kb6Ci+hCZgoEPAgDACBoQRMCCMgAFhBAwI8xjwiM8xEjAwiMeAjwQM\nOObzJfTFDv0qOwIGBvH6Hvgy9KvsCBgYxO9GrGPvW3WmD4KAgQ5boQFhBAwII2BAGAEDwggY\nEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggY\nEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwqIMmMKxFQQMCAsnYNM3bwQIGFsRTsDDB0HAQIeA\nAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyA\nAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAjzGXCZ2eu/h8SY9DRnELMDJnDEwmPA\nhTWmKm3762XpjEEQMNDxGPDe7MrrP/vi2vLeZNMHQcBAx2PAxpTdP9dX08ZOHwQBAx2vAV//\nsaZ3YeIgCBjoeH0JfamqQ/1PvQb+800wAQODeAz4Ymx2qXb2WnCemHz6IAgY6PjcjZR3W6Br\nhxmDIGCg4/dAjtM+qevdHYo5gyBgoLPJI7EIGLEgYEAYAQPC1gqY/cCAA+EEbPrmjQABYyt4\nCQ0II2BAGAEDwrwGfD7smne4u+w8ZxAEDHQ8Blwmva1UfKAfcMBjwJmxp+ajSFWRWz7QDzjg\nMWDbfpKwceED/YADvj/Q//HCyEEQMNBhDQwI8/seOG8/Rsh7YMANn7uR0t5W6KScPggCBjp+\n9wNnzX5guzuwHxhwgSOxAGEEPOkGQBgIeNINgDAQ8KQbAGEg4Ek3AMJAwJNuAIRhRsA/vvhm\nDgIGBpkd8CIZEzAwCAFPugEQBgKedAMgDAQ86QZAGAh40g2AMBDwpBsAYZgV8PAfU3A6VgQM\ndAh40g2AMHAk1qQbAGEg4Ek3AMJAwJNuAIRhVsDF/liflMnR2fi8DmL8XwfcgIARizkBF9bs\n6tPcGFu4G6WKgIGB5gScmH373ZLn1CTOxuhpEBP+OuAGBIxYzAg4N4f7dTtzcjM+z4OY8tcB\nNyBgxGJGwHvz+G7n4sfPDU4cxJS/DrgBASMWsw+l/HRhtuADpnCEYUbAloCBlc16CZ3fr8vb\n7dGuEDAwyIyAL4+dR4Xd2EYsAkYY5uxGyow91L8YejlYt9uwCBgYZtaRWIf7R5H2DsZk8Eeb\nCBjozDsWusjqnwzdHdweh8UaGBiIDzMscwPAC0cBXzI7e1R+DGLoXwfcgIARCxcBF4fEGAIG\n/JsdcHm61mvS/MuNpyFgYJCZAZ/SZqMxG7GAVcwJON9f27XZxf03yxIwMMisY6Gv9Z4r18dB\n9wcx5a8DbkDAiMWsTyNltzPORudlEFP+OuAGBIxYsAZe5gaAFw7eA58JePwDAE6wFXqdIQBO\nONoPvGM/8LgHAJzgSKx1hgA4wbHQ6wwBcIJPI60zBMAJAl5nCIATBLzOEAAnCHidIQBOEPA6\nQwCcIOB1hgA4QcDrDAFwgoDXGQLgBAGvMwTACQJeZwiAEwS8zhAAJwh4nSEATvgMuNw/vn/2\n7y8BIGBgEI8Bl7b58H/7Q8IEDDjgMeDMHK8VH23zS6QEDDjgMWDb3rGwSUHAgBMeA741W6Yp\nAQNOeAw4MeXtXErAgAseAz6afXeuMOnWA6ZwOOFzN1J2rzY3BAw44PVAjsvudq7YEzAwH0di\nBToEYAgCDnQIwBAEHOgQgCHWCpiNWIAD4QRs+uaNAAFjK3gJHegQgCEIONAhAEMQcKBDAIbw\nGvD5sGs/Epyd5wwigLwIGGHwGHCZ9LZSpTMGEUBeBIwweAw4M/Z0ac4VuTXZ9EEEkBcBIwwe\nA7bmcj9/MX/+IDgBA4N4DPhp7y4HcgAOsAYOdAjAEH7fA+dFc473wAQMN3zuRkp7W6GT8q9b\nEjCFYxC/+4GzZj+w3R3YDzz7BkDFkViyQwBqYQb8r/b11Pz4e2Vm/p1TTmVOf7X0jjVwCEMA\namGugQmYgDEIAYsOAagRsOgQgBoBiw4BqBGw6BCAGgGLDgGoEbDoEIAaAcc6BGwCAcc6BGwC\nATMECCNghgBhBMwQIIyAGQKEETBDgDACZghTHwABIGCGMPUBEAACZghTHwABIGCGMPUBEAAC\nZghTHwABIGCGMPUBEAACZghTHwABIGCGMPUBEAACZghTHwABIGCGMPUBEAACZghTHwABCCdg\nA2C0CaW5j3eFQWA2gRcJ8Q+BgDGV/MKvMQTndydgNAQW/hiG4PzuBIyGwMIfwxCc352A0RBY\n+GMYgvO7EzAaAgt/DENwfncCxiABLPwxDMH53QkYgwSw8McwBOd3J2AMEsDCH8MQnN+dgDFI\nAAu/wBBmImAsJYa8CHgSAo5BDHkR8CQEHIMY8iLgSQh4EwTyIuBJCBi19fNau8+fCBjhIuCf\nCBjhIuCfCBjhIuCfCBjhIuCfCBjhIuCfCBjhIuCfCBjhEgh4bQQMXQRMwBBGwF4DLvfGpHn3\nIH8+SvBPG4JAwD4DLm3zTfK79kH+fJR/NU455fTn6V8dfTY14MwcrxUfbdo8CGtgzMYa2Oca\n2LZ3LGxSEDC8mL0gBb8kegz41myZpgQML+JfkDwGnJjydi4lYPgQ/4LkMeCj2XfnCpMSMDyI\nf0HyuRspu1eb//hd0/ifd3gR/4Lk9UCOy+52rtgTMJYX/4LEkViIWPwLEgEDwggYELZWwGzE\nAhwgYEAYL6EBYQQMCAsnYNO3zCCA2HgN+HzYtR8Jzs5LDQLYFJ8f6E96q9h0kUEAG+Mx4MzY\n06U5V+TWZH8OAsAg40Oc/oH+y/38xdiJjzJjBELCNIQhhmkYa+4H+t8veBqBkDANYYhhGsZi\nDewA0xCGGKZhrBnvgfOiOffzPfAyIxASpiEMMUzDWJOnOe299U7K37d3PgIBYRrCEMM0jDVj\nP3DW7Ae2u8OP/cBLjUA4mIYwxDANY60+zauPgANMQxhimIaxVp/m1UfAAaYhDDFMw1jzvyx7\n5iPE8KQzDWGIYRrGImAHmIYwxDANYxGwA0xDGGKYhrEI2AGmIQwxTMNYqwcMYDoCBoSRHyCM\ngAFhBAwII2BAGAEDwggYEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYELZOwJk1Niv/uiJ8\nr6M8+eepVnV8HmHB+fA6DZrzYbJVJrT9UvjkjyvC9zrKF8kF5/I8woLz4XUaNOfDdGtM6NnY\nS3Wx5vz1ivC9jfLF7NYcn2muE9BfAATnw9s0SM6HGdYIODP59d+TOXy9Inxvo3xUGvvO0aRP\nC7/gfHibBsX5MMcaAe9M/bNovf8q364I39soH81xxdGZxmTP34gkOB/epkFxPsyxRsDdE/54\n3t+uCN/bKO9Mvjd2xs80ruDy+XeelebD2zQozoc5CHiaDwE30tXGaBr5gKu3gCXnw2QEPM2H\naThVVZmpvYCLLmDR+TAZAU/zZZRLtX0w0QXckpsPk60xr+zrcvJ2Rfi+jbLSNNSexldwPtQ+\nja/aNEy23lbo4nUrdKG09fPbKKstOB+2QkvNhxoBe3ZodjfmJvt6RfjeRtma+ghE7YVfcD7U\nXl5FSM6HyTgSa5q3Uc7qxb5sD4UQon8k1ss0iM6HyVZ5pZE8tvS3T36it+n/dRpK21whtvK6\nL/yy86F6mQbR+TDZKgGXzYde2uGblytUfJyGRG7nxXPAgvOh+jQNevNhsq281weiRMCAMAIG\nhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIG\nhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsAbYZjT\nUWK2bgQBx4nZuhEEHCdm60YQcJyYrRvRCzjfGWOz9nxmTUbcwph1G/GI9GAaTcFpfW5PwLqY\ndRvxiNSYU1Wdmsu5sZfqYglYF7NuI14jbS7vTF7VGbMUyGLWbUQ/0iI/pM3l7koC1sWs24he\npGn7Jrgi4Agw6zbiEeneJMe8IOA4MOs2or8R6/pPwXvgODDrNqIf8Lm6pGyFjgOzbiOMub3z\nzbpz5+r+dpilQBazbiMeAV/fBJv0nJtdfXVmr+cJWBezDpVJ1x4DTEXAW9YclFXuTLb2iGAq\nAt6y7rBou/Z4YDIC3rRjakzC+lcYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQ\nRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQ\nRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQ\nRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQ\nRsCAMAIGhBEwIIyAA2I6dpffr8uul7Pebc77pL7B6fkete+Pe7DG7F2M3eS/Yik86wHp1Zg9\nXfe4ye4e+fnlHt/n5KH+KwHHiWc9IP0cz+1Vp+bC6XaLtHeLSzUw4KS9rYOxm/xXLIVnPSC3\nCPLHS95rsdcX0Wl3g+v61x7LqiqO15vuqoHZeGmLgNfBsx6QewSX27niWmy9Bi1uV9uiu0Vy\nKKrv2eT7+lVz/vKw94tF0rxGLzNrbFbcb3RMTHJd8x+tSW8vAOqX7El7k+5h6pP8+v/Kvlur\nF3trkuN9IC+P2Q0JSyHggDxKu527rn0P9XvY7Hbp+O0eT26vtLuV9PML7DrJZqVe2N6r9etp\ne68ie1x5f8V+rvoBZ4/X8NW5PZ92f319zOTx8gFLIOCA9NfAtjlzzaGsytul9LYqfr/Hk/uW\nrrrgTwG3b6u71toHv9/FPtq/vlBPy+b/jd7L9ceb7n03hv034R8e81RhOQQckLf3wHm7/roG\nmff//nSPfj6t673M9Z1yWW99zt/vZtosuzzLfZtYe2393jq5NCdVdX/t3l56BGyvj7pvL57a\nS/UYmy+PiSURcEB6ObavT7ty83YVODTg/e2Vdtb+P/AecN49eNle7tav56eT53tU/YDru5ft\nxdv/Lfn94vNj5hUWRcAB6eXYLPjl0yvpwQGbrqJ6E5h5v5u5R3Z/1Vz186z6dylOWWpeA64e\np/cb3i8+PyYr4IURcEBuC3+atcv9sddnvU5936H7nvTTld8Cfhrapzy7k1Py9Ra/Av4wYCyA\nZzggrwt80ushqQZvhe6vge37jW4X7YeXyc8n9VEkyf54GR7wx8fEgniGA/KywJ9N37m54rYf\n+PzHfuDdz/fAt5vlb9c+nSRPG88+Bnx7kNPzxY/TgwXwDAfkZYHPHrtgju2u4PuRWPUG5q9H\nYv3eCt2cntoDqk/tlu5PAXcX/loDH9ut0Cd7X2e/PyYWxDMckPfSbtuAum2+ZW+vq/1+JNbj\niOn954dtz9wf7PkwjcdJ2vy3cdtF9DHgb/uBP2zLxhJ4hgPyvMCf+h8h2rVr4/LeZlK83+Pu\ndqv9h4d9XMy7W2W9a59Obq/hbdPj54C72+y6i58eEwviGQ7I8wKf9t9P5rdDEvO9rbcsfT7M\n+XHz+lbfj4XuzpXZ9V1u99njTwFXl/213v2luB3S1b/77bS43ibtHwv99phYEM8wIIyAAWEE\nDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEE\nDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEE\nDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCJgdc7I09VNUxMTZzOUIAhpsa\ncGnN1fFQ/2tSp6MEYKipAWfmut7NrNmXVdmc/2MQAAbxF7A1bZtlc2KXGASwMR4DNubxb/X3\n/xwEDAyywhq4/rdkDQw44DHg23vgrOzOux8EsDEeAx6xFZqAgUE8BjxiPzABA4P4DDioQQAx\nIGBAmGLA5A101gp4zn5gAgY64QQ8/PgwAgY6vIQGhBEwIIyAAWFeAz4fds073F12njMIAgY6\nPg+lTHpbqeYcSknAQMfrhxns6dKcK3I758MMBAx0vH6c8HI/f5nzcUICBjreP9D/6cLIQRAw\n0GENDAjz+x44L5pzvAcG3PC5GyntbYVOyumDIGCg43c/cNbsB7a7A/uBARc4EgsQRsCAMAIG\nhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIG\nhBEwIIyAAWEEDAjzGXCZ1T/HcEiMSU9zBkHAQMdjwIU1piotPy8KOOMx4L3Zldd/9sW15T0/\nrQI44PXXCcvun+uraX7cDHDA98+LWtO7MHEQBAx0vL6EvlTVof2N0fLvN8EEDAziMeCLsdml\n2tlrwXli8umDIGCg43M3Um4fPy96mDEIAgY6fg/kOO2Tut7doZgzCAIGOhyJBQgjYEAYAQPC\n1gqY/cCAA+EEbPqWHwEgBryEBoQRMCCMgAFhXgM+H3bNO9xddp4zCAIGOh4DLpPeVio+0A84\n4DHgzNhT81GkqsgtH+gHHPAYsG0/Sdi48IF+wAHfH+j/eGHkIAgY6LAGBoT5fQ+ctx8j5D0w\n4IbP3Uhpbyt0Uk4fBAEDHb/7gbNmP7DdHdgPDLjAkViAMAIGhBEwIIyAAWEEDAgjYEAYAQPC\nCBgQNiPgH189NwcBA4PMDniRjAkYGISAAWEEDAgjYEAYAQPCCBgQNivg4T9n5HSsCBjoEDAg\njCOxAGEEDAgjYEDYrICL/bE+KZOjs/F5HcT4vwIbMifgwppdfZobYwt3o1QRMDDQnIATs2+/\n3fmcmsTZGD0NYsJfgQ2ZEXBuDvfrduY05hF+DZWAgUFmBLw3j19XKH784O/LIxAw4ISrD/QP\nOJBjxIEfBAwMMiNgOzLgsyVgwK1ZL6Hz+3V5uz36b+XOpM3Wal5CA27MCPjy2HlU2GEbsU6m\nuR0BA27M2Y2UGXuof7P7crBDt2EVqdmVBAw4MutIrMP9De1+8L0PxuYEDLgx71joIqt/tHt3\nGHMc1iX5/dlDAgYGWePDDHsCBtxwFPAls7NH5ccghv4V2BAXAReH66tiAgb8mx1wearf06b5\nlxt/fRAO5ADmmxnwKW02Qo//MOF7wMO/YIuAgc6cgPP9NTWbXdx/sywBA4PMOhb6Wu+5WuKr\noQkYGGTWp5Gy2xlno/MyiCl/BTbE6xr4fNg173B3zd0mjxUBAx0H74HPAwMuk95Wqr+PnSZg\nYBCPW6EzY0+X5lyR29vL7yljRcBAx9F+4N2A/cDWXO7nL38f+EHAwCAej8Qa8RU8BAwM4vFY\naNbAgGseP410fQ+ct2+WeQ8MuOHz44Rpbyt0Uv51SwIGBvH6eeBz1uwHtrsD+4EBF9b4QP/c\nQRAw0CFgQBgBA8IIGBA269NIwz+D73SsCBjoEDAgjJfQgDACBoS5Cvg84NcJZw5i4F+BDZkb\ncMZ7YGA9MwN+9Dv2i6EHD2LsX4ENmRlw/bvAqSmK1Pw4unn6IMb+FdiQmQHXr5wP17XvZegP\nBI8fxNi/AhviIODcHF1/tSwBA4PMDHh3fQldmKQa+s2UEwYx9q/AhswMOK/DbT6ov3c2ShUB\nAwPN3Y10qC/tzd/fkDNvECP/CmwIR2IBwggYEDbr00hPn0jyN1YEDHQIGBDGS2hAGAEDwhwc\nidWwv39apSr3xqT5yx0njBUBAx1HARcD3gOXtv1176c7ThkrAgY6MwLOn74SK/l5v6w+Zro8\n2uZjDwQMODBnDZz0+/39cULb3rGwSUHAgBOu3gMPuV932zJNCRhwYu6nkUYcA52Y2y8SJikB\nAy54XAMf759YKkxKwIADMwN+rFUHyEx/+9f0sSJgoDMz4HKXjvgyrMv9u2eLPQED881+Cc2x\n0MB6CBgQxrHQgLC1AmYjFuCAq4DH/jbSe8DDf6uUgIHO3ID5bSRgRTMD5reRgDXNDJjfRgLW\n5OBQyuG/jXQ+7NqPBGc/cidgYBAHAQ/9baSy//HDv3snYGCQuZ9GGvHbSJmxp0tzrsjt3z/l\nQMDAIDMDHvPbSNZc7ucv5s/v0CJgYJC5u5FG/DaSeX3tPXWsCBjoeDwSizUw4JrHgK/vgfOi\nOcd7YKwsmmVoTsBFZo3Nhn+iP+1/Cd6fdyNgLCuaZWhGwEX7Pc+2GHzPc9bsB7a7A/uBsapo\nlqEZAe9NWlZlOmD78+RBTPkr8Fs0y9CMgG3zfVjF35ujpiFgLCuaZWhGwN2eILefQ3oexJS/\nAr9FswwRMLYommUozID/1b6emh9/55TT7Zz+XdInrIEhL5plaNYaePi34Dgdq2iefKwmmmWI\ngLFF0SxDfK0stiiaZYiAsUXRLEMEjC2KZhkiYGxRNMsQAWOLolmGCBhb5GQZCmFBJOAI8ISM\nRsCLIuBReEJGI+BFEfAoPCGjEfCiCHgUnpDRCHhRBDwKT8hoBLwoAh6FJ2Q0Al4UAY/CEzIa\nAS+KgEfhCRmNgKfg50WXwRMyGgGPx8+LLkXoCQllVAl4PH5edClCT0gooxpMwHMfw2PA/LjZ\nUoSekFBGlYAn3M98uzByEKEsBMEQekJCGVUCHo818FKEnpBQRpWAx/P486KeFpOolkY/QhlV\nAp7A38+LRhVwMJPrQiij6ing5eed3/3Avn5elIBH38KJYEbkJwJeFAGPGorQE0LAjkeEgGcg\n4NGDIWDHI0LAMxDw6MEQsOMRWSvgZfcDB7O8+hmK0BNCwI5HJJyADYDRVgp47UF4WlfEtEoS\nWouHsIPWEwJedByCyeKnYMY0lPhCmTE/EPCi4xBMFj8FM6ahxBfKjPnB74Ecbj7Q70IwS2Mo\ny0kwYxpKfKHMmB88BuzsA/0uBLM0hrKcBDOmocQXyoz5wWPAzj7Q70IwS2Moy0kwYxpKfKHM\nmB88Buzs44QuBLM0hrKcBDOmOk9IEDwG7OwD/UJ0JoSAX4QyHj9sdQ3sic6EEPCLUMbjB7/v\ngd18oF+IzoQQ8ItQxuMHn7uRXH2gX4jOhBDwi1DG4we/+4HdfKBfiM6EEPCLUMbjh60eieWJ\nzoQQ8ItQxuMHAl5UNBNSEXCYCHhR0UxIRcBhIuBFRTMhFQGHiYAXFc2EVAQcJgJeVDQTUhFw\nmKU11/sAAAXtSURBVAh4UdFMSEXAYSLgRUUzIRUBh4mAFxXNhFQEHCYCXlQ0E1IRcJgIeFHR\nTEhFwGEi4EVFMyEVAYeJgBcVzYRUBBwmAl5UNBNSEXCYCHhR0UxIRcBhIuBFRTMhFQGHiYAX\nFc2EVAQcJgJeVDQTUsU1LQOITC4BLyqaCanimpYBRCY3zID/1TgN69QEMh6cPp3+XdInkwMu\n98akefcgfz6KyP9+v0UzIVVc0zKAyOR6XAOXtv1pwvZBCFhNTNMygMjkegw4M8drxUfb/DAh\nAcuJaVoGEJlcjwHb9o6FTYrNBByTjc0Ukcn1GPCt2TJNCVjQxmaKyOR6DDgxt59TSVIC1rOx\nmSIyuR4DPpp9d64wKQHLYaaEyOd+4OxebW4IWA4zJUReD+S47G7nij0Bq2GmhCjMI7FYVgLE\nTAkRAWMgZkqICBgDMVNCtFbAbMQCHCBgQBgvoQFhBAwICydg07fMIIDYeA34fNi1HwnOzksN\nAtgUnx/oT3qr2HSRQQAb4/UD/fZ0ac4VuTXZEoMANsbrB/ov9/MXY5cYBLAxK3yg//3Ch5sC\nGGJCiOPv0hixBo5GTC8lYpqWuCZmpBnvgfOiOffzPXA0YlpOYpqWuCZmpMnTnvZW/En5+/YR\niGk5iWla4pqYkWbsB86a/cB2d/ixHzgaMS0nMU1LXBMz0panfayYnquYpiWuiRlpy9M+VkzP\nVUzTEtfEjDR72jd0qHNMUxrTtMQ1MSMR8HAxTWlM0xLXxIxEwMPFNKUxTUtcEzMSAQ8X05TG\nNC1xTcxIBDxcTFMa07TENTEjEfBwMU1pTNMS18SMtOVpB+QRMCCMgAFhBAwII2BAGAEDwggY\nEEbAgDACBoQRMCCMgAFhBAwII2BAGAEDwggYEEbAgDAC/iGzxma9X56Y/CtUQTg+j/jrxGl5\nnhjtGTPZ5iZ4pPYXZJL75Yv0cnJ5HvHXidPyPDHaM2a6zU3wOGdjL9XFmvuvx1zMbs3xmec6\nIf35/TZxUl4mRnrGzEDAf8pMfv33ZA63K46Ps3KOJn1a5t8mTsnrxCjPmDkI+E87U/+Gau9/\n96M5rjg685js+SsI3yZOyevEKM+YOQj4T90y8lhUdibfG6v5e8iXl+8QfZs4Ja8Tozxj5pCc\nef58CLiRrjZG88QTcPUWsPSMmUx15nnytowbc6qqMlN9vRZvwOIzZjLVmefJl2W8VN33Em/A\nLdkZM5nqzPPEflnGVRf6p/H+NnEqPo247MRMtbXpHandUFu8bahVXU4+bIV+nzgVBFwR8A+H\nZldpbu5bN62pjzyUXeiflu+3iRPz8nJCesZMRsB/ejtYKasX97I9BEJQREdivUyM+IyZjID/\nljx2TjTLS2mbK9RXWu1por3n5WlixGfMZAT8t7L5wE5ztl1e6isS2X0VzwH3Jk7R+8TozpjJ\nCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPC\nCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPC\nCBgQRsAbYZjTUWK2bgQBx4nZuhEEHCdm60YQcJyYrRvRCzjfGWOz9nxmTUbcwph1G/GI9GAa\nTcFpfW5PwLqYdRvxiNSYU1Wdmsu5sZfqYglYF7NuI14jbS7vTF7VGbMUyGLWbUQ/0iI/pM3l\n7koC1sWs24hepGn7Jrgi4Agw6zbiEeneJMe8IOA4MOs2or8R6/pPwXvgODDrNqIf8Lm6pGyF\njgOzbiOMub3zzbpz5+r+dpilQBazbiMeAV/fBJv0nJtdfXVmr+cJWBezDpVJ1x4DTEXAW9Yc\nlFXuTLb2iGAqAt6y7rBou/Z4YDIC3rRjakzC+lcYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgj\nYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgj\nYEAYAQPCCBgQRsCAsP/p0U2muFvMYwAAAABJRU5ErkJggg==", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The ACF has 7 significant lag values, indicating the remainder is not, in fact, stationary. \n\n## Exploring the Multiplicative Model with lowess\n\nHaving tried a simple moving average decomposition, you will now use a lowess model to determine the trend. Lowess is a sophisticated non-linear regression. The lowess trend model is combined with a moving window seasonal component model into the R **stl** function.   \n\nThe code in the cell below uses **stl** to decompose a time series. Plots are created of the components of the time series. Finally, the columns of the time series decomposition are added as new column to input data frame. Execute the code in the cell below to compute and view a decomposition of the milk production time series. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.decomp <- function(df, col = 'Milk.diff', span = 0.5, Mult = TRUE){\n  if(Mult) {temp <- ts(log(df[, col]), frequency=12, start=1)\n  } else {temp <- ts(df[, col], frequency=24, start=1)}\n  span = span * length(temp)  \n  dairyFit <- stl(temp, s.window = \"periodic\", t.window = span)\n  plot(dairyFit, main = 'Decompositon of dairy produciton')\n  cbind(df, as.data.frame(dairyFit$time.series))\n}\ndairyMult = dairy.decomp(dairy, col = 'Milk.Prod', span = 0.2)", "execution_count": 20, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nF/ncOjcAAAAASUVORK5CYII=", "text/plain": "Plot with title \"Decompositon of dairy produciton\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The time series charts show the original time series along with the components of the decomposition. The trend is a bit smoother than was obtained with the simple moving average decomposition. \n\nThe question remains, is the remainder from this decomposition stationary? To find out, execute the code in the cell below.  ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf(dairyMult)", "execution_count": 21, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nTkSuQmCC", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The first 4 lag values of the ACF have significant values, indicating that the remainder series is not stationary. Compared to the behavior of the ACF for the simple moving average decomposition, the behavior of the remainder is improved.  \n\nNow, plot the histogram of the remainder by executing the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "hist.ts(dairyMult, col = 'remainder')", "execution_count": 22, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAMFBMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////QFLu4AAAACXBIWXMAABJ0AAAS\ndAHeZh94AAAgAElEQVR4nO3di1biOhiA0SKIjhd8/7cdAZWCYApJmz9l77XOiBWaaPMdrkr3\nATSrqz0B4HYChoYJGBomYGiYgKFhAoaGCRgaJmBomIChYQKGhgkYGiZgaJiAoWEChoYJGBom\nYGiYgKFhAoaGCRgaJmBomIChYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAoaGCRgaJmBo\nmIChYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAp5C92W5fv/ZcOZsj78udfm8p5dKnesv\nT4uue0yfbZi/J5IzTc7w45xCd/DyveHXmV4X3a9LXTrv70tllPG0nZeA2+THOYVewN3r14Zz\nZzq7YVgRGWU8dN3brZf9TcCT8uOcwtey3bx8trJInGnw9iFfHWTKqARcmB/nFA7L9mF/I/q7\n6Kfl56nVv4+fK+n9qfeHbn10Dfz80C0e34/2tft4dKn9CC+P2xvEL4eBXz7HeDy5iv11prNz\n3k/jY7NedIv1YfTPyTx83o54XnTL1/15/60+tz/sz9KbdX/k98dF9/D8M9bJPr9G4moCnsIh\nkZf9vc39hvfF94NbJyk+fG/6uvDyzK3vCwF/nbVbfZ9pvf/8qOD+mQ67+DXn/TS+Z/k9+v7C\n7+vDxu/d7T47zLo/8uvXN/r11dN97kfiegKewiGQzedi/dnweTX4eeW7+VzVz8cpdrsvHFL4\nsujv63zAq58zr44v23+Q6uhMfwS8n8b3/2UWRztcHEZ5/qxv8/Gx/vkfwpmRF4fP+58ujkbi\negKeQi+Qfm6f/25vRB5Fvb+S2/QutV3nnzd2Xxb7RX4U8Omnn1fw3fPm86Z593NTfXvZx6NC\nz5zp/Jx309jnuXn8Gf3zs+ftlebb7sPH7m5B78bz8ay/Rv53+B66C/vkJgKewoWAt8v5+47o\nUYpHzzV9f/5ydA13PuDH7ZX51vrnpvr2spujRs+c6fycd8N+Xl1//e/ka/TXow+/vsvjWX+N\nvDp8D925fb58cBsBT+FCwE9ftzGPnxvuvlb3r6eRjgI5H/DPZd/PnvlnP2fP9GvO37cDerd3\nj0f9ueT7v/WyOw34zKQPnx7v0xXwrQQ8hUMixzeX19/L+P3jTGy3Bfzxx5lPZ5MI+Pvjt1+j\nfn3493DxHKmAL4/PIH50Uzgs0ZfjW62bf/tHcJcffwbcv0YefA28OLfPjz/OdH7OizM3k48/\nfN7B7R4en9+GB3x2n9zCj24KhyW6/P240cvjhWvLQwq7R2gP94G3+b2eDWV14e7tUSOXznR+\nzquje6jnAv56bvvXfeDjee3O8u/409OfDlfzo5vC9xJ9XR09F/Twczfz+4pw83E24G3B20dw\nnz52117r3UugD6EcLnXpAeajRgY/Cr37uH0A+XX3oXcz4ejD1yd/XQM/7x+F/rf4uc7+vU9u\n4Uc3hd59vv6V1WdJy/fdY1nblyFtF/f643zAe4ttqY9H9x9PL/Xzmor9069nA750pl9z3p/4\neQr3+GUahw/L3Qy+nyI6G/Cl54HPPJbNVfzopnDa7+mDWLtXIT12J1dIhxRWvcu+70+vv756\neqnvOI9/yfCkkfNn+jXn/YmXrzOvj+d0+PD6/f+XXY/nA/46z+rr03P75BZ+dFP4rne53vxs\n2H3c3f9d7u+Rbu8ZHt0l7aXwvH1V8dfvEr99Xmb5r38f9ehSL4+L3y9zPm3k7Jl+zfnr1Gb9\neVt/dfrcdO/DdkaLx7f371d2nRv5/XH3jX5/emaf3MKPDhomYGiYgKFhAoaGCRgaJmBomICh\nYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAoaGCRgaJmBomIChYQKGhgkYGiZgaJiAoWEC\nhoYJGBomYGiYgKFhAoaGCRgaJmBomIChYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAoaG\nCRgaJmBomIChYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAoaGCRgaJmBomIChYQKGhgkY\nGiZgaJiAoWEChoYJGBomYGiYgKFhAoaGCRgaJmBomIDD6n6rPSXCsSbC+n1oHCxOWRNhCZg0\nayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQl\nYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1\nEZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIw\nadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoI\nS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0\nayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQl\nYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1\nEZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIw\nadZEWAImzZoIS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoI\nS8CkWRNhCZg0ayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwadZEWAImzZoIS8CkWRNhCZg0\nayIsAZNmTYQlYNKsibAETJo1EZaASbMmwhIwabevidenVbe1Wr8WnA8/BEzarWti89AdLItO\niT0Bk3brmlh3i39vu1PvL4tuXW5CfBMwabeuiUX39nP6rVuUmQx9Aibt1jXRdZc+oRABk+Ya\nOCwBk5ZxH/jlfXfKfeCRCJi0m9fEsvco9MOm5JTYEzBpGc8Dr3fPAy9WT54HHoWASbMmwhIw\naSOtia5vnCFmT8Ck3bwmNo9dt3z52smfe7HsbiNg0m5+KeVi/0Lo/U4EPAIBk3b700jPnxU/\nL3YvgxbwGARM2u0v5Nh9eF88vAt4HAImLfellJvlUsDjEDBpt66Jh+77xRsPSwGPQsCk3bom\nnrvHr1Pv3VLAYxAwaTevifVPtS+Jp3otu9sImLTb18Tb6vvU+6OARyBg0iZYE5bdbQRMmoDD\nEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwB\nkybgsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBp\nAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwBkybg\nsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJOCwBkybgsARMmoDDEjBpAg5L\nwKQJOCwBkybgsARMmoDDEjBpAg5LwKQJuILujDPnGrCFeyfgCgbVKmAGEHAFAqYUAVcgYEoR\ncAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFXIGBK\nEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBg\nShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcg\nYEoRcAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFX\nIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQB\nVyBgShFwBQKmFAFXIGBKEXAFAqYUAVdwc8BnjDA9GiLgCgpeA/vh3jkBVyBgShFwBQKmFAFX\nIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQB\nVyBgShFwBQKmFAFXIGBKEXAFAqYUAVcgYErJXADPD123ehl1iBkSMKXcugD2f4xpuf+7TOtR\nhpgvAVNKVsDrbr35+Hhfd89jDDFfAqaUrIAX3WZ7etM9jDHEfAmYUrIC/v6jpn//cVNr7JSA\nKSUr4MfvgBdjDDFfAqaU2wNePT2/dP8+T27Wfz+KZY2dEjCl3B7wzxsDdN1iM8YQ8yVgSrl5\nAby9PT+vVruHstZ/9muN/SJgSvFKrAoETCkjLQDvv/UXAVOKa+AKBEwpAq5AwJQi4AoETCm5\nTyMNuJtrjZ0SMKXcugCeBXw7AVPK7c8DL5ZjDzFbAqaU2xfAW+LXgAsMMVcCppSMBfDcvY09\nxEwJmFI8Cl2BgClFwBUImFIEXIGAKUXAFQiYUgRcgYApRcAVCJhSBFyBgClFwBUImFIEXIGA\nKUXAFQiYUgRcgYApRcAVCJhSBFyBgClFwBUImFIEXIGAKUXAFQiYUgRcgYApRcAVCJhSBFyB\ngClFwBWcC/GMQZcbYXo0RMAVuAamFAFXIGBKEXAFAqYUAVcgYEoRcAUCphQBVyBgShFwBQKm\nFAFXIGBKEXAFAqaU/gJ4eHofewi2BEwp/QXQdd0YDVtjpwRMKf0FsPn3OEbD1tgpAVPK6QJ4\nfXoo3bA1dkrAlHJmAbwtPq+Hn0cd4s4JmFJ+L4CX5e532ZYjDnHvBEwpJwtg8/R59fvwsvms\neDXSEAiYYo4WwOv2Qaz12/4LxZaGNXZKwJRy9Dzw55Xv8+b7C4sxhmBLwJRy9Dzw6mXsIdgS\nMKUcPQ88/hBsCZhSjhbAZr293bxYly3ZGjslYErpL4D3xe6Rq65bFH0tljV2SsCU0l8Ay+5x\ne927WZd7Cul0CLYETCnHv8xweqL4EGwJmFL6C2DR7e/8bgQ8LgFTSn8BrLvl6+eH12W3HmsI\ntgRMKUcLYPn1nh7lXgf9awg+BEw5xwvg32qbb8HfRPo9BAKmnAkWwHzX2JA3JDt7uRs3nTvT\njXO49XIEI+AMgxIbdLmS18DDAr7xcgQj4AwCprajo7b9czrlb03Nd2EImNr6R+1pnLtD810Y\nAqa24xdyFH78+fcQ8yJgajv7UsrxhpgXAVNb/6itulF+I3i+C0PA1NY/au+L3UspxxxiXgRM\nbcc3oT2IdRUBU5uAMwiY2ryQI4OAqU3AGQRMbcdH7WW1vfW8Kvv2hPNdGAKmtqOjttzf/fVH\n7QYSMLX1j9pzt9z9NZ3n7nGsIeZFwNTWP2rbv4n19YdlxxpiXgRMbcdPI30I+BoCprb+UXv4\nugZ+6x7GGmJeBExtZ+4DvxT+raT5LgwBU9vRUVv5q5RXETC1/X4euFv9G3OIOREwtU1w1Oa7\nMARMbQLOIGBqE3AGAVPb8fPAfp3wKgKmNgFnEDC1nTlqr8ui7+8944UhYGo7d9Q2fplhmGYC\nHvRGSPM9TnN29qi5CT1MOwHfeDnCO3fUnrvF2EPMg4Cp7fyDWE9jDTEvAqa2cwE/lH2Hlfku\nDAFTmxdyZBAwtQk4g4Cp7cILOUq+mGO+C0PA1CbgDAKmtqOj9rR4+fz3deEX+ocRMLX1j9pT\n97b7+NYVfS3lfBeGgKnt+Cb06YniQ8yLgKmtf9QWP9fA/irlIAKmtv5RW3e7+8D+KuVQAqa2\no6O2/Hr8eT3eELMiYGo7Pmr/dn+V8mXMIeZEwNQ2wVGb78IQMLUJOIOAqe34qHmD76sImNp+\nP4j14Q2+hxIwtfWPmjf4vpKAqe34hRze4PsqAqa2/lHzBt9XEjC19Y+aN/i+koCp7cx9YC+l\nHErA1HZ01LzB93UETG2/nwf2Bt+DCZjaJjhq810YAqa2/lFblf0tpHNDzIuAqe30aaSRh5iX\noAEPeSszAc/E6dNIIw8xL0EDLrcrwusftc1q+TryEPMiYGo7vgld/G9Cnw4xLwKmNgFnEDC1\neRopg4CpTcAZBExt30dtpKeQ+kPMj4Cp7TjgUTKe78IQMLUJOIOAqU3AGQRMbQLOIGBqE3AG\nAVObgDMImNoOAf/92ysFhpgfAVObgDMImNomOGrzXRgCpjYBZxAwtQk4g4Cp7faj9vq0/yu0\nq3XirwDMd2EImNpuPWqbh95DXn//Hen5LgwBU9utR23dLf697U69vyy6P/+c5XwXhoCp7daj\ntujefk6/dYsxhohPwNR261E7eqr47+eN57swBExtroEzCJjaMu4Dv7zvTrkP/OeWYZcTMLe5\n+agte49CP/z5B+HnuzAETG0ZzwOvd88DL1ZPngf+Y8uwywmY20xw1Oa7MARMbSMdtdF+tSmU\nmQU85E3RCMY1cIaZBTxoE7EIOIOAqU3AGQRMbbceoivuK813FQiY2m49RM8CFjD13XyI3hZ/\n/xJhgSHCEzC13X6I3v5+AWWJIaITMLVlHKLn3u8zjDREcAKmNo9CZxAwtQk4g4CpTcAZBExt\nAs4gYGoTcAYBU5uAMwiY2gScQcDUJuAMAqY2AWcQMLUJOIOAqU3AGQRMbQLOIGBqE3AGAVOb\ngDMImNoEnEHA1CbgDAKmNgFnEDC1CTiDgKlNwBkETG0CznCmi0HvLyRgShFwhlETEzADCDiD\ngKlNwBkETG0CziBgahNwBgFTm4AzCJjaBJxBwNQm4AwCpjYBZxAwtQk4g4CpTcAZBExtAs4g\nYGoTcAYBU5uAMwiY2gScQcDUJuAMAqY2AWcQMLUJOIOAqU3AGQRMbQLOIGBqE3AGAVObgDMI\nmNoEnEHA1CbgDAKmNgFnEDC1CTiDgKlNwBkETG0CziBgahNwhmFdlHu/s+kDHub3BZmKgDPc\n4zWw6+lYBJxBwJc2MRUBZxDwpU1MRcAZBHxpE1MRcAYBX9rEVAScQcCXNjEVAWcQ8KVNTEXA\nGQR8aRNTEXAGAV/axFQEnEHAlzYxFQFnEPClTUxFwBkEfGkTUxFwBgFf2sRUBJxBwJc2MRUB\nZxDwpU1MRcAZBHxpE1MRcAYBX9rEVAScQcCXNjEVAWcQ8KVNTEXAGQR8aRNTEXAGAV/axFQE\nnEHAlzYxFQFnEPClTUxFwBkEfGkTUxFwBgFf2sRUBJxBwJc2MRUBZxDwpU1MRcAZBHxpE1MR\ncAYBX9rEVAScQcCXNjEVAWcQ8KVNTEXAGQR8aRNTEXAGAV/axFQEnEHAlzYxFQFnEPClTUxF\nwBkEfGkTUxFwBgFf2sRUBJxBwJc2MRUBZxDwpU1MRcAZBHxpE1MRcAYBX9rEVAScQcCXNjEV\nAWcQ8KVNTEXAGQR8aRNTEXAGAV/axFQEnEHAlzYxFQFnEPClTUxFwBkEfGkTUxFwBgFf2sRU\nBJxBwJc2MRUBZxDwpU1MRcAZBHxpE1MRcAYBX9rEVAScQcCXNjEVAWcQ8KVNTEXAGQR8aRNT\nEXAGAe83/fb7TIxDwBkEPHzvjEPAGQJ0EWBXAq5JwBkCdBFgVwKuScAZAnQRYFcCrknAGQJ0\nEWBXAq5JwBkCdBFgVwKuScAZAnQRYFcCrknAGQJ0EWBXAq5JwBkCdBFgVwKuScAZAnQRYFcC\nrknAGQJ0EWBXAq5JwBkCdBFgVwKuScAZAnQRYFcCrknAGQJ0EWBXAq5JwBkCdBFgVwKuScAZ\nAnQRYFcCrknAGQJ0EWBXAq5JwBkCdBFgVwKuScAZAnQRYFcCrknAGQJ0EWBXAq5JwBkCdBFg\nVwKuScAZAnQRYFcCrknAGQJ0EWBXAq4p80f9/NB1q5dRhwgsQBcBdiXgmm79Ue//dvdy/2e8\n16MMEV+ALgLsSsA1ZQW87tabj4/3dfc8xhDxBegiwK4EXFNWwItusz296R7GGCK+AF0E2JWA\na8oK+Ps9cH6/F07rb5Rz5u1+zvl9uTO7Krcp5q4G7t07KI0iK+DH74AXYwxRUztd1N9Vyb1z\nrdsDXj09v3T/Pk9u1n8/itXicZpZF81MlGvdHvDPraCuW2zGGKKmmXXRzES51s0/xLe35+fV\navdQ1vrPfps8TjPropmJcq0JfogtHqeZddHMRLmWgM+aWRfNTJRrCfismXXRzES5loDPmlkX\nzUyUawn4rJl10cxEuZaAz5pZF81MlGsJ+KyZddHMRLmWgM+aWRfNTJRrCfismXXRzES5loDP\nmlkXzUyUawn4rJl10cxEuZaAz5pZF81MlGsJ+KyZddHMRLmWgM+aWRfNTJRrCfismXXRzES5\nloDPmlkXzUyUawn4rJl10cxEuZaAz5pZF81MlGsJ+KyZddHMRLmWgM+aWRfNTJRrCfismXXR\nzES5loDPmlkXzUyUawn4rJl10cxEuZaAz5pZF81MlGtVD7jgm17d/I5kg6bQchfNTJRr1Q/4\n2gvk7uoeu2hmolxLwDFWrolyEwHHWLkmyk0EHGPlmig3EXCMlWui3ETAMVauiXITAcdYuSbK\nTQQcY+WaKDcRcIyVa6LcRMAxVq6JchMBx1i5JspNBBxj5ZooNxFwjJVrotxEwDFWrolyEwHH\nWLkmyk0EHGPlmig3EXCMlWui3ETAMVauiXITAcdYuSbKTQQcY+WaKDcRcIyVa6LcRMAxVq6J\nchMBx1i5JspNBBxj5ZooNxFwjJVrotxEwDFWrolyEwHHWLkmyk0EHGPlmuhwBd9Oq30CjrFy\nTXQ4V+Y9Ao6xck10OAH3CDjGyjXR4QTcI+AYK9dEhxNwj4BjrFwTHU7APQKOsXJNdDgB9wg4\nxso10eEE3CPgGCvXRIcTcI+AY6xcEx1OwD0CjrFyTXQ4AfcIOMbKNdHhBNwj4Bgr10SHE3CP\ngGOsXBMdTsA9Ao6xck10OAH3CDjGyjXR4QTcI+AYK9dEhxNwj4BjrFwTHU7APQKOsXJNdDgB\n9wg4xso10eEE3CPgGCvXRIcTcI+AY6xcEx1OwD0CjrFyTXQ4AfcIOMbKNdHhBNwj4Bgr10SH\nE3CPgGOsXBMdTsA9Ao6xck10OAH3CDjGyjXR4QTcI+AYK9dEhxNwT8iAh7x31bB3uNLF+LsS\ncE0hA77tTBEWs4nm7WoQAfcIOOqu7nKigwi4R8BRd3WXEx1EwD0Cjrqru5zoIALuEXDUXd3l\nRAcRcI+Ao+7qLic6iIB7BBx1V3c50UEE3CPgqLu6y4kOIuAeAUfd1V1OdBAB9wg46q7ucqKD\nCLhHwFF3dZcTHUTAPQKOuqu7nOggAu4RcNRd3eVEBxFwj4Cj7uouJzqIgHsEHHVXdznRQQTc\nI+Cou7rLiQ4i4B4BR93VXU50EAH3CDjqru5yooMIuEfAUXd1lxMdRMA9Ao66q7uc6CAC7hFw\n1F3d5UQHEXCPgKPu6i4nOoiAewQcdVd3OdFBBNwj4Ki7usuJDiLgHgFH3dVdTnQQAfcIOOqu\n7nKigwi4R8BRd3WXEx1EwD2NBFzujZAGvvPSrRMtt6umA7757a0GGTSrAIbNPXOM0ju8dogI\nyy3krkw0b1cBTDFRAUfdlYnm7SoAAV91pqaXm4mW3lUAAr7qTE0vNxMtvasABHzVmZpebiZa\nelcBCPiqMzW93Ey09K4CEPBVZ2p6uZlo6V0FIOCrztT0cjPR0rsKQMBXnanp5WaipXcVgICv\nOlPTy81ES+8qAAFfdaaml5uJlt5VAAK+6kxNLzcTLb2rAAR81ZmaXm4mWnpXAQj4qjM1vdxM\ntPSuAhDwVWdqermZaOldBSDgq87U9HIz0dK7CkDAV52p6eVmoqV3FYCArzpT08vNREvvKgAB\nX3WmppebiZbeVQACvupMTS83Ey29qwAEfNWZml5uJlp6VwEI+KozNb3cTLT0rgIQ8FVnanq5\nmWjpXQUg4KvO1PRyM9HSuwogdsCvT6vdX6perV9zhrDcqux9/hMNIHLAm4feX5tfZgxhuVXZ\n+/wnGkDkgNfd4t/b7tT7y6Jb3z6E5VZl7/OfaACRA150bz+n37rF7UNYblX2Pv+JBhA54KN3\nafr9lk3D38/p5ne4ggbd2Nvlfm683BXXwMBYMu4Dv7zvTiXvAwNjufkqfdm7WfCwKTklYKjb\nb5O/rnfPAy9WT4nngYGxxHz4DhhEwNAwAUPDBAwNEzA0TMDQMAFDwwQMDRMwNEzA0DABQ8ME\nDA0TMDRMwNAwAUPDBAwNEzA0TMDQMAFDwwQMDRMwNEzA0LAmA670rhjcjdorfLiGpnpQb9J3\nOPIdfsstVdHQVA/u8cgK+C5GvlpDUz24xyMr4LsY+WoNTfXgHo+sgO9i5Ks1NNWDezyyAr6L\nka/W0FQP7vHICvguRr5aQ1M9uMcjK+C7GPlqDU314B6PrIDvYuSrNTTVg3s8sgK+i5Gv1tBU\nD+7xyAr4Lka+WkNTPbjHIyvguxj5ag1N9eAej6yA72LkqzU0VeCUgKFhAoaGCRgaJmBomICh\nYQKGhgkYGiZgaJiAoWEChoYJGBomYGiYgKFhAoaGCRga1krA60W3WG8ubngd7/v4a+Tnh5Ov\nTTLqr69NNfB4325q5I9qh/jtsese30cbOlsjAS937xn3cGnDZjHa9/HXyOvdycUIS/qvUX99\nbaqBx/t2UyN/VDvEL6N+zwW0EfBrt3j7eFt0rxc2rEZ7Q8i/Rn7rHj8P7HP3OOmov7421cDj\nfbupkbfqHOKPxefJzapbjzR2vjYCXncvn//+657Ob/g33ju6/jXyaj/oCGP/Neqvr0018Hjf\nbmrkj2qH+N8u3U23GGnsfG0EvOq290LeutXZDe/dcrSj+/fIOyOM/deovycw0cBfRvpRxzzE\nj93bSKOW0kbA3en//I82LLv30Y7u3yNvbbrlpKP++tpUA++N8e2mR651iB+6j6fF7q5DVDMI\n+Kn7N9bVwpAV/by7wTXdqJUDHuPbTY5c7RB33Wr3INZIQxfQfsC7mzr1An5fjHBbNm7Ao1J6\nIEMAAAOqSURBVHy7qZHrHeJu+3jW5nGcBxyKaD/gh+1j/NUC3izGuEUZNuBxvt3UyPUOcbe7\nD/w+1pN2BcQOePck3OcUF6c/48OGx91NuuJHd8DIO8tRDu1fo/762lQDb43z7SZGHukQDxh5\n3P9bFhF3ZlvfGe0fF3w/faBwu6H7MfXI2w8Py1FepPPXqL++NtXA4327iZFHOsQDRh75qbMS\n4s6s72n3/+CXw/Pphw0jH90/Rt7+O9INyr9G/fW1qQYe79tNjFzxEO9Pvo/5jWdqI+DUy3TG\n+1/kXyOPd1xDvhJr3GUc9RA/bLYPYv0baex8bQT88bD7H/BuAe0PZG/DYePEIz+Od8Xw1/d7\n8q1PNvCI325i5I/DxqlHfhrzh11CIwFvdr8fsju5/xn3Nhw2TjzyiLfs/vp+T771yQYe94Zs\nzEP8eUt6Od4Pu4RGAgbOETA0TMDQMAFDwwQMDRMwNEzA0DABQ8MEDA0TMDRMwNAwAUPDBAwN\nEzA0TMDQMAFDwwQMDRMwNEzA0DABQ8MEDA0TMDRMwNAwAUPDBAwNEzA0TMDQMAFDwwQMDRMw\nNEzA0DABQ8MEDA0T8L06+473ZzcSmAN2rwQ8Cw4YPQJujQNGj4Bb44DNSNdtHrrV54nnh27x\nvN/y8dQtnj4+1l233m54WXXdYv31pc//3le7L39aLz7PsQ+4d/GvHRKVgGek61a7Tj///bTc\nbXnannxZbv/9/Mrus33L+4AX20+3Be/OsdoF3L/46it8ghLwjHxWt/n88LL9sFl2L19bnr/+\nXWw///fx8W+X6T7g3RcettsWbx9vi+3G04sTmYBnpOtetx9W3ba6zfa2737L5y3lj/79217A\nr1+nVrtTL/uTJxcnMAHPyFei3bfvLf1/31+elr2AP45OfZ08uTiBOUIzMiDg5fdXBDwPjtCM\n9Co82nL497F7eH55TwV8ukPicoRm5Ku31fbxp/6Wk07PBby/zOvhZH+HxOUIzchXb7tHlD+e\n949CHbZ/P2r1du4+8MvhUehfFycwR2hGvnvb39FdvP8OeP119/b1NOD9k7+PvfvJh4sTmCM0\nIz+9PT98xnh46qj372eiy9eX72vX/pefjl6J1b84gTlC0DABQ8MEDA0TMDRMwNAwAUPDBAwN\nEzA0TMDQMAFDwwQMDRMwNEzA0DABQ8MEDA0TMDRMwNAwAUPDBAwNEzA0TMDQMAFDwwQMDRMw\nNEzA0DABQ8MEDA0TMDRMwNAwAUPDBAwN+w+MJZKM73fr5QAAAABJRU5ErkJggg==", "text/plain": "Plot with title \"Distribution of  remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The distribution of the remainder values is much closer to a Normal distribution than for the original time series you created earlier. This result, combined with the ACF plot, indicates that the stl decomposition is effective.  \n\nYou will further, investigate the remainder (non-seasonal residual) component by making a box plot by month of the year. The code in the cell below plots a box plot by month of the remainder component using ggplot2. Execute the code in the cell below to display the box plot. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.box <- function(df, col = 'remainder'){\n  require(ggplot2)\n  p <- ggplot(df, aes_string('Month', col)) +\n    geom_boxplot() +\n    ggtitle('Variation of remainder component of dairy production by month')\n  print(p)\n}\ndairy.box(dairyMult)", "execution_count": 23, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8\nfHyMjIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enr6+vw8PD////agy6EAAAACXBIWXMA\nABJ0AAASdAHeZh94AAAgAElEQVR4nO2di3bavBYGHefWNE1OeP+XPdxlMOiPLcmM5NlrtVDs\nDp+29oRLSNttLMuqtrpHB7Asa34psGVVXApsWRWXAltWxaXAllVxKbBlVVwKbFkVlwJbVsWl\nwJZVcSmwZVVc+QXuu+/z9e+uv3mn1/f683bz5v+qn7eue574d+6H+I/bl6tDN24fGS/4Om+W\n/Pchv96qTH2cORqrqfyN+dO9n6+/d39u3un1vR5umLxLr13XvUz8O/dD/Mfty9X9BLcWvLDA\nv96qTH2cORqrqfyNGT7qDh+Noynmxei6r1l/7z+g+Zm5EtxacJG8/yVwEmJGksdvCrUKNOal\n+zxe+/zt4+NsgWf9tQdAMyW4dUSBV10FGvPZvR6vvR5Ufn/ePvH7t7+37ud5e/S4Hefbu12d\nd+nrre/6t6/D+Zv3vnv+HNDD0e74144LOaA3m38vW+rn8W//Ofztj+3Fx+V9Hu7t4g4+X7r+\nzzHFkHIEb04ndW8/N4Je3dX2lu3Vl8/r1Jd3eRH2ePPFsu4v+DLvaF270KfXyz/nF87DVOeF\nDcINoce7Olyclv37rTq0ZHdXPzdzjLbmJizc3y73v411VSW+svXdYcB/Dk+m+8Pg7ba22w7V\n9iXyYfvD7RdT8dkNz385Xz/U4Oi1wHv05u/h5vf9TX/21/+97S8+rrNc3cH7/trb/vYLygF8\nqMNJ/Tjo9V2dbnmPrenibk43X2p6d8EXecfr2oV+Pzbu7/mtiGGq08KG4YbQocDnZf9+q7bs\n013dzzHYmtuw8/0dTtTg6yoh8Ht3+JL6sZ+TP/td+7N/Nr3dmJ/Ncfsvb9+cfv/a7u3P5me7\n+d+7W/p/m5/X8Ez84ujFE6sj+mv/Zfrr5TDw/ecuTX+4eL5xn4M72KL/bseo391+SXn52YT7\n37J+XnYLuw56dVfbWw64r/trugp7uvni8ffugod5b6xrF/r7+Ij3cn4rYpjq3LHBPQyhA4EH\ny/71Vg3u6maOq37dg53ubxfgdf5bls1WCYG/jvv1vH/L5fnweHycq/As7/L289X346Pd22Fa\ndl+Pf8LcXhy9Evjf4YQ99Wf33PD8t0/PUcf3ObiD45edn767pgy+7L/tT9o/Fbwd9HxX3XFY\n+/f7a7oZ9nJZ9xc8zHtjXfvQr0fo+VtPw1Tnjg3uYQgdCDxY9q+3av+lYDcM7zdzXPfrHux0\nf1d061hFOvK8H41/5/36+vzzMhD1PIdXtx+9PozYd5iWwdxeHL0S+HjCqfYv8gZHTi/bLu5z\ncOwowXbYrikXK/sJVy+CXt/V6cHi9fn+mm7czfU93l/wMO+9dX3tX+OGZ64Xqc4dG9zDEHqj\nN5sJW3Vsyebw8HqdY9Sve7DB/V3thbWrIh352+2++/52+BK8e/fh9OLtYh9Gtw9PuRjl4VQM\nr9wQuLvtxOni+j5vaPPS3aRc3X806P6W41ev5+7+qXfC3ljW/QXv895b11bEr+Ez11upboU7\nNuFWoslbtb8c5Rj3626PxudboYp05Oe4v/uvsh/b11rvf79HAo9vzyPwvZt2F6P7vDFBdxW6\n+sMvBX7p7p96J+w0gWPr2j/0DZ653kp1U+D7QecJPMqhwJmqTEd2D76Hh+HT8+mRLzduP96c\n9BS6H3zUYTwlo/scT9D+i88NyuaIv/cU+vquTt95ij2FvhN2eI//ueCf2Lr2j3qDZ64XqY7n\n3Ao3fCl+CJrwFLq7lePG1vgUek6V6cju5e9xqI5N/xwJPL59//v70fu38JbnYN8ujt6a57fD\nCV+Dd3NH0zC4z8Gx14NNH7vrNyibI/7wZkofDXq4q8MbVIc3sW6feifs8B7vL3iY9966dre9\nD565XqQ6nnNxD5fQnxN0sOxfb9Xhm0PbUXi5meP64h5MgeNVqCN993n6ROXzbiMP35i4egQe\n3n7+Jsn2eeD74dsJXzf27eLoLYG/9t94/OoP35kZHjl8mb/KMjj2sf+2x9/9C8kblENtV/V1\n/H5KJOhh8HbfIfncP3bdO/VO2G4w6fcXPMx7b127NvfDH38Ypjqec3EPQ+hL9/pzhA6W/eut\n6vZvQ//tj1/Hr3NcX9yDXXz/TIFHVagju2/TH58wfZzeqPl3uQ/D25/vfjognH+oi08d3BD4\ndML76G8fJL3KMjzl8NmBP/vrY8qxDh9OeIkHPSzmNQS9d+rtsIdu/NeCh3nvrevw9wc/UDJM\nddWxwz0MoP8O2Y4Ptqdl/3qrLj7JMs4xurgDG96fAo+rUEe2L6LOL5s+dp+Q+/d5+Gbn4U67\nq9u/nsOzs6uP1A0uro/eFHjz/X76cN6NKbnOcnHK38FHE0eUU31so76PotwSeDf1pw8o3jv1\nZthDN/5rwRd576xrs9+JwQ+UDFOdz7n4KOUA+u859OO87F9vVXf4KOXpm+ijHKOL27CL+1Pg\nUdmRQkWZtY+LHyB+XKrLHFaugoxZewUR+Ku/+Pzww1Jd5bByFWPMGiyEwIPXoKcbGDmsXEUY\nsyYLIfDz6Uf1TvWgVKMcVq4ijJllWTNLgS2r4lJgy6q4FNiyKi4FtqyKS4Etq+JSYMuquBTY\nsiouBbasiiu/wP/7fU05txoMLA4LA4vDwkzgKHA5DCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDi\nsDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4\nLAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwO\nCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vD\nwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKw\nMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgs\nDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4L\nA4vDwhQVuN/W1fW+H15R4MycJjGwOCxMSYH782+X1/eX/cWpRQJXhIHFYWFgcViYRwh8IfOD\nBH56esrCcUbLY2BxWJhHCXzp7+ICPz1lMtgZLY+BxWFhHiDw4er5JfDepd8Bs9XT0yPu1bIY\nlUPgwbHN4o/AR4EzkHyQKY+BxWFhHvUIfHWtSOD7pcA1YWBxWJjlBe6vTniEwL4GrgkDi8PC\nPErgxz6F9l3omjCwOCzMIwUePBYXCVwRBhaHhYHFYWEW+SRWP7h+Nnr4QSwFZsVhYWBxWBg/\nC43AwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyM\nAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDguj\nwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8Io\nMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAK\njMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwC\nIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PA\nCAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vDwigw\nAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKwMAqM\nwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIj\nMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AI\nDCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDAC\nA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozA\nwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMw\nsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgM\nLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LAxEYMuyFisfgXNjYHFYGFgcFgbyCFwkcEUY\nWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYWh4VRYAQG\nFoeFgcVhYRQYgYHFYWFgcVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHFYWEUGIGB\nxWFhYHFYGAVGYGBxWBhYHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBg\ncVgYWBwWRoERGFgcFgYWh4VRYAQGFoeFgcVhYRQYgYHFYWFgcVgYBUZgYHFYGFgcFkaBERhY\nHBYGFoeFUWAEBhaHhYHFYWEUGIGBxWFhYHFYGAVGYGBxWBhYHBZGgREYWBwWBhaHhVFgBAYW\nh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYWh4VRYAQGFoeFgcVhYRQYgYHF\nYWFgcVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHFYWEUGIGBxWFhYHFYGAVGYGBx\nWBhYHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgc\nFgYWh4VRYAQGFoeFgcVhYRQYgYHFYWFgcVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaH\nhYHFYWEUGIGBxWFhYHFYGAVGYGBxWBhYHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVh\nYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYWh4VRYAQGFoeFgcVhYRQYgYHFYWFgcVgYBUZgYHFY\nGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHFYWEUGIGBxWFhYHFYGAVGYGBxWBhYHBZGgREYWBwW\nBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYWh4VRYAQGFoeF\ngcVhYRQYgYHFYWFgcVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHFYWEUGIGBxWFh\nYHFYGAVGYGBxWBhYHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhigrcb+v6en+8MjymwLA4LAws\nDgtTUuD+/Nvg+vWfFTgnp0kMLA4Lo8AIDCwOCwOLw8IsLXB/45gC0+KwMLA4LMziAp9eAp9v\nfNrV74CWZWWo1Efg3kfgQpwmMbA4LMzir4EVuCSnSQwsDgujwAgMLA4LA4vDwjzkTSwFLsVp\nEgOLw8I8QuB+o8CFOE1iYHFYmEU+iTX85NX1pQLn5DSJgcVhYYoK/PsqErgiDCwOCwOLw8Io\nMAIDi8PCwOKwMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAK\njMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwC\nIzCwOCwMLA4Lo8AIDCwOCwOLw8IocFo95cHAVsXCwOKwMAqcVgpcHgOLw8IocFopcHkMLA4L\no8BppcDlMbA4LIwCp5UCl8fA4rAwCpxWClweA4vDwihwWilweQwsDgujwGmlwOUxsDgsjAKn\nlQKXx8DisDAKnFYKXB4Di8PCKHBaKXB5DCwOC6PAaaXAkbI55TEKnFbOaKRsTnmMAqeVMxop\nm1Mes1qBMw2XMxopm1Meo8AIDGwqWD2GrYqFUWAEBjYVrB7DVsXCKDACA5sKVo9hq2JhFBiB\ngU0Fq8ewVbEwCozAwKaC1WPYqlgYBUZgYFPB6jFsVSyMAiMwsKlg9Ri2KhZGgREY2FSwegxb\nFQujwAgMbCpYPYatioVRYAQGNhWsHsNWxcIoMAIDmwpWj2GrYmEUGIGBTQWrx7BVsTAKjMDA\npoLVY9iqWBgFRmBgU8HqMWxVLIwCIzCwqWD1GLYqFkaBERjYVLB6DFsVC6PACAxsKlg9hq2K\nhVFgBAY2Fawew1bFwigwAgObClaPYatiYRQYgYFNBavHsFWxMAqMwMCmgtVj2KpYGAVGYGBT\nweoxbFUsjAIjMLCpYPUYtioWRoERGNhUsHoMWxULo8AIDGwqWD2GrYqFUWAEBjYVrB7DVsXC\nKDACA5sKVo9hq2JhFBiBgU0Fq8ewVbEwCozAwKaC1WPYqlgYBUZgYFPB6jFsVSyMAiMwsKlg\n9Ri2KhZGgREY2FSwegxbFQujwAgMbCpYPYatioVRYAQGNhWsHsNWxcIoMAIDmwpWj2GrYmEU\nGIGBTQWrx7BVsTAKjMDApoLV41wcVnMUOK0UuDxGgctjFBiBgU0Fq8cKnIejwOUwsKlg9ViB\n83AUuBwGNhWsHitwHo4Cl8PApoLVYwXOw1HgchjYVLB6rMB5OApcDgObClaPFTgPR4HLYWBT\nweqxAufhlBR4+XpCYdqsXM2xyZnLR+DcGNiXdVaPfQTOw1HgchjYVLB6rMB5OApcDgObClaP\nFTgPR4HLYWBTweqxAufhKHA5DGwqWD1W4DwcBS6HgU0Fq8cKnIejwOUwsKlg9ViB83AUuBwG\nNhWsHitwHo4Cl8PApoLVYwXOw1HgchjYVLB6rMB5OApcDgObClaPFTgPR4HLYWBTweqxAufh\nKHA5DGwqWD1W4DwcBS6HgU0Fq8cKnIejwOUwsKlg9ViB83AUuBwGNhWsHitwHo4Cl8PApoLV\nY5jArDQKjMDAzGP1GKYMK40CIzAw81g9hinDSqPACAzMPFaPYcqw0igwAgMzj9VjmDKsNAqM\nwMDMY/UYpgwrjQIjMDDzWD2GKcNKo8AIDMw8Vo9hyrDSKDACAzOP1WOYMqw0CozAwMxj9Rim\nDCuNAiMwMPNYPYYpw0qjwAgMzDxWj2HKsNIoMAIDM4/VY5gyrDQKjMDAzGP1GKYMK40CIzAw\n81g9hinDSlOfwCzzFDhSChwpBU4rFgZmHmvUYcqw0igwAgMzjzXqMGVYaRQYgYGZxxp1mDKs\nNAqMwMDMY406bK8UWIHHxTJPgctjFDitWBiYeQpcHqPAacXCwMxT4PIYBU4rFgZmngKXxyhw\nWrEwMPMUuDxGgdOKhYGZp8DlMQqcViwMzDwFLo9R4LRiYWDmKXB5jAKnFQsDM0+By2MUOK1Y\nGJh5Clweo8BpxcLAzFPg8hgFTisWBmaeApfHKHBasTAw8xS4PEaB04qFgZmnwOUxCpxWLAzM\nPAUuj1HgtGJhYOYpcHmMAqcVCwMzT4HLYxQ4rVgYmHkKXB6jwGnFwsDMU+DyGAVOKxYGZp4C\nl8cocFqxMDDzFLg8RoHTioWBmafA5TEKnFYsDMw8BS6PUeC0YmFg5ilweYwCpxULAzNPgctj\nFDitWBiYeQpcHqPAaQXDPOUBKXA1GAVOKxTm6SmTwQpcDUaB04qEeXrKZbACV4NR4LQiYRR4\nEQ4Lo8BpRcLkE5g1XAocKQVOKxQm22tg1nApcKQUOK1gmEzvQrOGS4EjpcBpxcLAlGGlge0V\nq8cKjMDAlGGlge0Vq8cKjMDAlGGlge0Vq8cKjMDAlGFhYHEUWIHHpcDlOSyMAqcVC6PAC3BY\nmBoE7rd1fX14eT6owApcntMkpqTA/fm3cP18W39x6oTArP4pcHkMLA4Lo8AIjAIvwGkSs7TA\npz9c+qvAClye0yTmYQKfXwLvPwf8O+Dh/AnnVoPJVaxV5WoOKw4LM6sSBe6v/rzxEdhH4AU4\nTWIe8QjcX5ygwLtS4PKcJjEPELi/PEGBd6XA5TlNYpYXuB8dU2AFXoLTJGZxga9fByvwvhS4\nPKdJzCKfxOrD9b4fXFHgcylweU6TGD8LjcAo8AKcJjEKjMDA4rAwsDgsjAIjMLA4LAwsDguj\nwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8Io\nMAIDi8PCwOKwMBM4ClwOA4vDwsDisDAKjMDA4rAwsDgsjAIjMLA4LAwsDgujwAgMLA4LA4vD\nwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8IoMAIDi8PCwOKw\nMAqMwMDisDCwOCyMAiMwsDgsDCwOC6PACAwsDgsDi8PCKDACA4vDwsDisDAKjMDA4rAwsDgs\njAIjMLA4LAwsDgujwAgMLA4LA4vDwigwAgOLw8LA4rAwCozAwOKwMLA4LIwCIzCwOCwMLA4L\nk0PglzcFhnCaxMDisDA5BO7TH5GLBK4IA4vDwsDisDA5BP56ef9WYASnSQwsDguTQ+DuXAr8\nYE6TGFgcFkaBERhYHBYGFoeF8V1oBAYWh4WBxWFhFBiBgcVhYWBxWJg8An+8bp8+v3wp8KM5\nTWJgcViYHAL/PO9f/3bdPwV+MKdJDCwOC5ND4LfufWvv5m/3osAP5jSJgcVhYfK8Cx1+KfBD\nOU1iYHFYGAVGYGBxWBhYHBYm41Po927+Z6KLBK4IA4vDwsDisDBZ3sTqDx/j6Od/oLJI4Iow\nsDgsDCwOC5Pn20h/nrvu+f1ntr8KzIrDwsDisDB+kAOBgcVhYWBxWBgFRmBgcSZhnmZVsTgr\nwyQL3A1LgR/MeYjAczZcgRU4rVgYWBwFrgaT5Sn068v3ZvP98jrbXwVmxVHgajA5BH7tDu8/\nd/MNLhK4IgwsjgJXg8n1Saxt/fgU+uEcBV4bJofAL93hKbSPwA/nKPDaMDkE/vaTWBROxQJn\n+m7UPMyUBbO2KsubWD/vu09i/fGTWA/n1CzwAzGTnhCwtsoPciAwsDgKnKs5xTEKjMDA4ihw\nruYUx2QR+L33gxwMjgIr8N0Ky70S9d1PYlE4CqzAdyssd/R/I33M6tqgigSuCAOLo8C5mlMc\nk/GDHClVJHBFGFgcBc7VnOKYnB+lTKgigfNhin9vETYVCpyrOcUxeT7I8dL4/07oh41iJ+dp\njgKX5oTlru4/N1Pg2Ml5mqPApTlhuQqceyhgU6HAuZpTHOMHOX518pw1KfCk5ihwaU5YrgL/\nphR4UnMUuDQnLPfyn9TxKXT6UMCmQoFzNac4RoF/dXLpoYBNhQLnak5xjE+hf3XynDUp8KTm\nKHBpTliuAv+mFHhScxS4NCcsd/TTSD6FThwK2FQocK7mFMf400i/Orn0UMCmQoFzNac4Js9P\nI329dN8/L92/Wc3bVZHA+TAKHDs5T3NYAlfzT2tl+mmkP93n5qd7mdW8qb1+AGbecBW/BwYm\nU3MeiRn/rUyYTOfm5owF/tz9SLBPoS/KR+BJzYE9AufB5OpxFk7IOfpxwr/f3fPmnwLP3s1H\nrCrXs0QFjsSJtH/CuXk4IeeVqDtzX3bvYb3NWvWuRqlKvwKpWeBM5uWaUQWOxIns4oRz83BC\nzutH2s/nzeat695nLXpfo1Sl21e1wHPSlJtRBY7EiezihHPzcELO8h/kYBkDiwObUQWOxIns\n4oRz83BCTgV+aBzYjCpwJE5kFyecm4cTclYjcKZXiwocW5UCR+JEdnHCuXk4IeeVwD9v2T+J\nxdpNBY6tSoEjcSK7OOHcPJyQc/RtJAX+FSbLNuBmVIEjcSK7OOHcPJyQc/RBjr+zljuoUao5\nEAWeFAfWHNaWr0rg5/z/sDtrNxU4tioFjsSJ7OKEc/NwQs7rfxf6+T31X3YfpZoDUeBJcWDN\nYW35qgTe/PU18K8wWbYBN6MKHIkT2cUJ5+bhhJy+iTUPk2UbcDOqwJE4kV2ccG4eTsjpm1jz\nMFm2ATejChyJE9nFCefm4YSco0fgWasd1ijVHIgCT4oDaw5ry1cl8Ob1Lfd/bsbaTQWOrUqB\nI3Eiuzjh3DyckLP8/43E2k0Fjq1KgSNxIrs44dw8nJBTgedhsmwDbkYVOBInsosTzs3DCTnr\n+WGGWWEUeNKqFDgSJ7KLE87Nwwk5FXgeJss24GZUgWNx8vw4XKSyCPzxuvtXdb5mLXpfWfqn\nwJPiwJrD2nJYcyKVQeCf5/3r3y7jvwvN2k3UNrQ6o6wthzUnUhkEfuved/+k7N+Efxe60Lpb\n3IZWZ5S15bDmRCrLu9Dh18wqtO4Wt6HVGWVtOa05OV5KhztQ4HmYSCkwa8tbbE44cvsp9HvO\nfxc6R2DcNkRKgVlb3mJzwpHrN7H6w8c4+vkfqCStG/5EyBnNj1lHc8KR0VPlP89dl/RT/aR1\nw7fBGc2PWUdzwhE/yFEfZh0zanMimHDkSuCX+a99T0VaN3wbnNH8mHU0JxwZ/Qffc/AXRVo3\nfBuc0fyYdTQnHLkS9uvl3Z8HpmPWMaM2J4IJR/xxwvow65hRmxPBhCMKXB9mHTNqcyKYcMR3\noevDrGNGbU4EE44ocH2YdcyozYlgwhEFrg+zjhm1ORFMOKLA9WHWMaM2J4IJRxS4Psw6ZtTm\nRDDhiALXh1nHjNqcCCYcUeD6MOuYUZsTwYQjClwfZh0zanMimHBEgevDrGNGbU4EE44ocH0Y\n/oz6rx0UxoQjClwfhj+jClwYE44ocH0Y/oxmEjgPh9acHJhwRIHrw/AFzoRR4HuYcESB68Mo\nsAKfSzZFVGgAABV3SURBVIHrw6xG4DmYdTQnHFHg+jDrmFGbE8GEIwpcH2YdM2pzIphwRIHr\nw6xjRm1OBBOOKHB9mHXMqM2JYMIRBa4Ps44ZtTkRTDiiwPVh1jGjNieCCUcUuD7MOmbU5kQw\n4YgC14dZx4zanAgmHFHg+jAFZzTLR59abQ4IE44ocH0YBZ7EaXFywhEFrg+jwJM4LU5OOKLA\n9WHWMaM2J4IJRxS4Psw6ZtTmRDDhiALXh1nHjNqcCCYcUeD6MOuYUZsTwYQjClwfZh0zanMi\nmHBEgevDrGNG8zWngffWFRgRR4HLYxQ4tUjrhg2XApfHKHBqkdYNGy4FLo9ZR3PCEQWuD7OO\nGbU5EUw4osD1YdYxozYngglHFLg+zDpm1OZEMOGIAteHWceM2pwIJhxR4Pow65hRmxPBhCO/\nFbjf1vX168tDkdYN3wZnND9mHc0JR34pcH/+LVy/vjwWad3wbXBG82PW0ZxwRIHrw6xjRm1O\nBBOOKPBMzAM/3bOOGbU5EUw4klXg/ZCO7ntW4F/csiDnBmZW5Ukz/lu05jwQs5bmnGqBR2DU\nY5WPwNFV1Y8p2JwHbvlDn0KjRt0ZzR6HhVHgm9WQwKBt4M1o/RgFvlkNvYkF2gbejNaP4Tcn\nxwCGO1DgxwqcJw5tRh+IUeDbdf7U1fC6n8RKxihwZowCpxZ7N2kzqsCZMXyBc2DCEQWuD7OO\nGbU5EUw4osD1YW7MaJ4H8kabkweDak44osD1YRR4EqfFyQlHFLg+jAJP4rQ4OeGIAteHWceM\n2pwIJhxR4Pow65hRmxPBhCMKXB9mHTNqcyKYcESB68OsY0ZtTgQTjihwfZh1zKjNiWDCEQWu\nD7OOGbU5EUw4osD1YdYxozYngglHFHgm5oHfeF3HjNqcCCYcqUdg1mcVIjXlZGc0N2YdzQlH\nFHhenEgpsAKXxoQjCjwvTqQUWIFLY8KRegSeFUaBJ62KNKM2J4IJRxR4HiZSCsza8habE44o\n8DxMpBSYteUtNiccUeB5mEgpMGvLW2xOOKLA8zCRUmDWlrfYnHBEgedhIqXArC1vsTnhiALP\nw0RKgVlb3mJzwhEFnoeJlAKztrzF5oQjCjwPEykFZm15i80JRxR4HiZSCsza8habE44o8DxM\npBSYteUtNiccUeB5mEgpMGvLW2xOOKLA8zCRUmDWlrfYnHBEgedhIqXArC1vsTnhiALPw0RK\ngVlb3mJzwhEFnoeJlAI/8ke3+c3JgQlHFHgeJlIKbHNKY8IRBZ6HiZQzanNKY8IRBZ6HiZQz\nmqs5eZ6Kw5qjwA/gKPAkTKbmZMLAmqPAD+Ao8CRMpuZkwsCao8CJnDzvkEZKgTM1JxMG1hwF\nTuNENnrCubk4CjyvFPhUChzuYcK5uTgKPK8U+FQKHO5hwrm5OAo8rxT4VAoc7mHCubk4Cjyv\nFPhUChzuYcK5uTi5BM701pwCR1alwBNKgR+yKgWOrEqBJ5QCP2RVChxZlQJPKAV+yKoUOLIq\nBZ5QCvyQVSlwZFUKPKEU+CGrUuDIqhR4QinwQ1alwJFVKfCEUuCHrEqBI6tS4AmlwA9ZlQJH\nVqXAE0qBH7IqBY6sSoEnlAI/ZFVtCsz6mJoCp3EiGz3h3Fwc2KqaFDgXJtcg5/hyEu5AgcM9\nTDg3Fwe2KgWOnQxqTrgDBZ7Rvnwc2KpIM4rDZHomniVO6L4Cz2hfPg5sVQr8SAxV4DxfuGCj\nnokDW5UCPxIDFThLYNyoZ+LAVqXAj8Qo8LgUWIGrwSjwuBRYgavBKPC4FFiBq8Eo8LgUWIGr\nwSjwuPACF//mogJXg1HgcdEFhmEU+JEYBR6XAitwNRgFHpcCK3A1GAUelwJP06v0K/Kam1Mc\no8DjUmAWBhaHhVHgcSkwCwOLw8Io8LgUmIWBxWFhFHhcCszCwOKwMAo8LgVmYWBxWBiIwBNq\nipQzBS5+D8U4TWJgcViYWRwfgWelWYDTJAYWh4WBPAIXCazAbWBgcVgYBR6XArMwsDgsjAKP\nS4FZGFgcFkaBx6XALAwsDgujwONSYBYGFoeFUeBxKTALA4vDwijwuBSYhYHFYWEUeFwKzMLA\n4rAwCjwuBWZhYHFYGAUelwKzMLA4LIwCj0uBWRhYHBZGgcelwCwMLA4Lo8DjUmAWBhaHhVHg\ncSkwCwOLw8Io8LgUmIWBxWFhFHhcjxB4SgcixRouBS6PUeBxKTALA4vDwijwuBSYhYHFYWEa\nF5j1//hFSoHLc5rEtC1wNRgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgF\nXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgF\nXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgFXoDTJEaBERgF\nXoDTJGbC5ChwOYwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPA\nCIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPA\nCIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPA\nCIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPA\nCIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPACIwCL8BpEqPA\nCAxMYFYa2F6xMAqMwMCUYaWB7RULo8AIDEwZVhrYXrEwCozAwJRhpYHtFQujwAhMLmVYGAUu\nj1FgBAZmngJXg1FgBAZmngJXg1FgBuYpD0iB14ZRYALm6SmTwQq8NkxRgfttXV8fXp4Prlzg\np6dcBitwNZhMPS4pcH/+LVw/39ZfnDohMGsbFDhSChwpBU4rEkaBF+GwMJUKfPrDpb8rF9jX\nwItwWJjaBT6/BN4P7++Ah/MnnFsPZlILaqlca4LtVR7MIytR4P7qz5vVPwLTHjp9BC6PqfgR\nuL84QYF3xTJPgctj0AIfnh/fEThoq8DnYpmnwOUxaIHvPOpeW6zA52KZp8DlMbUKfP06WIH3\nxTJPgctjKhA4fOoqXO/7wRUFPhfLvDYFZq2qBoF/XxMCs8xT4EgpcKQUOK1YGJh5rFGHKcNK\no8AIDMw81qjDlGGlUWAEBmYea9RhyrDSKDACAzOPNeowZVhpFBiBgZnHGnWYMqw0CozAwMxj\njTpMGVYaBUZgYOaxRh2mDCuNAiMwMPNYow5ThpVGgREYmHmsUYcpw0qjwAgMzDzWqMOUYaVR\nYAQGZh5r1GHKsNIoMAIDM4816jBlWGkUGIGBmccadZgyrDQKjMDAzGONOkwZVhoFRmBg5rFG\nHaYMK40CIzAw81ijDlOGlUaBERiYeaxRhynDSqPACAzMPNaow5RhpVFgBAZmHmvUYcqw0igw\nAgMzjzXqMGVYaRQYgYGZxxp1mDKsNAqMwMDMY406TBlWGgVGYGDmsUYdpgwrjQIjMDDzWKMO\nU4aVRoERGJh5rFGHKcNKo8AIDMw81qjDlGGlUWAEBmYea9RhyrDSKDACAzOPNeowZVhp6hOY\ntQ0KHCkFjpQCp5UCl8cocKQUOK0UuDymzeYosAKPizWjrB63uSoFTisFLo9pszkKrMDjYs0o\nq8dtrkqB00qBy2PabI4CK/C4WDPK6nGbq1LgtFLg8pg2m6PACjwu1oyyetzmqhQ4rRS4PKbN\n5iiwAo+LNaOsHre5KgVOKwUuj2mzOQqswONizSirx22uSoHTSoHLY9psjgIr8LhYM8rqcZur\nUuC0UuDymDabo8AKPC7WjLJ63OaqFDitFLg8ps3mKLACj4s1o6wet7kqBU4rBS6PabM5CqzA\n42LNKKvHba5KgdNKgctj2myOAivwuFgzyupxm6tS4LRS4PKYNpujwAo8LtaMsnrc5qoUOK1Y\nAj895QE1OeptrkqB0wol8NNTJoObHPU2V6XAaUUS+Okpl8FNjnqbq1LgtFLg8hgFjpQCp5UC\nl8cocKQUOK1IAvsaOF5NrkqB0wolsO9CR6vJVSlwWrEEhs0oq8dtrkqB00qBy2PabI4CK/C4\nWDPK6jFsVSyMAiMwsKlg9Ri2KhZGgREY2FSwegxbFQujwAgMbCpYPYatioVRYAQGNhWsHsNW\nxcIoMAIDmwpWj2GrYmEUGIGBTQWrx7BVsTAKjMDApoLVY9iqWBgFRmBgU8HqMWxVLAxE4OXr\nCYVps2wOtHwEzo2BfVln9Ri2KhYG8ghcJHC0FLg8xuaUxygwAgObClaPYatiYRQYgYFNBavH\nsFWxMAqMwMCmgtVj2KpYGAVOq+W3oSKMApfHKHBaKXCkFLg8RoHTSoEjpcDlMQqcVgocKQUu\nj1HgtFLgSClweYwCp5UCR0qBy2MUOK0UOFIKXB6jwGmlwJFS4PIYBU4rBY6UApfHKHBaKXCk\nWAK3+d/XKHBaKXCkUAI3+h/IKXBaKXCkSAK3+l+4KnBaKXCkFLg8RoHTSoEjpcDlMQqcVgoc\nKZLAvgZW4FulwJFCCey70Ap8oxQ4UiyB28QocFopcKQUuDxGgdNKgSOlwOUxCpxWChwpBS6P\nUeC0UuBIKXB5jAKnlQJHSoHLYxQ4rRQ4UgpcHqPAaaXAkVLg8hgFTisFjpQCl8cocFopcKQU\nuDxGgdNKgSPFEtiPUirwuBQ4UiiB/WEGBb5RChwpksD+OKEC3yoFjpQCl8cocFopcKQUuDxG\ngdNKgSNFEtjXwAp8qxQ4UiiBfRdagW+UAkeKJXCbmNUKzMLA4ihwNRgFRmBgcRS4GowCIzCw\nOApcDUaBERhYHAWuBqPACAwsjgJXg1FgBAYWR4GrwSgwAgOLo8DVYBQYgYHFUeBqMAqMwMDi\nKHA1GAVGYGBxFLgajAIjMLA4ClwNRoERGFgcBa4Go8AIDCyOAleDUWAEBhZHgavBKDACA4uj\nwNVgFBiBgcVR4GowCozAwOKwBG7zn9JQ4LRiYWBxUALn+ses2vw6oMAIDCwOSeBc/5yk/6id\nApfDwOI0KLD/rKwCF8TA4ihwpFg9VmAEBhZHgSPF6rECIzCwOA0K7GtgBS6IgcUhCey70Lk4\nClwOA4uDErhR8xQ4rVgYWByWwLBVsTAKjMDA4ihwNRgFRmBgcRS4GowCIzCwOApcDUaBERhY\nHAWuBqPACAwsjgJXg1FgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYW\nh4VRYAQGFoeFgcVhYYoK3G/r+np/vDI8psCwOCwMLA4LU1Lg/vzb4Pr1nxU4J6dJDCwOC6PA\nCAwsDgsDi8PCLC1wf+OYAtPisDCwOCzM4gKfXgKfb9z/vPbvgJZlZajUR+DeR+BCnCYxsDgs\nzOKvgRW4JKdJDCwOC1NG4MPzZAVenNMkBhaHhXnIm1gKXIrTJAYWh4V5hMD9RoELcZrEwOKw\nMIt8Emv4yavrSwXOyWkSA4vDwhQV+PdVJHBFGFgcFgYWh4VRYAQGFoeFgcVhYRQYgYHFYWFg\ncVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHFYWEUGIGBxWFhYHFYGAVGYGBxWBhY\nHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBxWBgFRmBgcVgYWBwWRoERGFgcFgYW\nh4VRYAQGFoeFgcVhYRQYgYHFYWFgcVgYBUZgYHFYGFgcFkaBERhYHBYGFoeFUWAEBhaHhYHF\nYWEUGIGBxWFhYHFYGAVGYGBxWBhYHBZGgREYWBwWBhaHhVFgBAYWh4WBxWFhFBiBgcVhYWBx\nWBiIwBMq0/9kyMLA4rAwsDgszCyOAufGwOKwMLA4LIwCIzCwOCwMLA4Lo8AIDCwOCwOLw8Io\nMAIDi8PCwOKwMPUJbFlWWimwZVVcCmxZFZcCW1bFpcCWVXE9RuA+nXCoZGR/dZlSGVaVjZSH\nMSLNheYJc7njjwX1FxdJSZLCVCtwJuSxdzkGo09fVsY0KIEztOZ05zk2qg+/D9EzIOkCz73/\nUynw8CKpFDhCyNLflAhx0AyB83w9SX7O9TiBj88c+s2sZxDhr6Ry+vB7IE0HDbZ0PmacZv7X\n+dNf7mf35iZpJiFM+3Ft01HDryMpe94Prxy7PJ3TX6xm9k4NBT6lmJTmYQKfR+KwEzMIgysp\nnLMyF6Tpdbr/U5DELyd9+HO6wPN6c4s0F3D+daLM+Op2nuu0dQ1HZ/66+vOSknZqIHB/dfm7\neuxT6MlxA6E/fxVO4wwe84ak6XVrSjOlmfmEILU390hzAOPWzFtUhj0fCTwrzEjgeTt1T+Bf\n1wMFHjzzSHkE7lM5gwe8wXOheYESZ/1OmsoFvt2auXn61D3PJvARkE3gfs78PfA18CbtkfPq\nSgaBh4mmg66nKlXg8Gv2VxSKwDdbkyJwuPpQgTcXL71m7dT1I/DkLIsLfL2JHIGThjT7I3DK\nWGTq8T3SLEh6nv58kb7npwsFnlwXTzhyCdxvUt4MGzzyzn4KHbrfD3AZ0qQKnNDje6Q5jM1p\nIf1wbdM4A1M2SXven3+f/4WpP6NCd2d05/qLyeTdWv4p9ODN8hyPwBm+HXX+NUg0N09/DpIo\ncPhWy5xVZenxPdJURLg8rWnWt5FCmMQ9H4DOpBnfRjpfhFjzklytqoZvI7Vc80RZEsioDMtq\ntDOTSoFzlwL/ZyU8IxhzVl4KnLsyT1Wmj++zKtNPJbTYmqmlwJZVcSmwZVVcCmxZFZcCW1bF\npcCWVXEpsGVVXApsWRWXAq+o+teP7/2V74/XO99D/djd3jkV1ZRbtaLquu5tf+Wtu+fo/nYF\nrqfcqhVV1z0fPzb/rMCNlFu1ouq6P92/7eW/7eVu47+3j8Rv3/sD369d/75/jO72Ar/v/2jh\nS4FXVF23VXd7udV45+lPv/O1/9kd2F99Pwv8evijhS8FXlFt5eyft5fP3f5Z8nv3stm8dPsH\n3pefzUfXn59Cb//4p/NnBSooBV5Rbe186743393bXtTn7fXtH573T6EPh08Cn/5o0ctNWlFt\nlfzsPrYPtX+DrLeuhT9a9HKTVlRbJX+2T5tfuh8FbqXcpBXVTsmtvbuXvtdPoU+HFbiycpNW\nVDslP7rX3TvR129inQ4rcGXlJq2odkp+d133dbg6/DbS6XB3fitagasoN2lFtVey784fdx58\nkON0+EOB6yo3ybIqLgW2rIpLgS2r4lJgy6q4FNiyKi4FtqyKS4Etq+JSYMuquBTYsiqu/wPY\nubI1QQ11pwAAAABJRU5ErkJggg==", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "The remainder component shows only limited vairation from month to month. The differences are within the interquartile range, indicating that the seasonal model is a reasonably good fit.  \n\n****\n\n### Exercise: Decomposition of Ice Cream Production Time Series\n\nIn this exercise you will decompose the **Icecream.Prod** column of the **diary** data frame. Create plots to answer the following questions. \n\n- Does icecream production have a noticable seasonal component or are the values all close to the average over time? Is there a strong seasonal component for icecream production. \n- Does the acf plot indicate that the remainder series is stationary?\n- Do the values in the histogram have an approximately normal distribution?\n- Does the interquartile range for each month overlap, indicating that the decomposition has produced a reasonably good model of the seasonal variation. \n\nIn the code cell below, use the **dairy.decomp**, **dairy.acf**, **dairy.hist**, and **dairy.box** functions to create new plots of the ice cream production time series and answer the questions above. \n\n****\n", "cell_type": "markdown", "metadata": {}}, {"source": "print(df)", "execution_count": 30, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "function (x, df1, df2, ncp, log = FALSE) \n{\n    if (missing(ncp)) \n        .Call(C_df, x, df1, df2, log)\n    else .Call(C_dnf, x, df1, df2, ncp, log)\n}\n<bytecode: 0x00000000085ca5e0>\n<environment: namespace:stats>\n"}]}, {"source": "dairyMult2 = dairy.decomp(dairy, col = 'Icecream.Prod', span = 0.2)\ndairy.acf(dairyMult2)\nhist.ts(dairyMult2, col = 'remainder')\ndairy.box(dairyMult2)", "execution_count": 31, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAABNTU1oaGh8fHyM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\nAAAAAElFTkSuQmCC", "text/plain": "Plot with title \"Decompositon of dairy produciton\""}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAMFBMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////QFLu4AAAACXBIWXMAABJ0AAAS\ndAHeZh94AAAgAElEQVR4nO3di1biSBRA0aA0Oj7//29H8AVF6lIgkLph77Wm1YJUyoQzvOx2\neAfSGqZeAHA6AUNiAobEBAyJCRgSEzAkJmBITMCQmIAhMQFDYgKGxAQMiQkYEhMwJCZgSEzA\nkJiAITEBQ2IChsQEDIkJGBITMCQmYEhMwJCYgCExAUNiAobEBAyJCRgSEzAkJmBITMCQmIAh\nMQFDYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEBX8Pw5X71+jMwcrV/e1vVr1tudehakYfFMPw7\nfLU28UL+skxGOJzXMPx6+h7Yu9LzYtjbqnbd/a3+UMbDel0CzsnhvIatgIfnr4GxK40OtBXx\nhzLuhuHl1G33CfiqHM5r+LrZvj19tLI4cKXm8ZZLm1wzKgGfmcN5Db8327vPB9HfRT/cf3y2\n/O/9507687PXu2G1cw/8eDcs/r3uzLX5uLPV5x6e/q0fED/97vjpYx//irvYvSuNrvlzGe9v\nq8WwWP3u/WMxdx+PIx4Xw/3z53X/W36M331eZWvV23t+/bcY7h5/9lXM+bUnjibga/hN5Onz\n2ebnwOvi+8WtIsW776Gvje9HHn1XAv666rD8vtLq8+udgrev9DvF3po/l/G9yu+9f278uvod\n/J5u89Xvqrf3/Pz1jX5dWs75uSeOJ+Br+A3k7ePG+jPwcTf4cef79nGrftxNcdhc8JvCl8X2\nXOMBL3+uvNzddvtFqp0rBQF/LuP7/zKLnQkXv3t5/Kjv7f199fM/hJE9L36/3v5ysbMnjifg\na9gKZDu3jz/XDyJ3ov68k3vb2mp9O/94sPu0+LyR7wRcfvlxBz88vn08NB9+Hqqvt/23U+jI\nlcbXvFnGZ55v/372/vHV4/pO82Xz4X3ztGDrwfPuqr/2/N/v9zBU5uQkAr6GSsDrm/P3E9Gd\nFHfea/r++mnnHm484H/rO/O11c9D9fW2bzuNjlxpfM2b3X7cXX/97+Rr7887H/a+y91Vf+15\n+fs9DGNzPr1zGgFfQyXgh6/HmLvvDQ9ft+69t5F2AhkP+Gfb19Er/8wzeqW9NX8/Dth6vLu7\n158tX/9b3Q9lwCOL/v1yd053wKcS8DX8JrL7cHn1fTN+fR+J7bSA34Mrl6s5EPD3x297e/36\n8N9d9RqHAq7vnyYO3TX83kSfdh+1vv33+Qru/XsY8PY9cvM98GJszvfgSuNrXow8TN798PEE\nd7j79/jSHvDonJzCobuG35vo/f7rRk//KveWvylsXqH9fQ68zu95NJRl5entTiO1K42vebnz\nDHUs4K/3tveeA++ua3OV/3a/LI8OR3PoruH7Jvq83Hkv6O7naeb3HeHb+2jA64LXr+A+vG/u\nvVabH4H+DeV3q9oLzDuNNL8Kvfm4fgH5efNh62HCzoevL6J74MfPV6H/W/zcZ+/PySkcumvY\nes63fWf1UdL96+a1rPWPIa1v3Kv38YA/Ldal/tt5/lhu9fMzFZ9vv44GXLvS3po/P/l5C3f3\nxzR+P9xvVvD9FtFowLX3gUdey+YoDt01lP2WL2Jtfgrp31DcIf2msNza9vXz89XXpeVW33Hu\n/iXDopHxK+2t+fOTp68rr3bX9Pvh+fv/L5sexwP+us7y68uxOTmFQ3cN3/Xer95+BjYfN89/\n7z+fka6fGe48Jd1K4XH9U8Vff5f45WOb+/+2n6PubPX0b7H/Y85lI6NX2lvz12dvq4/H+svy\nvemtD+sVLf69vH7/ZNfYnl//bb7R7y9H5uQUDh0kJmBITMCQmIAhMQFDYgKGxAQMiQkYEhMw\nJCZgSEzAkJiAITEBQ2IChsQEDIkJGBITMCQmYEhMwJCYgCExAUNiAobEBAyJCRgSEzAkJmBI\nTMCQmIAhMQFDYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEBQ2IChsQEDIkJGBITMCQmYEhMwJCY\ngCExAUNiAobEBAyJCRgSEzAkJmBITMCQmIAhMQFDYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEB\nQ2IChsQEDIkJGBITMCQmYEhMwLdg2Df1kjgPJ/IW7J9l530mnMhbIODZciJvgYBny4m8BQKe\nLSfyFgh4tpzIWyDg2XIib4GAZ8uJvAUCni0n8hYIeLacyFsg4NlyIm+BgGfLibwFAp4tJ/IW\nCHi2nMhbIODZciJvgYBny4m8BQKeLSfyFgh4tpzIWyDg2XIib4GAZ8uJvAUCni0n8hYIeLac\nyFsg4NlyIm+BgGfLibwFAp4tJ/IWCHi2nMhbIODZciJvgYBny4m8BQKeLSfyFgh4tpzIWyDg\n2XIib4GAZ8uJvAUCni0n8hYIeLacyFsg4NlyIm+BgGfLibwFAp4tJ/IWCHi2nMhbMBLwiAkW\nxl85a7eg6R7YTSEjZ+0WCHi2nLVbIODZctZugYBny1m7BQKeLWftFgh4tpy1WyDg2XLWboGA\nZ8tZuwUCni1n7RYIeLactVsg4Nly1m6BgGfLWbsFAp4tZ+0WCHi2nLVbIODZctZugYBny1m7\nBQKeLWftFgh4tpy1WyDg2XLWboGAZ8tZuwUCni1n7RYIeLactVsg4Nly1m6BgGfLWbsFAp4t\nZ+0WCHi2nLVbIODZctZugYBny1m7BQKeLWftFgh4tpy1WyDg2XLWboGAZ8tZuwUCni1n7RYI\neLactVsg4Nly1m6BgGfLWbsFAp4tZy2RYUTbhg0jp98UTl0VZ+BQJ3JydRcO+HxTcSyHOhEB\nU3KoExEwJYc6EQFTcqgTETAlhzoRAVNyqBMRMCWHOhEBU3KoExEwJYc6EQFTcqgTETAlhzoR\nAVNyqBMRMCWHOhEBU3KoExEwJYc6EQFTcqgTETAlhzoRAVNyqBMRMCWHOhEBU3KoExEwJYc6\nEQFTcqgTETAlhzoRAVNyqBMRMCWHOhEBU3KoExEwpT8e6se7YVg+nWcpHCJgSqce6s/fX3X/\n+ausVmdcEHUCpvSngFfD6u39/XU1PJ5zSdQImNKfAl4Mb+vP34a78y2IOgFT+lPA378H1u+D\nvQ4BU/pTwP++A16cazlEBEzp9ICXD49Pw38fn76tvIp1HQKmdHrAnzafLt7OuSRqBEzp5EP9\n8vL4uFxuXspa6fc6BEzJoU5EwJQudKiHbZfZxQ0SMKUrHGpn81wETEnAiQiYkoATETClv76N\n1PA019k8FwFTOvVQPwr4+gRM6fT3gRf3l94FBQFTOv1Qv7T+AKWzeS4CpvSHQ/04vFx6F+wQ\nMCWvQiciYEoCTkTAlASciIApCTgRAVMScCICpiTgRARMScCJCJiSgBMRMCUBJyJgSgJORMCU\nBJyIgCkJOBEBUxJwIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQEnIiAKQk4EQFTEnAi\nAqYk4EQETEnAiQiYkoATETAlASciYEoCTkTAlASciIApCTgRAVMScCICpiTgRK4e8NDmxFVx\nBgJO5PoBnzjklF+NgBMRMCUBJyJgSgJORMCUBJyIgCkJOBEBUxJwIgKmJOBEBExJwIkImJKA\nExEwJQEnImBKAk5EwJQEnIiAKQk4EQFTEnAiAqYk4EQETEnAiQiYkoATETAlASciYEoCTkTA\nlASciIApCTgRAVMScCICpiTgRARMScCJCJiSgBMRMCUBJyJgSgJORMCUBJyIgCkJOBEBUxJw\nIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQEnIiAKQk4kbF4RrRsKOCZEHAil01MwBkJ\nOBEBUxJwIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQEnIiAKQk4EQFTEnAiAqYk4EQE\nTEnAiQiYkoATETAlASciYEoCTkTAlASciIApCTgRAVMScCICpiTgRARMScCJCJiSgBMRMCUB\nJyJgSgJORMCUBJyIgCkJOBEBUxJwIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQEnIiA\nKQk4EQFTEnAiAqYk4EQETEnAiQiYkoATmVnAw4imDfkl4ETmFnDTECEBJyJgSgJORMCUBJyI\ngCkJOBEBUxJwIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQEnIiAKQk4EQFTEnAiAqYk\n4EQETEnAiQiYkoATETAlASciYEoCTkTAlASciIApCTgRAVMScCICpiTgRARMScCJCJiSgBMR\nMCUBJyJgSgJORMCUBJyIgCkJOBEBUxJwIgKmJOBEBExJwIkImJKAExEwJQEnImBKAk5EwJQE\nnIiAKQk4EQFTEnC3hn0jVzpxaOxK59uhgK9GwN266N2me+CZEHC3BMxhAu6WgDlMwN0SMIcJ\nuFsC5jABd0vAHCbgbgmYwwTcLQFzmIC7JWAOE3C3BMxhAu6WgDlMwN0SMIcJuFsC5jABd0vA\nHCbgbgmYwwTcLQFzmIC7JWAOE3C3BMxhAu6WgDlMwN0SMIcJuFsC5jABd0vAHCbgbgmYwwTc\nLQFzmIC7JWAOE3C3BMxhAu6WgDns9CP2/LDc/Pqc5er5Uru4bQLmsO0jdvfw2rzd293Wr8C6\nb94F7QTMYdtH7CPF5oZXw+K/l81nr0+LYdW6C9oJmMO2j9jbf/+aG14MLz+fvwyL1l3QTsAc\nVh6x54e7poaHofbFwV3QRsAcNnLEXhYf98OPB7ZzD3xxAuaw/SP2dN/wwtT6OfDT592058AX\nImAOK47Y28PH3e/d09tHxct4w/utV6Hv3o7YBY0EzGE7R+x5/SLW6vOxcfy8dn3l1eZ94MXy\nwfvAFyFgDtt5H/jjvvTx+840fl576i5oJ2AO23kxefl0tmm3nWvSORtG7F9pZLvLTnXi0Kmr\nEvDRdt4HvvwuqLj23eb1Az51iNDOEXtbrR83L1bnLdlJaSDg2hCh7SP2utg8qhmGRfvPRB+5\nCyoEXBsitH3E7od/6/vet9Wht5De957StO6CCgHXhgjtvIg1lJ/UPQr4rARcGyK0fcQWw+eT\n37eWF45fFgd+Vmt0F1QIuDZEaPuIrYb79c9kPN/HPxr55aXpWu9OShMB14YI7Ryx7x+PbLtv\nfdz6+wzNu2CcgGtDhHaP2H/rn468P/Q3kf60C0YJuDZE6ApHzElpIODaECEB90HAtSFCAu6D\ngGtDhHaO2MNdy/u6f9oF4wRcGyK0fcQeLvMXiJyUBgKuDRHaPmKLg/8S1p93QYWAa0OEto/Y\nhf7mrpPSQMC1IULbR2w5XORvBDspDQRcGyK0fcReF/cH/nmrP++CCgHXhgjtPoT2ItZUBFwb\nIiTgPgi4NkToCkfMSWkg4NoQIQH3QcC1IUK7R+xpuX70vDzrP4nlpLQQcG2I0M4Ru/98+usf\ntbs+AdeGCG0fscfhfvOv6TwO/y61CyoEXBsitH3E1v8m1tc/LHupXVAh4NoQod23kd4FPBEB\n14YIbR+xu6974Jfh7lK7oELAtSFCI8+Bn878t5KclAYCrg0R2jliy6P+VcqTdsE4AdeGCO0e\nsfX7wMPyv0vuglECrg0RusIRc1IaCLg2REjAfRBwbYiQgPsg4NoQoe0j5q8TTkfAtSFCAu6D\ngGtDhEaO2PP94d/v/cddUBJwbYjQ2BF785cZrm5mAY84dXZCo0fMQ+irm1nAZ5yd0NgRexwW\nl94FBQHXhgiNv4j1cKldUCHg2hChsYDvzvsbVpyUBgKuDRG6whFzUhoIuDZESMB9EHBtiND4\nc+Cz/jCHk9JAwLUhQgLug4BrQ4R2jtjD4unjz+eFv9B/dQKuDRHaPmIPw8vm48tw1p+ldFIa\nCLg2RGj3IXT5ydl3QYWAa0OEto/Y4uce2L9KeW0Crg0R2j5iq2HzHNi/SjkBAdeGCO0csfuv\n159Xl9sF4wRcGyK0e8T+2/yrlE+X3AWjBFwbInSFI+akNBBwbYiQgPsg4NoQod0j5hd8T0XA\ntSFC+y9ivfsF3xMQcG2I0PYR8wu+pyPg2hCh7SPmF3xPR8C1IULbR8wv+J6OgGtDhLaPmF/w\nPR0B14YIjTwH9qOUExBwbYjQzhHzC74nI+DaEKHdI+YXfE9FwLUhQlc4Yk5KAwHXhghtH7Hl\nef8W0tguqBBwbYhQ+TbShXdBhYBrQ4TKt5EuvAsqBFwbIrR9xN6W988X3gUVAq4NEdp9CH32\nfxO63AUVAq4NERJwHwRcGyLkbaQ+CLg2REjAfRBwbYjQ9xG70FtI27sgIODaEKHdgC+SsZPS\nQMC1IUIC7oOAa0OEBNwHAdeGCAm4DwKuDREScB8EXBsiJOA+CLg2ROg34B2X2AUBAdeGCAm4\nDwKuDRG6whFzUhoIuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLug4BrQ4QE3AcB14YICbgP\nAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLug4BrQ4QE3AcB14YI\nCbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLug4BrQ4QE3AcB\n14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLug4BrQ4QE\n3AcB14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLug4Br\nQ4QE3AcB14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUhQgLu\ng4BrQ4QE3AcB14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdBwLUh\nQgLug4BrQ4QE3AcB14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAhAfdB\nwLUhQgLug4BrQ4QE3AcB14YICbgPAq4NERJwHwRcGyIk4D4IuDZESMB9EHBtiJCA+yDg2hAh\nAfdBwLUhQgLug4BrQ4QE3AcB14YICbjVMOKiUwm44oxnIj8Btzrj/UUHXaQO+MTtZknArQQ8\nzezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPM\nfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn\n226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7t\nZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226W\nBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknA\nrQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxKwNPMfr7tZknArQQ8zezn226WBNxK\nwNPMfr7tZumP3/nj3TAsny66i14IeJrZz7fdLJ18G9xseD9srC6yi84IeJrZz7fdLP0p4NWw\nent/f10Nj5fYRWcEPM3s59tulv4U8GJ4W3/+NtxdYhedEfA0s59vu1n6U8DDsPVFcfGW01fX\nEwFfY/Z9p243k5vdIX8K+N93wItL7KIzAp5k9svemed3esDLh8en4b+PT99W8atYMzmSAp5k\ndgHHTg/453HKMCzeLrGLzgh4ktkFHDv523x5eXxcLjcvZa3CfudyJAU8yewCjl3h25zJkRTw\nJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BMwK0EPMns\nAo4JuJWAJ5ldwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4Bj\nAm4l4ElmF3BMwK0EPMnsAo4JuJWAJ5ldwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBb\nCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BMwK0EPMnsAo4JuJWAJ5ldwDEBtxLwJLMLOCbgVgKe\nZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BMwK0EPMnsAo4JuJWAJ5ld\nwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BM\nwK0EPMnsAo4JuJWAJ5ldwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3Ar\nAU8yu4BjAm4l4ElmF3BMwK0EPMnsAo4JuJWAJ5ldwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCT\nzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BMwK0EPMnsAo4JuJWAJ5ldwDEBtxLwJLML\nOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l4ElmF3BMwK0EPMnsAo4J\nuJWAJ5ldwDEBtxLwJLMLOCbgVgKeZHYBxwTcSsCTzC7gmIBbCXiS2QUcE3ArAU8yu4BjAm4l\n4ElmF3BMwK0EPMnsAo7dXsDDvrbtmoaa9tfBjTlPwOc7fLN0gwE3jLRt1xjw+Yb6nCrPQudI\nwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs\n4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALu\nenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5n\nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYB\nxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BMwALuenYBxwQs4K5nF3BM\nwALuevazLnTf/pWSEbCAu5796gtNRsAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC\n7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCu\nZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2\nAccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdw\nTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccELOCuZxdwTMAC7np2AccE\nLOCuZxdwTMAC7np2AccELOCuZxdwbPKAhxGn7qjNiUtou0Gcb6qZddHBVCefrxFt5/l8t+36\nQs494bG7OPWO7eSpMt/cupxq/gsdccaF/o2AZ3dzs9Bzzz5CwMGlAr787BZ6xHYjBBxcKuDL\nz26hR2w3QsDBpQK+/OwWesR2IwQcXCrgy89uoUdsN0LAwaUCvvzsFnrEdiMEHFwq4MvPbqFH\nbDdCwMGlAr787BZ6xHYjBBxcKuDLz26hR2w3QsDBpQK+/OwWesR2IwQcXCrgy89uoUdsN0LA\nwaUCvvzsFnrEdiMEHFwq4MvPbqFHbDdCwMGlAr787BZ6xHYjBBxcKuDLz26hR2w3QsDBpQK+\n/OwWesR2IwQcXCrgy89uoUdsN0LAwaUCvvzsFnrEdiMEHFwq4MvPbqFHbDdCwMGlAr787BZ6\nxHYjBBxcKuDLz26hR2w3QsDBpQK+/OwWesR2IwQcXCrgy89uoUdsN0LAwaUCvvzsFnrEdiME\nHFwq4MvPbqFHbDdCwMGlAr787BZ6xHYjBBxcKuDLz26hR2w3QsDBpQK+/OwWesR2IwQcXCrg\ny89uoUdsN0LAwaUCvvzsFnrEdiMEHFwq4MvPbqFHbDdCwMGlAr787BZ6xHYjZhDw88Ny8yvH\nl6vnv+xCwJPMbqFHbDcifcBvd8Ov+z/sQsCTzG6hR2w3In3Aq2Hx38vms9enxbA6fRcCnmR2\nCz1iuxHpA14MLz+fvwyL03ch4Elmt9AjthuRPuBhqH3xNbLlwERwO07srd7PidsdcQ8MXMof\nngM/vW4+O/gcGLiUk+/S77ceFty9nXNJQKvTH5M/rzbvAy+WDwfeBwYu5exPqoHrETAkJmBI\nTMCQmIAhMQFDYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEBQ2IChsQEDIkJGBITMCQmYEhMwJCY\ngCExAUNicw94ol+gwUxNfXve09+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH\n76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq\n0t+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH76/D\nNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KzqvH76/DNXW4JGtq0t+KgGYChsQEDIkJGBITMCQm\nYEhMwJCYgCExAUNiAobEBAyJCRgSEzAkJmBITMCQmIAhsRkGvFoMi9XbztDjUL9smjX9Dkzx\nW7OC5ThE0Zo6uCkV5hfw/eZk320PvXyf/JHLplnT78DLBLfOYDkOUbSmDm5KpdkF/DwsXt5f\nFsPz79DHV0PtsmnWtDXwMiyvvJpwOQ5RsKYObkp7Zhfwanj6+PO/4eFn5HG4/zrq+5dNtKat\ngcerryZcjkMUrKmDm9Ke2QW8HF7fd/+nPazev476/mUTrWlr4HF4vPJqwuU4RMGaOrgp7Zld\nwF8HeOsZ00s5ePVnU3v73RpYDk//hsWql+U4RMGaOrgp7Zl8Aec2emS7DnjjvpPlOETBmvYH\nBXx2PR71uJj/3t/fVtd8lJgt4AkO0fia9gcFfHY9HvXo1vnp7ZpvSGQL+NNVD9H4EvYHBfyV\nj+MAAANDSURBVHw2328VLoKjPnrZFGvaX8g1bwnRcq59iFrW9GX6NW19NdVx2jP5As7lO5bP\nlwdfd18e3Hnp8PVqLx1W17S/kGveEqLlXPsQtazpy9Vj6emmVDWbgL89bN6gexp2XrT8Ouqj\nl02xpq2BxbD+cbyr3hKi5ThEwZrWJr4p7ZldwKM/ItPxT2Kt1reBt8+fC+hgOQ5RsKY1P4l1\naXe/7zn8POj6/uRumvcj9tf0O/C22Hx61f+TB8txiKI1vU9/UyrNL+C3zV8T2Xy6d9S3Lpt2\nTVsD60/vrvsOyaHlOESVNb1Pf1MqzS9guCEChsQEDIkJGBITMCQmYEhMwJCYgCExAUNiAobE\nBAyJCRgSEzAkJmBITMCQmIAhMQFDYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEBQ2IChsQEDIkJ\nGBITMCQmYEhMwJCYgCExAUNiAr5Vw9ipHx2kY07YrRLwLDhhbBFwNk4YWwScjRM2I8Pwdjcs\nPz55vBsWj58j7w/D4uH9fTUMq/XA03IYFquviz7+e11uLv6wWnxc4zPgrc2/JqRXAp6RYVhu\nOv3488P9ZuRh/enT/frPj0s2X322/BnwYv3luuDNNZabgLc3X36FT6cEPCMf1b19fHhaf3i7\nH56+Rh6//lysv/7v/f2/TaafAW8uuFuPLV7eXxbrwXJzeibgGRmG5/WH5bCu7m392Pdz5OOR\n8vv289utgJ+/PltuPnv6/LTYnI4JeEa+Eh2+fY9s//n69HC/FfD7zmdfnxab0zFnaEYaAr7/\nvkTA8+AMzchWhTsjv3/+G+4en14PBVxOSL+coRn56m25fv1pe6TodCzgz22efz/dnpB+OUMz\n8tXb5hXl98fPV6F+x79ftXoZew789Psq9N7mdMwZmpHv3j6f6C5e9wNefT29fS4D/nzz99/W\n8+TfzemYMzQjP7093n3E+PvW0dafH4nePz9937tuX/yw85NY25vTMWcIEhMwJCZgSEzAkJiA\nITEBQ2IChsQEDIkJGBITMCQmYEhMwJCYgCExAUNiAobEBAyJCRgSEzAkJmBITMCQmIAhMQFD\nYgKGxAQMiQkYEhMwJCZgSEzAkJiAITEBQ2IChsT+B9ERDuwvQck5AAAAAElFTkSuQmCC", "text/plain": "Plot with title \"Distribution of  remainder\""}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8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", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "## Moving Average Models\n\nNow that you have explored the decomposition of the time series you, will now construct and test Autoregressive Moving Average (ARMA) models for the remainder of the time series. You will create and test these models in three steps, creating a moving average (MA) model, creating an autoregressive (AR) model and creating an autoregressive moving average (ARMA) model. \n\nThe function in the cell below computes an Autoregressive Integrative Moving Average (ARIMA) model. The summary statistics for the model are printed and the model object returned. By assigning values to the order of each operator different time series models can be specified, as order of MA model, order of Integrative model, and order of AR model. Since the de-trended remainder is being modeled, the **include.mean** argument is set to FALSE in the **arima** function. \n\nThe ACF of the remainder from the **stl** decomposition of the milk production time series had 4 significant lag values. As an inital model, you will now create an MA model of order 4. Execute the code in the cell below to compute the MA(4) model and examine the model summary. ", "cell_type": "markdown", "metadata": {}}, {"source": "model.dairy = function(df, col = 'remainder', order = c(0,0,1)){\n  ts = ts(df[, col], frequency = 12, start = 1995)\n  dairy.mod = arima(ts, order = order, include.mean = FALSE)\n  print(dairy.mod)\n  dairy.mod\n}\nma1 = model.dairy(dairyMult, order = c(0,0,4))", "execution_count": 32, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ma1     ma2     ma3     ma4\n      0.7259  0.5308  0.2976  0.0193\ns.e.  0.0659  0.0776  0.0748  0.0589\n\nsigma^2 estimated as 0.0001876:  log likelihood = 654.34,  aic = -1298.67\n"}]}, {"source": "Examine the values of the model coefficients and their standard errors (SE). Notice that the SE of the ma4 coefficient is actually greater than the value of the coefficient itself. This indicates that the value of this coefficient is poorly deterimind and should likely be set to zero. \n\nThe foregoing result indicates that the order of the MA model should be reduced. Generally, the order of an MA model is reduced in unit steps until all the coefficients appear to be significant. The code in the cell below computes an MA(3) model. Run this code and examine the model summary. ", "cell_type": "markdown", "metadata": {}}, {"source": "ma1 = model.dairy(dairyMult, order = c(0,0,3))", "execution_count": 33, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ma1     ma2     ma3\n      0.7224  0.5211  0.2861\ns.e.  0.0645  0.0698  0.0660\n\nsigma^2 estimated as 0.0001877:  log likelihood = 654.28,  aic = -1300.56\n"}]}, {"source": "The small standard error compared to the magnitude of the coefficients indicates that the order of the model is reasonable. \n\nTo test how well this model fits the data, and results in a stationary result, you will plot the ACF of the residuals of the MA(3) model. Run the code in the cell below to plot the ACF of the model result. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf(ma1$resid[-1], is.df = FALSE)", "execution_count": 34, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nNsNVg7VmKfgAAAAASUVORK5CYII=", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Note that only the 0 lag of the ACF is significant and that there are no significant lags for the PACS. These observations indicate that the MA(3) model is a good fit. ", "cell_type": "markdown", "metadata": {}}, {"source": "## Autoregressive Models\n\nThe MA(3) model has been shown to be effective. Next, you will test an autoregressive model. The PACF of the reminder indicates that an AR model might not be the best choice. None the less, a low order AR model might fit these data. To compute an AR(2) model exectue the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "ar1 = model.dairy(dairyMult, order = c(2,0,0))", "execution_count": 35, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ar1      ar2\n      0.7148  -0.0288\ns.e.  0.0665   0.0665\n\nsigma^2 estimated as 0.0001899:  log likelihood = 653.04,  aic = -1300.08\n"}]}, {"source": "Examine the values of the coefficients and their standard errors. Note that the standard error of the second coefficient is of the same magnitude as the coefficient. Clearly, the AR(2) model is over parameterized. \n\nNext, you will try an AR(1) model, by executing the code in the cell below.", "cell_type": "markdown", "metadata": {}}, {"source": "ar1 = model.dairy(dairyMult, order = c(1,0,0))", "execution_count": 36, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ar1\n      0.6946\ns.e.  0.0475\n\nsigma^2 estimated as 0.00019:  log likelihood = 652.95,  aic = -1301.9\n"}]}, {"source": "The standard error of the AR(1) model is an order of magnitude less than the value of the coefficient, which is promising.\n\nNext, exectue the code in the cell below to plot the ACF and PACF of the AR(1) model", "cell_type": "markdown", "metadata": {}}, {"source": "options(repr.plot.width=8, repr.plot.height=8)\ndairy.acf(ar1$resid[-1], is.df = FALSE)", "execution_count": 37, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nTkSuQmCC", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Note that only the 0 lag of the ACF is significant and that there are no significant lags for the PACF. These observations indicate that the AR(1) model is a good fit. Compare these results to those of the MA(3) model, noting that they are nearly identical. Evidently, either the MA(3) or AR(1) model is a good choice for these data. ", "cell_type": "markdown", "metadata": {}}, {"source": "## Autoregressive Moving Average Models\n\nYou have found that both MA(3) and AR(1) models are good fits to the remainder series. You will now investigate the use of autoregressive moving average (ARMA) models on the remainder series. \n\nAs a starting point you will try an ARMA(1,3) model by executing the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "arma1 = model.dairy(dairyMult, order = c(1,0,3))", "execution_count": 38, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ar1     ma1     ma2     ma3\n      0.1532  0.5750  0.4288  0.2274\ns.e.  0.3874  0.3889  0.2588  0.1805\n\nsigma^2 estimated as 0.0001876:  log likelihood = 654.39,  aic = -1298.78\n"}]}, {"source": "In each case, the standard error is of the same order of magnitude as the value of the coefficient, indicating this model is a poor fit to the data.\n\n\n****\n\n### Exercise: Test Another ARMA Model\n\nIn this exercise you will test an ARMA(1,1) model and evaluate its coefficients to answer these questions. \n\n- How do the standard errors compare to the values of the coefficients?\n- Do you think this model fits the data well or is it over parameterize?\n\nAdd code to compute the ARMA(1,1) model and plot iots ACFG and PACF to the cell below, and answer the questions above.\n\n****", "cell_type": "markdown", "metadata": {}}, {"source": "arma2 = model.dairy(dairyMult, order = c(1,0,1))\ndairy.acf(arma2$resid[-1], is.df = FALSE)", "execution_count": 40, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ar1     ma1\n      0.6777  0.0330\ns.e.  0.0661  0.0856\n\nsigma^2 estimated as 0.0001899:  log likelihood = 653.02,  aic = -1300.05\n"}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\nhBEwIIyAAWEEDAgjYEAYAQPCCBgQ9h8B2EmJYY46qwAAAABJRU5ErkJggg==", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "\n## Exploring the Difference Series\n\nUsing a difference series is a method to remove trend from a time series. The difference can be computed for any number of lag values, depending on the order of the trend.  In this case you will use a first order difference series to model the trend in the milk production time series. \n\nUsing the code in the cell below, you will compute the first order difference series. Notice that the difference series is  necessarily of length one less than the original series. Execute the code in the cell to compute the difference series. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.diff <- function(df, col = 'Milk.Prod', out = 'Milk.Diff'){\n  ln <- nrow(df)\n  temp <- ts(df[, col], frequency = 12, start = 1995)\n  df[2:ln, out] <- diff(temp)\n  df <- df[2:ln, ]\n  df\n}\ndairyDiff <- dairy.diff(dairy)", "execution_count": 41, "cell_type": "code", "metadata": {"collapsed": true}, "outputs": []}, {"source": "Next, compute the stl decomposition of the difference series. Since we are working with a difference series, which has positive and negative values, we use an additive model. No logarithm is taken. Execute the code in the cell below to compute and display the decomposition of the difference series.  ", "cell_type": "markdown", "metadata": {}}, {"source": "dairyDiff = dairy.decomp(dairyDiff, col = 'Milk.Diff', span = 0.5, Mult = FALSE)", "execution_count": 42, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAABNTU1oaGh8fHyM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\n", "text/plain": "Plot with title \"Decompositon of dairy produciton\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Examine the results shown above. The difference series is shown in the uppermost plot. Notice the small magnitude of the remaining trend indicating that the first order difference model removed most of the trend. However, the seasonal series exhibits a pattern with a 24 month cycle which is a bit odd. \n\n****\n\n### Exercise: Analysis of the Difference Series\n\nIn this exercise you will analyize the remainder of the difference series following these steps. \n\n- Does the acf plot indicate that the remainder series is stationary?  \n- Is the dispersion of these values greater or less than the dispersion obtained directly from the decomposition of the time series (without diferencing). \n- Is the interquartile range of these values greater or less than the interquartile range obtained directly from the decomposition of the time series (without differencing). \n\nIn the code cell below, use the **dairy.acf**, **dairy.hist**, and **dairy.box** functions to create new plots of the difference series and answer the questions above. \n****\n", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf(dairyDiff)\nhist.ts(dairyDiff)\ndairy.box(dairyDiff)", "execution_count": 44, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\ngDACBoQRMCDsPw2QW5H8pIxtAAAAAElFTkSuQmCC", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAMFBMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////QFLu4AAAACXBIWXMAABJ0AAAS\ndAHeZh94AAAgAElEQVR4nO2diXbaMBBFZfYQlv//24KBYMB2hSVZ86R7z2lDVPNmhHRrA1nc\nGQBkcbkbAIDpIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADC\nIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwC\nAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIPBM\nuDvLzfFvoOew9ce9ho99v9f/jhpj2zi3fh9sG761e2xvf7bUV/Mx1Wa196od0nf18NDNhHuy\nfwx8HPTbuI97DR37ea8AEbbXvvoF/mlv/kwQ+MLGpzgCB8BDNxOdXe1+7wN9B/UOjG/xx78G\niLBw7tAbfLlkaG8upwl8m+p/QOAAeOhm4r5LT/uLK81/DvIe9/lXL/oj3J+13Zsv9xj7b2jf\nd1nuXRy84KGbiecuXdwuoh9Gb68nt9XP+e/Mdbt1XFyvPzua7BauWR9fstqPL/e6VdivrxfE\n+2fh/aXG+u0U+3FQb8+rW7P79tbgGfjyz83xc6qHt9m8FT0f141b7BA4BB66mXju0v3tvHQb\nODZ3AZdvKi4eQ/c7L3uuvgcEvh/qVo+DNrfPXwzuHvSM+Oh5d2t23d4aEvj44m9nqm+zeevs\n9z5zBA6Ah24mnrv0dNnPfwPr9lWi02UT715VdO0/PDW503Sz+gVe/R28er1v93L25aAxgVdt\nycathgW+/CfU9fflDNx0Z/PWWfP3KbtwMjx0M9HZpV3d3O19mhepb2fcU+deV3P3tyeVP+c3\ngd8/3V+1O10uzd3fpfr1vusXTXoO6u/5sLue9S/nyt1hSOBT83Zyf4Q9ngM/ZvNW9Oc5KXbh\nZHjoZmJA4Ovu/XtO2FXx5b2mx+f7v0vet3/tfHq92m0/3fzpc73v6UWTnoP6ez5cLo+313eZ\njoMCLx9vNXXu9seh0/1b0dVzUuzCyfDQzcSAwNv71e3re8PX81p34O/OL9fK/QL/3ffYe/Bf\nTu9BHz0fLv/FLM6Ly6XwoMDu/e3ejr/7brG3om+Tgknw0M3Ec5e+Xi7fX2C6PYv8kG2awOeR\ng9+7+a/Al/Nm+7LbmMB3MZ93a1luXv4Xei+KwDHgoZuJ5y7dv161nn5ur80uz6MCd13wPgM3\nfZnnkYM+ej5cn6ourhfJgwI327dT8HvYx3XFrSgCx4CHbiaeu3T5+brRfj1wtnxq0j7NfD4H\nvprw2yvwauDp7YsmQwd99Hy4fxX0cVjg3+s726fXu/VOfdX/HPgHgQPgoZuJxy79Xb28F7T4\ne374OBGezr0CXw2+vmC7PbevfG3aL4F+uvS819ALzC+aeL8KfWxbvF7zH4cEbtM2r3frnfpb\n0d3tVegfXoUOgYduJlyHx0s753ZTL4/ta1lXBa57eXPuF/hGczV1/fz8/Hmv5d8/rjsRb1oN\nHPTR8/n2LL0T3/dh2b7c3F+p8/lbUd4HjgAP3Uy8+/v+Ilb7PQNr9/pcuKPJqnPf21Vt+wVW\nffd6ePL6TYZvmvQf9NHz+Xbi7Jyl+z4cHl8P0hv2/Py16P0rsVb9xcELHrqZeNj7eGn2eWHZ\n+nd7cnh9XvjylLSjye769cz3L3g6XO6z/Ok+uXy5137dfH6Z87smvQd99Hy+vYPcua7v/bC6\nnoL/L/Br0fNx3c4cgQPgoQMQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFg\nAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQ\nBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQ\nGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEBhEFgAGEQGEAYBAYQBoEB\nhEFgAGEQGECYcIEd/wcA5AKBAYSZap97JWpPAODJVPV+GwQGyM5k9U4rtzy2CdgLkIsA+36c\n+zkjMEBGQuw7Lt3qhMAA+Qizb+uaPQIDZCPQvsOCV7AA8hFs3xqBAbKRyD7eY4I5cT14HTV/\nq5GZYQb6DxJYp89WnyH9vYnAUAAIrF0CKgeBv76f/1MJ/QcJrIPA37JDYLADAn/NoVmmLgHg\nCQJ/z8FtUpcA8AOBJ7Bzh9QlALxAYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaBy\nEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuX\ngMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkI\nrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA\n5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATW\nLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaBy\nEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuX\ngMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkI\nrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAn/Nae3ccn8PGU3Rf5DAOgj8LafG\nXVndQhAYsoLA37Jxu4vFu2bZhiAwZAWBv6W53fHYLI4IDLlB4K/vd7/jablEYMgNAn/Lwp0e\nt5YIDJlB4G/ZufX91tEtERjygsBfs/mzdu8QGPKCwN9zWD1uHdcIDFlBYO0SUDkIHDu2S5oS\nAH8gsHYJqBwE1i4BlYPA2iWgchD46/s576e5+g8SWAeBv2WHwGAHBP6aw+0bkVKWAPAEgb/n\n4DapSwD4gcAT2LlD6hIAXiCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0C\nKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCw\ndgmoHATWLgGVg8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGV\ng8DaJaByEFi7BFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgmoHATWLgGVg8DaJaByEFi7\nBFQOAmuXgMpBYO0SUDkIrF0CKgeBtUtA5SCwdgnIifskafhUWxHYbAnISVIvItqKwGZLQE4Q\nOCMIDKEgcEYQGEJB4IwgMISCwBlBYAgFgTOCwBAKAmcEgSEUBM4IAkMoCJwRBIZQEDgjCAyh\nIHBGEBhCQeCMIDCEgsAZQWAIBYEzgsAQCgJnBIEhFATOCAJDKAicEQSGUBA4IwgMoSBwRhAY\nQkHgjCAwhILAGUFgCAWBM4LAEAoCZwSBIRQEzggCQygInBEEhlAQOCMIDKEgcEYQGEJB4Iwg\nMISCwBlBYAgFgTOCwBAKAmcEgSEUBM4IAkMoCJwRBIZQEDgjCAyhIHBGEBhCQeCMIDCEgsAZ\nQWAIBYEzMn0Gv9uVu7La/KYqARIgcEamzuC0cE+WSUqACAickakz2Ljm59DeOu4bt0lRAkRA\n4IxMnUHjDn+3D65JUQJEQOCMTJ2Bc0OfRCsBIiBwRjgDQygInJGA58D7Y3uL58C1g8AZmTyD\nZedV6MUpSQnQAIEzEvA+8KZ9H7hZbXkfuG4QOCN8JRaEgsAZSTQD1yVNif8Unbm2ISI+DH5R\nRgX26V1/f5R0BvZb2OKJ+DAYOLFxBh4HgYsDgf2H9PcHAhcHAvsP6e+PSM+OUpT4vqeMtQ2B\nwP5D+vtj6gx2CGwVBPYf0t8fk2dwaMa/iTBCiW9B4BYE9h/S3x/TZ3AY/wLKGCW+BIFbENh/\nSH9/BMxg1/l+hkQlvgOBWxDYf0h/f/AqdHEgsP+Q/v5A4OJAYP8h/f2BwMWBwP5D+vsDgYsD\ngf2H9PcHAhcHAvsP6e8PBC4OBPYf0t8fCFwcCOw/pL8/ELg4ENh/SH9/IHBxILD/kP7+QODi\nQGD/If39gcDFgcD+Q/r7A4GLA4H9h/T3BwIXBwL7D+nvDwQuDgT2H9LfHwhcHAjsP6S/PxC4\nOBDYf0h/fyBwcSCw/5D+/kDg4kBg/yH9/YHAxYHA/kP6+wOBiwOB/Yf09wcCFwcC+w/p7w8E\nLg4E9h/S3x8IXBwI7D+kvz8QuDgQ2H9If38gcHEgsP+Q/v5A4OJAYP8h/f2BwMWBwP5D+vsD\ngYsDgf2H9PcHAhcHAvsP6e8PBC4OBPYf0t8fCFwcCOw/pL8/ELg4ENh/SH9/IHBxILD/kP7+\nQODiQGD/If39gcDFgcD+Q/r7A4GLA4H9h/T3BwIXBwL7D+nvDwQuDgT2H9LfHwhcHAjsP6S/\nPxC4OBDYf0h/fyBwcVgQuAe/gj73Q+AOCFwcFgSe2sLUKATWLjFYSH+BvgeB/Yf09wcCFwcC\n+w/p7w8ELg4E9h/S3x8IXBwI7D+kvz8QuDgQ2H9If38gcHEgsP+Q/v5A4OJAYP8h/f2BwMWB\nwP5D+vsDgYsDgf2H9PcHAhcHAvsP6e8PBC4OBPYf0t8fCFwcCOw/pL8/ELg4ENh/SH9/IHBx\nILD/kP7+QODiQGD/If39gcDFgcD+Q/r7A4GLA4H9h/T3BwIXBwL7D+nvDwQuDgT2H9LfHwhc\nHAjsP6S/PxC4OBDYf0h/fyBwcSCw/5D+/kDg4kBg/yH9/YHAxYHA/kP6+wOBiwOB/Yf09wcC\nFwcC+w/p7w8ELg4E9h/S3x8IXBwI7D+kvz8QuDgQ2H9If38gcHEgsP+Q/v5A4OJAYP8h/f2B\nwMWBwP5D+vsDgYsDgf2H9PcHAhcHAvsP6e8PBC4OBPYf0t8fCFwcCOw/pL8/ELg4ENh/SH9/\nIHBxILD/kP7+QODiQGD/If39gcDFgcD+Q/r7A4GLA4H9h/T3BwIXBwL7D+nvDwQuDgT2H9Lf\nH5NncFy7Zns+7xau2SQq8S0I3ILA/kP6+2PqDE6Nu7DbXv92yyQlvgaBWxDYf0h/f0ydwcZd\nzrubxq1P51N7O36Jr0HgFgT2H9LfH1Nn0LR3dO7UfmhSlPgaBG5BYP8h/f0xeWnd8+/Hh5d/\n7jC9uy978hoqHqMC9zBzVPECL7ZH7/s1HYFPnIEtYVTg/FHFC3z5j8zb4cdz4M3pftuvRFIQ\nuAWBg9LF6M7g9LP2dphXoc2CwEHpYrzP4He78HOY94GtgsBB6WL0zOBwPbnukpZIAwK3IHBQ\nuhifM9gvPS6Lw0okAoFbEDgoXYy3GZy2l9PvYn+6WLxKVCIdCNyCwEHpYrzM4Pf6ItbmcPuH\naHND4HlB4KB0MbozuL58tTs9/mH0vd2pJZKCwC0IHJQuRncGbrVPXSIpCNyCwEHpYnRncBo8\nKlqJpCBwCwIHpYvxMoPT5nrd3GzimozA84LAQelidGdwbNpXrpxr/L8m+ssSSUHgFgQOShej\nO4Pl9bt7r+fheG8hvZdICgK3IHBQuhgvL2K59xvRSyQFgVsQOChdjO4Mmtu3559PCKwMAgel\ni9GdwcYtfy8ffpfj3x4YUiIpCNyCwEHpYrzMYHn/8Qbxvg76o0RKELgFgYPSxXidwc/qqm/E\n70T6LJEQBG5B4KB0MWaYAQLPCwIHpYuBwMWBwEHpYiBwcSBwULoYLzO4/jid+D8JFoHnBYGD\n0sXozmCb5kc5I/C8IHBQuhjdGTQxfxJWf4mkIHALAgeli9GdQaLfoYDA84LAQelidGewckm+\nIxiB5wWBg9LF6M7g2LRfSpmyRFIQuAWBg9LFeL2E5kWsAkDgoHQxELg4EDgoXYwZZoDA84LA\nQeliIHBxIHBQuhivM9ivrlfPq6g/EguBZwaBg9LFeJnB8vb0lx9qJw0CB6WL0Z3Bzi3bn6az\nc+tUJZKCwC0IHJQuRncG15+Jdf/BsqlKJAWBWxA4KF2M7gzay2cEVgeBg9LF6M5gcT8DH9wi\nVYmkIHALAgeli9HzHHgf+buSEHheEDgoXYyXGaz4qZQFgMBB6WK8zuD6PrBb/aQskRAEbkHg\noHQxZpgBAs8LAgeli4HAxYHAQeliIHBxIHBQuhjdGfDthEWAwEHpYiBwcSBwULoYPTP4XUb9\n/d4IPDMIHJQuRt8MTnwzg+shqLcZ0RHY50FG4HF6Z8AltPLJXEfgmaOqEXjnmtQlkoDALQgc\nlC5G/4tY21QlkoLALQgclC5Gn8CLuL9hBYHnBYGD0sWYYQYIPC8IHJQuBgKnjpodBA5KF6P/\nOXDUt00QeF4QOChdDAROHTU7CByULsbLDLbN/vL3b8M39CPwF1EInJHuDLbu0H48uKhfS4nA\n84LAQelivF5Cv9+IXiIpCNyCwEHpYnRn0Pydgav/qZQI/EUUAmekO4ONa58D81MpEfirKATO\nyMsMlvfXnzfpSqQEgVsQOChdjNcZ/LQ/lXKfskRCELgFgYPSxZhhBgg8LwgclC4GAqeOmh0E\nDkoX43UG/ILv+FGzg8BB6WJ8voh15hd8I/BXUQicke4M+AXfKaJmB4GD0sXozoBf8J0ianYQ\nOChdjO4M+AXfKaJmB4GD0sXozoBf8J0ianYQOChdjJ7nwHwpJQJ/FYXAGXmZAb/gO0HU7CBw\nULoYrzPgF3zHj5odBA5KF2OGGSDwvCBwULoY3Rms4n4XUl+JpCBwCwIHpYvRnUGi39+FwPOC\nwEHpYnRncH0bKXGJpCBwCwIHpYvRncFptfxNXCIpCNyCwEHpYrxeQif5XbgIPC8IHJQuBgKn\njpodBA5KF2OGGSDwvCBwULoYCJw6anYQOChdjMcMEr2F1C2RHARuQeCgdDFeBU6iMQLPCwIH\npYuBwKmjZgeBg9LFQODUUbODwEHpYiBw6qjZQeCgdDEQOHXU7CBwULoYCJw6anYQOChdjKfA\nL6QokRwEbkHgoHQxEDh11OwgcFC6GJNncNo0l7+3C+eW//kRPAg8LwgclC7G1Bkcm8tp+tT4\n/BA8BJ4XBA5KF2PqDNZudbr8tT5eXF6P/0ZwBJ4XBA5KF2Py0l5/eoe7/QiPk2tSlPgaBG5B\n4KB0MaYLfL7+MqXOJ2//nOgVsdGeeoZ6mDlqdvx69zrIgHUIPM70S+jD+by9/nU9A48+CTZ2\nBp4s8MSo2bHphYEoBO5wcM3mcF41F4P3C7dPUeJrELjFphcGohC4y755Xmht05T4FgRusemF\ngSgEfuVnvbjau9oek5X4DgRusemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBAC\nDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBB\nYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZ\nsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgE\nNltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBAC\nDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBB\nYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZ\nsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgE\nNltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBAC\nDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBBYiBw6qjZsemFgSgENltisBACDwwh8NBB\nYiBw6qjZsemFgSgENltisFDf0CeTo77v8Qt6Go3XOwIPHSRGhQJHu19qgSe2YNMLA1EIbLbE\nYCEETh9VWKNiIDACm05H4HEQGIFNpyPwOAiMwKbTEXgcBEZg0+kIPA4CI7DpdAQeB4ER2HQ6\nAo+DwAhsOh2Bx0FgBDadjsDjIDACm05H4HEQGIFNpyPwOAiMwKbTEXgcBEZg0+kIPA4CI7Dp\ndAQeB4ER2HQ6Ao+DwAhsOh2Bx0FgBDadjsDjIDACm05H4HEQGIFNpyPwOAiMwKbTEXgcBEZg\n0+kIPA4CI7DpdAQeB4ER2HQ6Ao+DwAhsOh2Bx0FgBDadjsDjIDACm05H4HEQGIFNpyPwOAiM\nwKbTEXgcBEZg0+kIPA4CI7DpdAQeB4ER2HQ6Ao+DwAhsOh2Bx0FgBDadjsDjIDACm05H4HEQ\nGIFNpyPwOAiMwKbTEXgcBEZg0+kIPA4CI7DpdAQeB4ER2HQ6Ao+DwAhsOh2Bx0FgBDadjsDj\nIDACm05H4HEQGIFNpyPwOOEzcP+LQOBplOWFgSgE7k9A4DSU5YWBKATu3u+VFCW+72niEAIb\nTkfgcabO4LdBYASeIR2Bx5k8g9PKLY9tQl+Et90xmbyKPUxN7zloMl4tTOx9ugRTG504ZEFg\nvwc5DwGN/Dj3c+Y58P+wuZk5Aw8d1MPsF19fENLIcelWJwT+DzY3MwIPHdRDqQKfz1vX7BF4\nHJubGYGHDuqhXIHPh8X/nw4gcKwhm1GFNdpDwQKfz2sEHsfmZkbgoYN6KFpgEyUGCyFw+qjC\nGu0BgefBwh6JGFWWFwaiENhsicFCCJw+qrBGe0DgebCwRyJGleWFgSgENltisBACp48qrNEe\nEHgeLOyRiFFleWEgCoHNlhgshMDpowprtAcEngcLeyRiVFleGIhCYLMlBgshcPqowhrtAYHn\nwcIeiRhVlhcGohDYbInBQgicPqqwRntA4HmwsEciRpXlhYEoBDZbYrAQAqePKqzRHhB4Hizs\nkYhRZXlhIAqBzZYYLITA6aMKa7QHBJ4HC3skYlRZXhiIQmCzJQYLIXD6qMIa7QGB58HCHokY\nVZYXBqIQ2GyJwUIInD6qsEZ7QOB5sLBHIkaV5YWBKAQ2W2KwEAKnjyqs0R4QeB4s7JGIUWV5\nYSAKgc2WGCyEwOmjCmu0BwSeBwt7JGJUWV4YiEJgsyUGCyFw+qjCGu0BgefBwh6JGFWWFwai\nENhsicFCCJw+qrBGe0DgebCwRyJGleWFgSgENltisBACp48qrNEeEHgeLOyRiFFleWEgCoHN\nlhgshMDpowprtAcEngcLeyRiVFleGIhCYLMlBgshcPqowhrtAYHnwcIeiRhVlhcGohDYbInB\nQgicPqqwRntA4HmwsEciRpXlhYEoBDZbYrAQAqePKqzRHhB4HizskYhRZXlhIAqBzZYYLITA\n6aMKa7QHBJ4HC3skYlRZXhiIQmCzJQYLIXD6qMIa7QGB58HCHokYVZYXBqIQ2GyJwUIInD6q\nsEZ7QODgCD+8asfcI9FaKN8LA1F96RGXMA8iAicdshlFo7GjZr/4mgMEthpFo7GjEDhbCZlV\npFHDUQicrYTMKtKo4SgEzlZCZhVp1HAUAmcrIbOKNGo4CoGzlZBZRRo1HIXA2UrIrCKNGo5C\n4GwlZFaRRg1HIXC2EjKrSKOGoxA4WwmZVaRRw1EInK2EzCrSqOEoBM5WQmYVadRwFAJnKyGz\nijRqOAqBs5WQWUUaNRyFwNlKyKwijRqOQuBsJWRWkUYNRyFwthIyq0ijhqMQOFsJmVWkUcNR\nCJythMwq0qjhKATOVkJmFWnUcBQCZyshs4o0ajgKgbOVkFlFGjUchcDZSsisIo0ajkLgbCVk\nVpFGDUchcLYSMqtIo4ajEDhbCZlVpFHDUQicrYTMKtKo4SgEzlZCZhVp1HAUAmcrIbOKNGo4\nCoGzlZBZRRo1HIXA2UrIrCKNGo5C4GwlZFaRRg1HIXC2EjKrSKOGoxA4WwmZVaRRw1EInK2E\nzCrSqOEoBM5WQmYVadRwFAJnKyGzijRqOAqBs5WQWUUaNRyFwNlKyKwijRqOQuBsJWRWkUYN\nRyFwthIyq0ijhqMQOFsJmVWkUcNRCJythMwq0qjhKATuclo7t9zfQ0ZTENhgOo1GT8/D1EZO\njbuyuoUgcPwoGo0dhcAdNm53sXjXLNsQBI4fRaOxoxC4Q3O747FZHBE4SRSNxo5C4O797nc8\nLZd9ArsuAe094pIO2Yyi0dhRnuk9+B3lc7/oTK2xcKfHrSVn4BRRNBo7ykKj0ZlaY+fW91tH\nt0TgBFE0GjvKQqPRmVxj82ft/j/XCghsMJ1G80RFZ3qNw+px67hG4PhRNBo7ykKj0ZmhBgIb\nTKfRPFHRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtR\nNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCr\nUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFg\nq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FB\nYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPR\nQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ygHR\nDZ8AAAlHSURBVEKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvK\nQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7\nykKj0UFgq1E0GjvKQqPRQWCrUTQaO8pCo9FBYKtRNBo7ykKj0UFgq1E0GjvKQqPRQWCrUTQa\nO8pCo9HJLrDzwitVZhUNpKd9kG1Gzd+o14McRn6BfYakV9FkOo2aiQoDga1G0WjsKKONhoHA\nVqNoNHaU0UbDQGCrUTQaO8poo2EgsNUoGo0dZbTRMBDYahSNxo4y2mgYCGw1ikZjRxltNAwE\nthpFo7GjjDYaBgJbjaLR2FFGGw0Dga1G0WjsKKONhoHAVqNoNHaU0UbDQGCrUTQaO8poo2Eg\nsNUoGo0dZbTRMBDYahSNxo4y2mgYCGw1ikZjRxltNAwEthpFo7GjjDYaBgJbjaLR2FFGGw0D\nga1G0WjsKKONhoHAVqNoNHaU0UbDQGCrUTQaO8poo2EgsNUoGo0dZbTRMBDYahSNxo4y2mgY\nCGw1ikZjRxltNAwEthpFo7GjjDYaBgJbjaLR2FFGGw0Dga1G0WjsKKONhoHAVqNoNHaU0UbD\nQGCrUTQaO8poo2EgsNUoGo0dZbTRMBDYahSNxo4y2mgYCGw1ikZjRxltNAwEthpFo7GjjDYa\nBgJbjaLR2FFGGw0Dga1G0WjsKKONhoHAVqNoNHaU0UbDQGCrUTQaO8poo2EgsNUoGo0dZbTR\nMBDYahSNxo4y2mgYCGw1ikZjRxltNAwEthpFo7GjjDYaBgJbjaLR2FFGGw0Dga1G0WjsKKON\nhoHAVqNoNHaU0UbDQGCrUTQaO8poo2FMD/zdrtyV1eY3pASrmCWdRs1EhTE18LRwT5YBJVjF\nLOk0aiYqjKmBG9f8HNpbx33jNtNLsIpZ0mnUTFQYUwMbd/i7fXDN9BKsYpZ0GjUTFcbUQOeG\nPrmPdPhPEEA9TPRt2J+J9/viDAwAqQh4Drw/trf++xwYAFIx+ZS+7FwWLE4xWwIAX6Zfk/9u\n2veBm9X2P+8DA0Aqoj+pBoD5QGAAYRAYQBgEBhAGgQGEQWAAYRAYQBgEBhAGgQGEQWAAYRAY\nQBgEBhAGgQGEQWAAYRAYQBgEBhAGgQGEQWAAYRAYQBgEBhAGgQGEQWAAYSwLnOmXX0D55N7a\n8bA8Fcu9fUUpEyllHuVMxPZULPf2FaVMpJR5lDMR21Ox3NtXlDKRUuZRzkRsT8Vyb19RykRK\nmUc5E7E9Fcu9fUUpEyllHuVMxPZULPf2FaVMpJR5lDMR21Ox3NtXlDKRUuZRzkRsT8Vyb19R\nykRKmUc5E7E9Fcu9fUUpEyllHuVMxPZULPf2FaVMpJR5lDMR21Ox3NtXlDKRUuZRzkRsT8Vy\nb19RykRKmUc5EylqKgD1gcAAwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AAwiAwgDAI\nDCAMAgMIg8AAwiAwgDAIDCCMOYF3C9dsTp2BTfM2IML7RER/rdZp7dz60B0RXZCPiYguyBvW\n+t+0D2rz3B/LdmCRsaVpvE/kILpfmrbrzsZXXZD3iaguyBvG+j+49WXL79z6MfDrmsP50Ljf\nnF1N4GMiB7fK2c9UNtcZbDq9qy7Ix0REF+QdYwKvbv08/1/cuP3l7x+3zdXRRD4mspObQkvj\nrtcQnfOU6oJ8TER0Qd4xJvCd5+O8csez8P+WXYF3ORsJwzV/N7UXpDMR6QV5YlLgk1s+brr3\nM5kUnYms3H7tmk3Obiaz6ex16QXpTkR5QTqYXIdde5nWIr1fuhNZ3V4yWY4dbpMf5zrbXHhB\nXieiuyAvWFyHY/O8PhPeL+8T+bmckTeC1227VdN5uii8IO8TUV2QFwyuw6np/K8ovF9eJ3If\nEnz/5cL6uc2VF+RlIjdEF+SJwXVYdh/SRni/LHv2huRELtv878Uf5QV5mcgd0Yn8Ya7942J5\n7Hx6e9HzKPii59tE7ojul/e3BRQXpOXj8RddkD+stb9/e1Vh274MtHdyrxa+T+T2PqTcxn+0\n/XcxobogHxMRXZB3jAl8fH9VUPULfz4msrlu+dPm+bK0Bu0XMJ1Wz6eOqgvyMRHRBXnHmMBr\n9/wK1dvFzULzxf6PiZxuX4urduK6fwlx+/hLL8jHRFQX5A1jArsPgU/tN79kbut7+ieyEHzP\n4tm29IL0T0RxQV4xJjAAfAMCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADC\nIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwC\nAwiDwADCIDCAMAgMIAwCAwiDwADCIDCAMAgMIAwCl0Wz2h3bG8fdqjnffhn9488LrqVZH8fS\nPu4F1mCFyuIi5bq9sXatff8R+KLwmMEIbB5WqCycWzTtjWbxZ9+AwNe/T0u3GU2L3yFEhRUq\nC+c27nD5eLh89BD4fHLNaFqCFiEmrFBZOLd3u8vHnfvpuYTeuO3zwOdH504Lt7rea+EWu9v4\nprmcmxHYPKxQWVxcbFVcueOnwBu37BzYfmjPwM6t3PVSetk+K26PaW+uENg8rFBZXJRbtOI2\n5w+Bu/7eBT62z4Ev0p4un/y45nA+NO7neZPtYR1WqCwuym3c7/nXrT8EfvH3+Sr06Xr79zq0\ncvvL3/vrYat2ZI/A5mGFyuKi3M/lie72chp9E3h51/TvwOf7wHdPOx9eR8AurFBZXJQ7Xk6h\nS3d8F9g1bvF64PttBBaEFSqLq3KNu780de4K/Htw12e33QPfbiOwIKxQWVyVW7vN9cuxPl7E\n2nbf8+0R+PEcePW4+YvA5mGFyuKq3I9rz7WfbyMtnm8D9wnceRV6z6vQIrBCZXFV7ngR+Ngn\n8OUi+vTQtUfg7vvAq+utNQKbhxUqi1a5xj2+EentK7G218vjYYHPu+bvK7G2fCWWBKwQgDAI\nDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AA\nwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAMAgMIg8AAwiAwgDAIDCAM\nAgMI8w8R80bLRZ/dfAAAAABJRU5ErkJggg==", "text/plain": "Plot with title \"Distribution of  Milk.Prod\""}, "output_type": "display_data", "metadata": {}}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAANlBMVEUAAAAzMzNNTU1oaGh8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\n4CAwIQUHgQkpOP8DXD0wid3k2/0AAAAASUVORK5CYII=", "text/plain": "plot without title"}, "output_type": "display_data", "metadata": {}}]}, {"source": "## Autoregressive Integrative Moving Average Model\n\nIt is clear from the exploration of the ARMA model, that the remainder of the decomposition of the dairy production time series is not stationary. You will now model the remainder series with an autoregressive integrative moving average (ARIMA) model.\n\nExecute the code in the cell below to compute an ARIMA(1,1,1) model.", "cell_type": "markdown", "metadata": {}}, {"source": "arima1 = model.dairy(dairyMult, order = c(1,1,1))", "execution_count": 45, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nCall:\narima(x = ts, order = order, include.mean = FALSE)\n\nCoefficients:\n         ar1      ma1\n      0.7015  -1.0000\ns.e.  0.0482   0.0114\n\nsigma^2 estimated as 0.0001908:  log likelihood = 648.11,  aic = -1290.22\n"}]}, {"source": "The standard error of the ar1 coeficient is only about half its value. This model seems to be a reasonable fit. \n\nNext, plot the ACF and PACF of the model by executing the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.acf(arima1$resid[-1], is.df = FALSE)", "execution_count": 46, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAM1BMVEUAAAAAAP9NTU1oaGh8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\ngg==", "text/plain": "Plot with title \"PACF of remainder\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "Note that only the 0 lag of the ACF is significant and that there are no significant lags for the PACF. These observations indicate that the ARIMA(1,1,1) model is a good fit. Compare these results to those of the MA(3) and AR(1) models, noting that they are nearly identical. The ARIMA(1,1,1) model is a good choice for these data as well. \n\n\n## Modeling and Forecasting\n\nNow that you have explored the properties of the decomposed time series, you will now compute forecasts of dairy product production. In this exercise you will compute a time series model using the R **forecast** package, and use this model to forecast the next 12 months of dairy product production. \n\nThe R **forecast** package contains the **auto.arima** function which automatically steps through the ARIMA model parameters to find the best fit to the data. The ARIMA model used in the **forecast** package also includes modeling of seasonal differences.  The **auto.arima** function has multiple arguments, specifying the range of parameter values to search. The first argument is a time series object of class **ts**. \n\nThe code in the cell below does the following:\n\n- Creates a time series of class **ts**.\n- Automatically finds and computes an ARIMA model.\n- Prints a summary of the ARIMA model.\n\nExecute the code in the cell below to compute and print the summary of the ARIMA model. ", "cell_type": "markdown", "metadata": {}}, {"source": "temp <- ts(log(dairy[, 'Milk.Prod']), frequency=12, start=1995)\n#install.packages(\"forecast\")\nlibrary(forecast)\nfit.dairy = auto.arima(temp, max.p=3, max.q=3,\n      max.P=2, max.Q=2, max.order=5, max.d=2, max.D=1,\n      start.p=0, start.q=0, start.P=0, start.Q=0)\nsummary(fit.dairy)", "execution_count": 47, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stderr", "output_type": "stream", "text": "Warning message:\n\"package 'forecast' was built under R version 3.4.3\""}, {"name": "stdout", "output_type": "stream", "text": "Series: temp \nARIMA(0,1,1)(0,1,2)[12] \n\nCoefficients:\n          ma1     sma1    sma2\n      -0.1506  -0.9076  0.1129\ns.e.   0.0743   0.0794  0.0838\n\nsigma^2 estimated as 0.0002584:  log likelihood=577.8\nAIC=-1147.6   AICc=-1147.41   BIC=-1134.12\n\nTraining set error measures:\n                        ME       RMSE        MAE         MPE    MAPE      MASE\nTraining set -0.0003536657 0.01549906 0.01109068 -0.01955938 1.05342 0.2902694\n                    ACF1\nTraining set 0.005145456\n"}]}, {"source": "Examine the summary of the model, noticing the following points.\n\n- The model uses an MA(2) model for the seasonal difference. The coefficients of this model, sma1 and sma2, along with their standard errors can be seen in the summary.\n- The model of the remainder is and MA(1) model. The coeficient and its standard error can be seen in the summary above. \n- Error metrics, including RMSE, are provided in the summary. Notice that the RMSE is much smaller than the values of the milk production time series indicating good model performance.\n\nThe **forecast** function is used to compute the forecast of the next 12 months using the model created using **auto.arima**. Execute the code in the cell below to compute a forecast and print its summary. ", "cell_type": "markdown", "metadata": {}}, {"source": "dairy.fit = forecast(fit.dairy, h=12)\nsummary(dairy.fit)", "execution_count": 48, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "\nForecast method: ARIMA(0,1,1)(0,1,2)[12]\n\nModel Information:\nSeries: temp \nARIMA(0,1,1)(0,1,2)[12] \n\nCoefficients:\n          ma1     sma1    sma2\n      -0.1506  -0.9076  0.1129\ns.e.   0.0743   0.0794  0.0838\n\nsigma^2 estimated as 0.0002584:  log likelihood=577.8\nAIC=-1147.6   AICc=-1147.41   BIC=-1134.12\n\nError measures:\n                        ME       RMSE        MAE         MPE    MAPE      MASE\nTraining set -0.0003536657 0.01549906 0.01109068 -0.01955938 1.05342 0.2902694\n                    ACF1\nTraining set 0.005145456\n\nForecasts:\n         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95\nJan 2014       1.259101 1.238502 1.279700 1.227598 1.290605\nFeb 2014       1.193990 1.166963 1.221016 1.152656 1.235324\nMar 2014       1.303803 1.271607 1.335999 1.254564 1.353043\nApr 2014       1.278470 1.241827 1.315113 1.222429 1.334511\nMay 2014       1.307799 1.267193 1.348405 1.245697 1.369900\nJun 2014       1.256228 1.212012 1.300443 1.188606 1.323849\nJul 2014       1.253456 1.205904 1.301007 1.180732 1.326179\nAug 2014       1.243199 1.192531 1.293867 1.165709 1.320689\nSep 2014       1.198112 1.144508 1.251716 1.116131 1.280092\nOct 2014       1.232666 1.176279 1.289053 1.146429 1.318903\nNov 2014       1.209167 1.150127 1.268206 1.118874 1.299460\nDec 2014       1.252931 1.191354 1.314509 1.158757 1.347106\n"}]}, {"source": "Much of the summary is the same as before. A 12 month forecast is printed below the model summary. There is a point forecast (the expected value) along with 80 and 95 percent confidence intervals. Notice, that the confidence intervals generally get wider for forecasts further out in time. It is hardly suprising that the forecast has more uncertaintly as time increases from the present. \n\nFinally, you can plot the forecast by executing the code in the cell below. ", "cell_type": "markdown", "metadata": {}}, {"source": "plot(dairy.fit)", "execution_count": 49, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAOVBMVEUAAAAAAP9NTU1oaGh8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\nMAIGhBEwIIyAAWEEDAgjYEDY/9DCKB/kCNxKAAAAAElFTkSuQmCC", "text/plain": "Plot with title \"Forecasts from ARIMA(0,1,1)(0,1,2)[12]\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "The original time series of milk production is show in black in the plot above. The forecast is show in Blue. The 80 and 95 percent confidence intervals are shown in lighter shades of blue-gray.  \n\n****\n\n### Exercise: Forecast Ice Cream Production\n\nIn this exercise you will forecast the production of icecream for a 12 month period following these steps. \n\n- Create a time series object with **frequency = 12** and **start = 1995** from the **Icecream.Prod** column of the **dairy** data frame.\n- Fit a model with the **auto.arima** function, following the hint given below.\n- Print a summary of the model. What is the order of the MA and AR components of the seasonal and remainder models? Note there will be a drift term, which accounts for linear trend in the time series.\n- Compute the forecast of icecream production for the next 12 months. \n- Plot the forecast and note the behavior. \n\nIn the code cell below, use the **ts**, **auto.arima**, **summary**, **forecast**, and **plot** functions to create the new model, print the summaries and make the plots. **Hint** use the time series of icecream production as the first argument to the **auto.arima** function. You can copy and paste the other arguments from the milk production model, but set **max.p = 1** to prevent having an over-parameterized model. \n\n****\n", "cell_type": "markdown", "metadata": {"collapsed": true}}, {"source": "temp2 <- ts(log(dairy[, 'Icecream.Prod']), frequency=12, start=1995)\n#install.packages(\"forecast\")\nlibrary(forecast)\nfit.dairy = auto.arima(temp2, max.p=3, max.q=3,\n      max.P=1, max.Q=2, max.order=5, max.d=2, max.D=1,\n      start.p=0, start.q=0, start.P=0, start.Q=0)\nsummary(fit.dairy)\ndairy.fit = forecast(fit.dairy, h=12)\nsummary(dairy.fit)\nplot(dairy.fit)", "execution_count": 50, "cell_type": "code", "metadata": {"collapsed": false}, "outputs": [{"name": "stdout", "output_type": "stream", "text": "Series: temp2 \nARIMA(3,0,1)(0,1,2)[12] with drift \n\nCoefficients:\n          ar1     ar2     ar3     ma1     sma1     sma2  drift\n      -0.1996  0.1658  0.3746  0.4086  -0.5043  -0.2039  6e-04\ns.e.   0.1767  0.0755  0.0636  0.1925   0.0699   0.0672  2e-04\n\nsigma^2 estimated as 0.001583:  log likelihood=389.7\nAIC=-763.4   AICc=-762.7   BIC=-736.4\n\nTraining set error measures:\n                      ME       RMSE        MAE        MPE      MAPE      MASE\nTraining set 0.001360524 0.03809705 0.02972694 0.02906281 0.7001261 0.7583233\n                     ACF1\nTraining set -0.004410837\n\nForecast method: ARIMA(3,0,1)(0,1,2)[12] with drift\n\nModel Information:\nSeries: temp2 \nARIMA(3,0,1)(0,1,2)[12] with drift \n\nCoefficients:\n          ar1     ar2     ar3     ma1     sma1     sma2  drift\n      -0.1996  0.1658  0.3746  0.4086  -0.5043  -0.2039  6e-04\ns.e.   0.1767  0.0755  0.0636  0.1925   0.0699   0.0672  2e-04\n\nsigma^2 estimated as 0.001583:  log likelihood=389.7\nAIC=-763.4   AICc=-762.7   BIC=-736.4\n\nError measures:\n                      ME       RMSE        MAE        MPE      MAPE      MASE\nTraining set 0.001360524 0.03809705 0.02972694 0.02906281 0.7001261 0.7583233\n                     ACF1\nTraining set -0.004410837\n\nForecasts:\n         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95\nJan 2014       4.159970 4.108976 4.210965 4.081981 4.237960\nFeb 2014       4.233898 4.181801 4.285995 4.154223 4.313574\nMar 2014       4.354554 4.302074 4.407033 4.274293 4.434814\nApr 2014       4.378331 4.322309 4.434353 4.292653 4.464010\nMay 2014       4.417831 4.361797 4.473864 4.332135 4.503527\nJun 2014       4.517751 4.461459 4.574044 4.431659 4.603843\nJul 2014       4.462807 4.406146 4.519469 4.376151 4.549463\nAug 2014       4.409070 4.352409 4.465731 4.322414 4.495726\nSep 2014       4.319325 4.262580 4.376070 4.232540 4.406109\nOct 2014       4.259274 4.202501 4.316048 4.172446 4.346103\nNov 2014       4.116758 4.059984 4.173532 4.029930 4.203587\nDec 2014       4.010205 3.953413 4.066997 3.923350 4.097061\n"}, {"data": {"image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAPACAMAAADNCOCpAAAAOVBMVEUAAAAAAP9NTU1oaGh8\nfHyMjIyampqnp6extc6ysrK9vb3Hx8fQ0NDZ2dnb29/h4eHp6enw8PD////LQifVAAAACXBI\nWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO2diZajOAwAvTm6p++E///YDfeNZRBgQdV7u50Y\nWTLgCoSQjEsAwCxu7wEAwHwQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgM\nYBgEBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaBAQyDwACGQWAAwyAw\ngGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgMYBgEBjAMAgMYBoEBDIPA\nAIZBYADDIDCAYc4isGugnvxtfNHHxbmJxT7eX8N9L59UK3D/rBqq9kfW8mitYKt38vfqmP79\nvjl3/WzXeb5f3OX92S1/L3K9/v61k3g6VDxece7+3UrS3At1hzpSspeqgLf20+ngzvNq5yzY\nQ3uDwIv5uYxn/EjrLZgerfE2VuFWNlTtX1nLV79DlasQ6L2ZoeBxydouj3b177J7qW2VxNeh\n2eCKl5EqSWMv1B0akQECl9t+lsDlzpnagdFjeOhBrCjwVMZrdeiaxVfDzfY6fDYqN4S8NVew\n3fvlzzWpRWkcmrNhZlxb1b/rXOV6FEn8HXKerfGWSeq9UHdoRgYIXMbNErgxnuliMWN46EGs\nuJOmUi8s+/LxvT5YVpP9vTCnKXA1keuS7d7vuctvr+PgM3X7Upf5eT37S/5eR9WfuvFxb+T6\nKoQvkvg75LyOcbe/5PmWj7dMUgY1O7QjxdttnsBBnSPH8NCD6O2k77f0/Om7Wvq4ZrMrf29X\nnBk+318v0rci5iudbtd80fMjPdTdv5LqsNhu7JWtC/QKJ59Xd3158Hlxt5+kxSPV7Fq+v22s\nQ/v4k1Z1Ls34nT1yg70vefv7/fLsbo9Cy6/WYTk9qjcrXppJ/B0yboXh1UAvnY1SdehF1nmu\n+aL0GP3MV+taBNTbPv3/zyvHW/uc/vF2Sd/u10nzndAqUicxidmBB9LdRbdiv1Xvyq7Zsap4\nb5dPpvLJe7NDuqhckPao9n+zsS5aT7C8QL9w3vB4r+tWvNo+0mPTe3cdegJ/5u+037JHbqj3\nT/U2tljWeGdevrFthaRP6or3bGxlEkGHvNe9dYzLkzQErjt0Ipt5ilVIT7eLV42PIYHzDdh6\nV/5T7JA66bXcZ3VnBDZBd2aVOuYzMH/4lR1h8nmQtpZP0oPby4vbM5v498yTV+zzVr9hc+3G\numg9wfICg4XTgk2tSy7pMedZne2W6/B4q3sXfz7vWdDF3WuB270/G+NKB3FpXEGujWpspPTM\no27Iu3+233xPdWhSel90L4MGOvy01yxf3fy0OjtxSbJXwMeQwAXNK4aXujlJGjsBge3hWvsy\nfTX/fM3uj9zO7ECYTuhc02fu4mf2Ri818ppUp6Llvk+fPPOZVU+PRmNdtvybFRgunEp3/Us+\nO/PoOz9mF6fH7YtYnfPNv8+06TX9P//KJJ3e98bltLsrU/ZG2dtqxaP8EvK9c9lnokOTa1Gu\nuA7dDOp0KCNbzdfs3Ll2tb3RyzSXn+z1tfHWPn2j/8r2famDs50QdgUscgwPPYi2wG/l4ag4\nlXT1LC/28L2a+s/rx6OVJ39lf/tuNXUb28uqAgOFf1p/mp0bb2y76/DdzJ4K/CjOlx+VwJ3e\n9ZvhIlHr5Nfr46P/MjbdocGtfFvxaMk30OHW+YAs5yN9Pf0pXre+szPoAQezfdXqV752fdfB\n3e02PmgrGB56EG2BXSFqduND43kddOnv18fX+y3v/5HHvLWmQ7uxLlv+fTb/NgonvT8F1dnv\npTu6j2creyrwK+j68uuSlAJ3ezdzP9tn+iIfXXHqIe5QcavP11sr3e9QR7aaH+mLXXrdLH0z\n/J6/how42OpXPamDn53no4M2g+GhB9HeSfWz9pRqad7u8nWtl5Q3Q+SXTMq4VmOnUH+u+AX+\nbIymfuf5uNUVmgK/ju3f6UQvBe727szS1pn+mgKn470+WotHBG5GtvNcs8vpl+xF6tK6kh0q\n8OBzBDZAT+DqQHhpLL0M7v+U9KaI61v1DvP5lV88vjXjmo2dHI2/Q4UHBa5eMVz7w9HqPLMl\n8Fd2ifWrErjbu3qZuV96a3fPj2p/3YtoowJLOhTb5NK5LN8Jqh+3Itt53rMXp/fqb3+LIfDR\nae+ke/+taNlenwHfmu+BB66uZB/odlOXjZ2yjQJDhYcE/nFNmm+RL+XtVU2B87ugH6XAvd5l\n52KtHs3LPYMf63YG1BJY0qHaiO/dxcMCtyLbefKV+a7eB/e32KCL5d78QmD7tHfSwMXgrP0r\nv5j5lR0LWlehi4hcj2v1prQ8ij67jZ2y5d+RwkMCv9d3QX7mc7tc/FOWqLvlLzHpQIs3173e\nt+L600e2Vo+WLt9DN1a1B5R/5FsmEXTIeWudjzwmrkK/DZ65FGSfB+XNvVVPmu/wW/0+86vQ\nX5fu5h0QuPe1DCucU+D6toz8c8NqafXJ4U/zyWd5fCg+kUg/oXlUdxikbe/dxk7ZqsBw4SGB\nXXm2XV1crRbfe/dCJ/VXj6rYdu+3UrZqrZ51xuatzcPHx59swFUSX4fG611BnWSwQyeys7ve\nXXWjSrF1i4CLa7+2tfv1PwduFS2fX1zvTMIOJxW4EqnzbbTmt2fSb6lUT8pT0vygU16vyo4Z\nb8WDVmOnbF1+sPDAtP1q3pNwr+8/SHm41pXl/E869Oqg3u9d3chR3jHWPPNofrloWOD2jRze\nDsXft7ZBn/3raeXjTmRnd6Vb/6tYx59ugeZ1iHa/Yqfdu0k7z8skJjmrwK83q5f2Lck52e3P\n9+/ySfVl1uTvtZsvb3/FWWD2VvdWfBBzL2xpNbYTN8oPFR6Ytrfm2/Hv+g7AjPfWuWj+p7xX\nOHvW711fcGp8lbfKONTWepzfwjGdpL++nUNgcR/IUIexg2VB45O0dr97+6De6Zfes3b77G3e\n7vP7oq987stZBIZL9yUsRdpWvrNXSdJ7MR2KZGLKYDudhff27ZMZz+7HQCNtyXf9dcLlSRBY\nEbbTWXgMvNH77F5FHmkrP/jVSVKfKQ/jWw4N2E6n4d7/dZD7kGYDbb2f1FmUBIEVYTudhv59\nU2L6P2q3JAkCK8J2AjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaBAQyD\nwACGQWAAwyAwgGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgMYBgEBjAM\nAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGGYDgR0AiJhhl76wO5QAOAIIDGAY\nBAYwDAIDGAaBAQyDwACGQWAAwyAwgGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBh\nEBjAMFsK/Hy/vP7/cXXu9rVSCYBzsaHAj4tzyfOS/xDIbZUSACdjQ4Hf3P35+t/b4+Xym3tf\nowTAydhQYOeexf9eZ9PuskYJgJOxqcCv/11c44l6CYCTsekp9F+SfKT/S4/Ak2+CERhAxIYC\n/7nL+19yv7wM/r667zVKAJyMLT9G+r7UP0f9sU4JgHOx7Y0cX2/X1N77x2O1EgBngjuxAAyD\nwADx8BvaAYEB4sGMwHwODNDHsMAL/81EgANgRuDdSwBECAIDGAaBAQxjQ2Dve1wEhnOCwACG\niVlg58QXmhEYzknMAv9cEBhgkpgFTp53d8u+xcApNMAgUQucJF/Opb9HicAAg0QucPK4pb9s\nh8AAg8QucPqbOpdvBAYYJH6Bk7+r/15nBIZzYkDg9NftEBhgiN9Qg7mVEiAeEBjAMAgMYBgE\nBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGCYfwgMYBcEBjAMAgPY5ReBAeyCwACGQWAA\nw7wEDjQYgQGiAYEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaBAQzz+y/0XkoEBogG\nBAYwDAIDGAaBAQyDwACGQWAAwyAwgGFSgcMMRmCAaEBgAMMgMIBhEBjAMAgMYBgEBjAMAgMY\n5h8CA9gFgQEMg8AAhvn3L/ReSgQGiIVfBAawCwIDGAaBATTZeCIiMIAmCDwPBIYo2EXgIIMR\nGGAUBJ4HAkMUIPA8EBiiAIHngcAQBQg8DwSGlZFNMbftTERgABkIvCYIDCuzucCSTAgMIAOB\n1wSBYWUQeE0QGFYGgdcEgWFlRFPMKc5EscBhN0MjMJySOAX+7z8EBhAgOjneQeD/EBjADwKv\nCQLDyiDwmiAwrEzMAocYjMBwSoQC601FBAbQY3uBBZkQGEAGAq8JAsPKIPCaIDCsDAKvCQLD\nykQp8D8EBhWOvwMQeE2OP38i5/g7AIHX5PjzJ3KOvwMKn6ZXdGOBfxEYdDj+DkDgNTn+/Imc\n4++A4i7JzQSW3JVZCBx0MzQCwwDH3wG5UJ7DIgLP5PjzJ3I2/jnV7SnU9AusJbFY4MCvIyEw\nDIDAZVRqHgJHWAKmQOAyCoHncPTpEz0IXEalIQgcYQmYAoHLqF0EDjAYgWGAkwjss2qvi1gI\nDMtA4DIKgedw9OkTPQhcRjX+LCyIwLAZCFwEtf4uK+jN8ovA4EW2aRG4CGr9XVYQgUEBBM7Y\nQWBvGgQGPwicUdqLwKtw9OmzIzI1NX/RPErKD4EReBUOPnv2BIEzEHhVDj579gSBM+IU+GVv\n6PcJEfhkIHAGAq/KwWfPniBwBgKvysFnz54gcIZr/DcZlPiC5AVFAv8L/DoSAp8MkZqC2VaE\nWQWBV8XwzIgdBM5QFVi4rRAYloPAGSI3txX4F4HBDwJnaAqs9I88IDAIQOAMBF4VwzMjdqQC\nS8OMEqXA/xAYPMjURGB5kPB0JUxgucEIfC4QOAeBV8XwzIgcTYEt3+0RJLA3CoG3L3FSEDgH\ngVfF7sSIHQTOEbkpDkLg7UucFATOQeBVsTsxYsdV//NFITACz8buxFgNpU2CwDl7COwJawgc\n8EHwaQS2O9dyEFiV+AT+ReCtU24KAquCwKuCwF2Ev/MqUhOBZW66gUcjUQrXBUuBA++lRGAb\nCH9IA4GFxChw6u4vAm+XckuEN8wjsBA1gZ0voBGHwHGl3JLtBZZE2d2oWwvs36II7Elpd7Il\nQlec6ntgBEbg2SBwBwRWBoFXJXKBla4IB1WMT2BJuWhB4FVB4F4uBFYlOoF/EdiTUlNgUa4T\nCGzXYAReFQTupUJgVZQFFm0sBF6UUtUnSTIEjpgoBX6p+xv6dSQEnpMLgRMEbi1C4LVLKF/E\nkvikVxGBtUHgVUHgGQVFQp1BYNlrnT94Y4H/IfB0ys0PiAi8Dwis3iWCEtYFllmHwMm2Ajtv\nRGM5Ai/KqHfhSVFgcUEEFmNR4N9a4OwPAvcznkFg2URafrwQD2oPTAsc+kEwAs8oLHxLisD7\nEK3AE1EI7M+IwMkeAm/vOAKrd9m/hFRgUWW7AjtZVXEqBBbWRODlGRE4TGBP1OEFdoMPR4IQ\neOUS0QosthyBQ17uxCEIvAbxCyzxCYGzEMWdGa/Asg2PwIsyqs026RmtVsF4BZaciWgKLN49\n4pDB4O6mXF3gXwQWZERgBO6FRCPwPwT2ZURgBO6FIPAa7Cew7I2rJBkCFwHbCyx4VRl41F2M\nwPNB4F49BBYn21BgT55uoF/gBIHHM2oJLPYJgfcQWBKEwOuCwPMKRimw3t4UblIFgTvTZQeB\npQYjcCfMrMAioRC4ytR71Fy8l8C/CDyRMUKBA+633FBgUZS6wDLtdLZp1AIHfSEYgTthWwus\nVnBjgYXHcgRuLkbgZRmVhEJgcSYEbi2eEPhfKfAvAo9mlMw2TYG1pjcC1xEIPDYCMQislwuB\nexk9EZsJ3FyAwLuXQODm4kVRThDTipbtTeHtFwg8NgIxCKyXy7zAomGJdicCNwUW38mBwN0o\nBPbIicDiPL3AsSgEFmVEYASuM3UfdcayvcDpmTMCT2XcXGDvrETgOtCgwM4f0l6MwIsyagq8\nTIJGFAKXgWq7Z7nAnSQCgf07eiqoOIO2IrD3xfZ0Ak9GieptKLDzx7RTmRd4LKNYYN/WQmBv\nSVHaPQTOJDYnsOvGTqVC4EMI7NqsUcKTEYH3EViyP53i7rEscOgXgjcU+OeCwMMFPVMOgRu5\nEHh8COt1yXne3e2RZdjpFFo0RbYX2Dd3ETgoFwLrdyn5cu4rQeBOQQROENiGwMnj5u5PBO4V\nXC5wkJoIPPCoM5YdBS4eidhY4CT5cJdvBA6KElkXkgmBYxP4nx2Bk7+r5wrW8hKjCRFYkipI\nYNGwENgT1BQ47OtI2wucJG8IHBSFwEG5dAR23ZbpNAoCF+98DQi8Q4kAgSUzRBAWtcCLcs0Q\nWLZNERiBPQkRWGFU8Qss3YVj6fqDGdkS/pDOwuMIvPGNHAjcXrhI4PYxDoGnQjoLjyyw+Dat\nOWNC4PbERuChh+ODQeCVSyAwAjfCEFi5y+olEFggcMM7BB56OD6YrQROktCvIyFwLwyB9QSW\nbYUEgW0JrP858A4Ca6iJwM1AHYHlmfqPR5sEAk8W9W14BBYulxw2DytwY7tvLfBi7erlRxS4\ncSt0xAKv+YV+BPZmckmwwINhLtEVuKHlRCon3Az2BQ78OtKGAq/4hX7xIT0ygWVCxS3wolPH\npLXNpwR2ss2AwKt0yVnvC/2HFlgpkxNF+ZMh8EjrQoEraeMVeL0v9CMwAjfzIbByl4qVvtAf\nn8AyVbYWePhJWLKeINsIXO3jeAR2gpjuMusCr/SFfgRG4NHxTQ1rOHZngX+jFniVL/QjsGGB\n64QInD2JXOA1vtDv/QooAu8s8MS4hAKLNvvQ+CaHFafAATdD7yGwfgkEjlNgJ4gSCdwoisDi\nqnpd1i6hJLD3ONBKgsDeXKoC+8tVy2MT2HcigsAI7M2kKfB0w+CisSjXMA6BsycIPJ5QQ2Al\nocRRCOw1rhuKwMpd1i6BwN5MbuJZUDIEHmlE4PklxAJLLLAosG+GRC6w82VCYH9qMfEJ7ER7\n1Z95DYFl3iHwdKbjC5z6i8D+hAjszYXACLwUBA6sF6fAEu1c4fDyTI3FvkQqAnfbEHh2CQRG\n4NZi0wKHfZsBgXtRewgs2fubCTydzLjATpAOgZeCwIH1jiHweKpAgScS7SzwcBQCI7AvEQLn\nSxH48AJLc8Up8FgYAudLIxU487cUOOT7hAjcj4pU4CUzBIGrpd3JgsArgMBDQYtMQeBiKQIb\nFFimU5wCh8WMRbnJpyEV5QL7PCnbtxbY+1qGwEtB4LkxJgX2n2McXOB/gwKLDEbgfphQ4MVq\nInDR7t2iokzNxVNj8m+KeQIvePkpBc6fIfBEPgReOqpYBW6dGCGwbpd1S7TmgCffRgL7zpkC\nxrWnwKLZbU1gb8sOAuf+1gLLb4ZG4H4YAk+F6Qrc1u3kAhfGIvBEPgQOGdUigZ0kSl1gN5kI\nged1WbcEAu8qsO+QGDCuRQI31dUWWO9UBIFHoiVmCsM2E1gUhcAIPAEC98MQeCoMgceatARO\nEHg83yEFFsxvBB7rjMArgMBDSzYR2GkJLKuIwCnFp0htgWX3UiJwPwyBp8KOL/BQ51UF/kVg\nBPZESQXu3Csco8CjmRrzIF6Bh6IQ2NcFgRF4rG+MAgd8HQmB+2HnFrj1r6Uj8HgbAmuVCBF4\nMg6B02YEFvVDYLUSCDz6ZLR1QmDPsIQCC6e3kwSFCyx8KZC2bCPwLwIL8iHwVC5BGAKPNSHw\nvBKek6bOwk0EdiOP5wxrS4ElczJegbMFCLxGl1VLIPDRBZYG+QWevT5LBPa+/IwJLDEYgfth\nCDwVhsBjTQg8r4SawM4f0lqMwBO5EHikHYGHg48qsCDGO0EGWhF4vEkmsHA79NoReDgYgSej\n1AQWKSBLNXdYZxBY/HUkBO4vQuCJMAQO6tdvFwgc8n1CBO4vWiSw6y5A4IAoBM4bEHg0n8Sn\n6fIILMm1h8ClxKMxMQg8EIbAvi5bCuw6CxA4IAqB8wYEHs13ToGFsw2Bx/puIPBvV2DRrVgI\nPLAIgYP6IXBQTQQeDN5MYDfwqLkYgaWpBhoROG9A4NF8qwucdP79yvFkThIVLPDs+TfUeAKB\nZSOdL7AgfSlw3XBCgYVHui0EFhwR5cPaV2DR7EZg37g8YQjs6YPAhxJ4fA1rgaU2DbVFILD8\n+4QIPLBomcCddgQOiDqewJKwcws8vcd6iwwLLDwvRGB5psE2BF6MbYE9DWHD8geJp7d/WNYF\nbrx9QWDNLmuWQGBBQdMCBxhmU+B/CDzdB4E3F3hmQQTOQODxdIoCz58OAcNCYDMCz+6IwJ4+\nMoE9h9aBhQisXnChYRYE7jcVv7+BwJJ0CDyRC4HFQasKnCDwaDqJKQg83oLA41EIPKcEAgsK\nIrBKek/UQoEbLQg8mm4sTHaa3V6IwOoFETij+Eb/QD5JTf0ua5Y4tsBu9Mlo69xpNNiGwGNt\nCKxUAoEFBWWzTdKkOG+lmocYtpbAq26I/PdzEFiUDoGXNSHweNTcDdG7hlV+n3BoIIKa+l3W\nLGFWYIGbCCwdg2WBfxHY00fpUNdbhsDqBWW5xlMh8Cpd1iyhI7CbeDYaGYXAIccnhSYrAgs3\n1lAbAi8GgeVBCNxsQuBVuqxYwnPO1FuEwMuaIhd4OlO8Av8iMAKHjEpTYMXsCFw0IfBYOgRe\n1oTAAWOQhQ0J/IvAI+k2F3g0CoEROOO3dx8HAk+kG45DYGHT9gIrDnR7gSUFEdjXR1Ngz9E8\nYB8i8EkF7jYisK9PsAUIvFP2swr8i8DGBHYIPNiEwHkTAo+mQ+CQpl7b8QUe3hUIvFIJBBbV\nm9uEwAH59QROEHg0HQKPtiHwaMftBRZ+IRiBhxoReLQNgZcNa6ARgT193MSz4UYEHm0zI/Ds\n7YDAy9lb4PFkPqGkAkv/FeGzCTxbRAQWc1aBXW+BosBjw0fgwwv8i8CePn6B5RIgsCw7Ak8k\nGxS4HYLAo9nmC+y6CxB4tA2BJ5Ih8FDoIQX2D102cxF4vK3biMDLQeDBVgQOiUJgvS4rlthQ\n4LRVTeA50waBQ6LWFXj+dkDg4VAEDh9DeJRwCOuqicCeAupdViyxpcCCD28ROKAJgVPS2567\n/p5HYDfwaDpbLAILotQEnm8+AgdEaQr8ezqBxzsdRmDVuXxGgWdvZFkUAoeX2FZgfyoEDmha\nV2DNjSyMmrXlEdjXaTWB57/sI7Cw3pKxRytwuxWBfZ0UBfY2bS7w/Im7psCKx1YEngSBB9sQ\nWD4CBF5WMRO4G4HAo9kQOCgsToFFYcYFHmqWlFyjy3olVhJYUxUEXhS1vsCCCdJvRmCdEgg8\nOzkCDzdHIXCCwGMLEDgoDIGHm9UE/kVgXycERuCpXHsL/N9/A78fi8BjC2IQWKj5sQSWuYnA\nRTMCjyxA4KAwBB5uRmCdEgg8c1QIPNaMwMtB4OFWVYFnCWVJYGkuBFYHgYdbTyBwrxGBJ0Hg\n4TYEFo8AgScaBQL/GxdY8K+bIfBwGwKLR4DAE40ILI9E4JBRDbXGIrDzBiHwdAHtLuuV2E7g\ndcWffTRC4KUFu+0IvBwEHm48h8DtHy5C4EkQeLgNgYfbYhF43rjWFrj3c/1CgQeuNv+OiO0Z\nlgRrAgu2PAKPhiFwQMFeuyAXAvs6KVmAwKOZdAV2653RxiJwsx2BfZ0QWCiwJEpT4NGzUOcN\nOoXArwUj3QUVdLusVwKBZ45Klr3XOjrMGZ4jcMq5BZ6xqxE4IHuvdTRGT+BZe3XJGu4q8Mj3\n+RF4vB2B5dl7rQgcNC4EDghE4JBRybL3WtcXOJm1V9cXOPzkWBQ1JnCCwGPtCCzP3msdi/H/\nq1EIPNiOwN5O/r0ochOBp2IQeGYUAns7IXCEArvRXAOB/mEdVWD/F4IReKQnAg+2qgnsEDgD\ngb2dTiewbOwIPNK+scBjniLwWDsCy7P3WvVOod34XkbgqQVT9UQgcFgqBB5odEn/mztjgf4g\nTYEXFUTgwBIIbEjgZqtU4PGZgMCTFXS7rFYCgeMQuHs+LBFYpAoCe0DgkZ4IPNiqKfAoagJ3\nmxF4ZpfVSgi2vGA2I7A4CoEDUi0TeOzzpal6IhA4LBUCD7QKBZ4I21FgJ0yFwEGBJxBYc+wI\nPNyOwAooCiyZ8ggsjkLgBIEVSyAwAk8FRi/wLwJ7OlkWeNWxrymwXyeZwFNRCDxZQbfLaiVO\nL/DcA/dQqyBq3BPTAotGhsArlPAKLFIFgaVRCJw9Et7HLRP4v//+IfBop3UFljkwV3M1gWWz\nG4GlMeoCD4Ug8FgjAgeFKQrcOQsdBYETBB5vROCgMATuLdhE4LEfjJ6sJwKBxxtNCSyb3iIz\ndQWuli4WWBi1o8Dj/wghAo80ygSe5yYCCwsicM7JBfbPGgQeC+q3I7AwBoG1SiAwAksrTuZD\nYF0kJVw3TiqwpgVxCiwzE4EHF2wicLUAgT2dEHg0CIEHFyCwAggs7YjA0oqT+SQC10t6PwE2\nvyACezoh8GjQ+QQWjX6hwMKKEoF/ERiBJ4J0BW4tQmBfspbAw5oi8Fjj8QWedX65gcBNB6ZA\n4CQXePjYLKqg2mWNEgg8WhCBh9sReG6XNUr0/3UdmQMIPNaOwMIgBNYogcCjBU8hsGxgwQJL\n1hCBNUog8GhBBA4LWk1gf9To9/ljFPj55tztu0gi3zdjMccSWCa1VOAZsxuBfSXPLvDz4lLu\neRIE9rcZFVgyuxE4x5LA7+7zZfHn5ZYlQWB/m02Bp3beUQQWpTqawJe84+NyfSDwzCgEHhmL\nlsDSwWsJ/G9c4EzuieH4Smh2yfsVHZ+3GwLPjELgkbEgsJy5Al/ds3x0Q+B5UQg8MhYEljNX\n4E/3Vjx6uBsC60StL7BwRoY54NnBCJwSm8DJe2Xttzu1wIqaI/B05FoCy4Z1MIGTv3v56PGG\nwN5GBN5cYFnB0wqsWsIlkn8ST03g4SEhcH8RAgcURGBPLwSWBiGwuCACa5QQCawnFAJPZUqE\n0xuBO0t8Ahf4naAAABQySURBVHu/0b+XwAoXsWYLPEs7BJ7KlAinNwJ3lkwKLPlJjngEdk1E\nw0BgVYElUeYEDvQJgXUQCux3DIHFQQgsLojAGiUQeHxYpxPYb4osCoF1QOCxMAQOHFfsAr/8\ntSew9z0uAo+FIXDguBBYo0s3AwILohA4UoGnB39cgZ0TX2hG4LGwUwmsaYosah+BR2JiE/jn\ngsAhUQiMwFEJnDzv7vbIMiicQrt+GAKPtI9uzmDNlwosU3N7gUUVtxY4iU3gJPly7itBYD2B\nRWrKZjcCSyueWODkcXP3JwKLohAYgaMTOEk+3OUbgbWiENgXicAaXZr8Xf33OiPwolElc2a3\nROCp/YLAc4ZlUOAkeUPg2VGdVgT2RSKwRpcVSiDweEwyZ3YjsLQiAmuUkNm6QDuRKgjcX4bA\n8noIHN400IrAU2EIPHdYCBwWMlfgkWoI3Gu3LbBg9JsJXC6b+DYhAo8mQuChJQiMwFocS2BN\nzRF4cDAIHIB9gWUWIHCvHYGDhiUoOPFtQgQeT4TAA0sQGIG1MCOw7Gx8B4Fl8wiB51REYI0S\nCDwxqkQ4j0wLHLyKCDy7ywolEHhiVEn47FYTWMEBBM5BYAQWByGwv+IOAo/e5CGpoddlhRII\nPDGqJHx2I7DSsBQFThAYgaVBCKw0LASWlUDgiVEl4bMbgZWGhcCyEocTeFYUAvsiEVijywol\nEHhiVEn47EZgpWEpC+y7DI3AsQq8ZFRJ+OxGYKVhIbCsxFkFlkmHwEFB6wg8GYfAc5v6zQgs\nLYjA/ihNgf/57+RA4O0tj1Pg0SgEDhpWsMC/CBzU1G9G4Mmoowgs8AmBlUDgcwsc5NN0JAJr\ndFmhBAJPBSFwf0mMAmdvgRE4qKnfjMCTUQjcyaB5BP6HwKFN/eZIBJblkkknnEeyXLIpicAz\nCiJweFO/GYGnwxC4nQGBNUog8ERMIpxHCDynIAJrlEDgiZhEOI8QeE5BbYHHgwQ/yYHACOwL\ni19gybgUBBZFIbCsxFBIvw2BEVgShMC6ILA9gYNOMBEYgUVtCIzAkiAE1gWBEdgfhcDewWh1\nWaEEAk/EJMJ5hMDtMARW4pwCt9uPKbDioS5SgYMO+QjsaVPTTuScZYGXpkLgbh3RgXryPg4E\nRmBpEAKrDwuBg0OOJLDkjBaBBeNCYIUuK5QQCayn3aJM3XYE3kFgSTIEVuLYAo+uHQIHRSGw\nfzBKXVYogcCTQQjcXYbAC7qsUGJ9gUU+IXB3IQKLCiKwpE2kil2BJfNWU2DRlETggIJ+gX3/\nOBICI7A4CoFDhoXAwSEIHBiFwO2wXQSeiEFgUW8EFkYhcMiwEDg4BIFXiULgWcNC4OAQBF4l\nKlaBZQOzLrDnMjQCI7AvCoGDhoXACDwVhMDditNxCKzQZYUSCIzACIzAU1FnEnhxEALPKYjA\n020ILI1CYLVhhQk8dR/HkQUejEDg2VEIrDYsBEbgqaAjCOzdvwicg8CS7scWWDS7ERiBNUHg\nmAQWTkkEDi+IwNONCIzACKzQRb9ELAKHZ0JgBK4XI/BkIwIjMAIrdNEvgcCqaiLwbgJPBiGw\npHs0AjeXILCuwKJcsnEhsEIJBEbgEwj8z/urdocSuNdqV+CJLXAagYWaI3AgCLwoEwIjcL0Y\ngSdbERiBEVihi34JRYH1ghDYG3QegUUFEXi6FYE11URgBFYrgcAIrC6wcNppCjx9HwcCS7oj\nMALnAQishVGBZZYjsLLAGsOKVGD/v252LIG7zScWOOjwdGSBi8UIvKSLfglbAstOtKMVWPNQ\nh8CtMASebEZgBFYXWGYmAs+KQOBeWGQCixxA4AIEFnTfWmCJm1EKrHfqiMBygT3/uhkCI7A3\nFQI3cyGwRokTCyy0DoFbUbEKPB10OoE77Qi8ucAi6xAYgUXtCIzACKzQRb8EAiMwAgvK6HTR\nL4HACIzAgjI6XfRLbCFwcwkCI3CiKnAegMCT7QhsVOAAzRE4FARelAmBEbgOQODJdgQ+tMDa\n40JgLRAYgRE4QWAE1rAcgYOGhcDHFlii5tYCyyabZYFFuRBYi+gEXnpsReBWGAKXAQg82X5o\ngUU+ITACK3TRL4HACIzAkjIqXfRLIDACI7CkjEoX/RLRCCxzM1TgyQ2AwEEloxbYw8kF1tNu\naaawY6tNgYWmqAusM6xIBf7333/Lsyzvol8CgREYgYVZlnfRL4HACIzAwizLu+iXQODNBdax\nHIE7cdMgsD8OgRE4EQosiUJgBEZgBM5BYH8cAiNwgsCqzBe4tQCBERiBNbrolzArsETN+AQW\nTW8EbhRE4JkRpgWuliKwOEqr4isEgbVAYEEQAiMwAmsGTQ5bpCYCh0chcCgIPFYQgRG4qoXA\n8yIQOCRqB4FFqRC4AIG9YZsEIXBYKgQuQGBvGAIjcBGGwFogsCAIgREYgRFYkCpB4EYuBNYo\nEY/A9TIEVktlX+AFU7jJUQUeD0DgkCgEboYhsBYILAjSE1iyRwXTe3uBZWGWBf5FYF8YAp9A\nYKU1RGCtEvYEDjql3Uxg6WRD4IBcCIzACCwbFgIj8LYCy6xDYATOQWBfmEhNBE6ccEYiMAIj\nsJ7Avi2JwI0wBNYCgQVBCCzPhcDLuqiXQGAEDsmFwMu6qJc4uMCSTAgckCtGgUWDQmBfmORY\nh8CbC6wchcDLuqiXQOCtBZaeExoWWGY5AmuUQGAEDomyK7Dv2wwILCqDwAgsLojACLw8CIGb\nUQi8rIt6CQRG4JAoBF7WRb0EAlsWWMsUBEZgBYGrhdsKLFJTUWA/CFzFIPDsgECBRcc6FYFF\n+/UMAuuZgsDHFlhy3ovAgiApTpYLgRtxHhDYE4bAgiAp2wsscxOBl3ZRL4HASvMoYoFFo0Jg\nQZLlXdRLIDACy8MQeGkX9RJWBZad9yLwHgILT9kRWKMEAiOwPExRYEkuBEZgQRQCi8MQeGkX\n9RIIrCiw2g5F4DoPAs8NcJIgBA4YlBgErvMoCez9x5EQWFQGgSVEK7BsDdUKSreDpB4CT0fJ\nBNaIQuAqTGYKAqcg8HQUAiNwnUupIAKfVuAiAIFVBRauIQKrsb7AAaZ4w2SHTQSuwhBYXs/3\nq3YILCmDwDIU71lE4BwEngxDYEkmMQhcJULguQH7COwQONlFYKF1alEIrFIiKoELexEYgetE\nCDw3YBeBHQLn2RA4QWCLAgt2LAKXUQgsr4fAk2FbCiw5zUbgwCipdYqpZGoi8NyAPQR2oh27\ng8A6QWJsCyysd2KBfz7uLuX+/rOwBAIjcFlSK0jGiQV+Xl3NbVGJqeXaAgumuFhg2dunowss\nDFIUWJETC/zuLl9/2aPH98W9LykhEng6ibbAggmHwI2i/qBIBRadYxxS4Iv7qx7/ucuSErEJ\nnP0PgRG4DJK9lZDUi0jg1qpPb4etBJbUQWA5CFwEKQr8TyHJ4i4ZER6BlQTOYxEYgcugQwr8\neg/8/cgeRfMeWFDHIXAAivdVIHBGRAInt8ZV6OtzSYkYBZbIgsBV0W2j9DizwMnPe/Y58OX+\nsfBzYARG4J04tcBqJRAYgXdi61u0EXgqTFVgL5EKrLk/ETgoShCDwFNhkoPmDgKLVh+BdwGB\niySTWRB4eZBMTgQOBIGLJL0srsmCIWgLrDfHtxZYUhCBA0FgjRIILBuT5LPpHQQW5tJLpQgC\na5RAYOGYEFgbBNYooSSwwCenOMd3EFhSD4FDQOBEsHoIvDxIRsQCxwkCJwg8GZPIVl/JFAQO\nZPPf2otHYOfEF5qPKbBktyJw5JxY4J9LTALLpq6ywMIQuwJH+sZVkc1/qisegZPn3d2y7xPG\ncAqNwGUqBA7hzAInyZdzXwkC+0IQOF7OLXDyuLn7E4E9IQgcMVsL/KuQY3GXBh/u8o3A0yEI\nHDFnFzj5uy6719m73EmCELhKhcBBnF7gJHlbKvD0YifKkQYIBE4QODTfwVFcQ6sCLy6BwNEK\nfHwQeHkJBEbg3UDg5SWUBBb6hMDQAIGXl7AqsAAEjp2tNxcCj8YhcCJ7IwENEHh5CR2BpSty\ncIHxNwwEXl7iwAKL5ETgHUHg5SUQGIF3A4GXl0BgBN4NBF5eQklgKZte50HgyEHg5SUQGIF3\nA4GXl0BgBN4NBF5eAoEReDcQeHkJBEbg3UDg5SUQGIF3A4GXl0BgBN4NBF5eYmuBt9xnCBw5\nCLy8BAIj8Gk4q8CKo4xRYLUhIXDkIPBiohNY8105AkcOAi8GgWE/EHgxCAz7cT6B88UILKyH\nwHGDwItBYIgWBPaDwBAtFgWWfEyKwNJ6CGwaBPaDwBAtCOwHgSFaENjPsQXWSgS7gMB+EBii\n5YgCq97sn0QpsN6IENg2RxVYc5AIDNGCwAIQGGIFgQUgMMQKAgtAYIgVBBaAwBArCCwAgSFW\nEFgAAkOsWBRY0t+ywP5yCAwFCCxKtx0IDCEgsCjddmwtMNgGgUXptgOBIQQEFqXbDgSGEBBY\nlG47ZAJvMBAwwUEFtjvDERhCQODIQGAI4ZgCG57hCAwhIHBkIDCEgMCRgcAQAgJHBgJDCAgc\nGdpfxIBjc1CB7YLAEAICx4byTShwbBA4NhAYAkDg2EBgCACBYwOBIQAEjg0EhgAQODYQGAJA\n4NhAYAgAgWMDgSEABI4NBIYAEDg2EBgCQODYQGAIAIFjA4EhAASODQSGABA4NhAYAkDg2EBg\nCACBYwOBIQAEjg0EhgAQODYQGAJA4NhAYAgAgWMDgSEABI4NBIYAEDg2EBgCQODYQGAIAIFj\nA4EhAASODQSGABA4NhAYAkDg2EBgCACBYwOBIQAEjg0EhgAQODYQGAJA4NhAYAgAgWMDgSEA\nBI4NBIYAEDg2EBgCQODYQGAIAIFjA4EhAASODQSGABA4NhAYAkDg2EBgCACBYwOBIQAEjg0E\nhgAQODbcmVceQkHg2EBgCACBYwOBIQAEjg0EhgAQODYQGAJA4Og49cpDIAgcHadeeQgEgaPj\n1CsPgSBwdJx65SEQBI6OU688BILA0XHqlYdAEDg6Tr3yEAgCR8epVx4CQeDoOPXKQyAIHB2n\nXnkIBIGj49QrD4EgcHSceuUhEASOjlOvPASCwNFx6pWHQBA4Ok698hAIAkfHqVceAkHg6Dj1\nykMgCBwdp155CASBo+PUKw+BIHB0nHrlIRAEjo5TrzwEgsDRceqVh0AQODpOvfIQCAIDGAaB\nAQyDwACGQWAAwyAwgGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgMYBgE\nBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaBAQwTqcAAIGKGXfrCGhvA\nEiwP3vLYTQ9ed+y7b4ndB7AEy4O3PHbTg0fgeLA8eMtjNz14BI4Hy4O3PHbTg0fgeLA8eMtj\nNz14BI4Hy4O3PHbTg0fgeLA8eMtjNz14BI4Hy4O3PHbTg0fgeLA8eMtjNz14BI4Hy4O3PHbT\ng0fgeLA8eMtjNz14BI4Hy4O3PHbTgz+YwAAwHwQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjA\nMAgMYBgEBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDBbC/xZFny/uNt39+Hsf+JpCz6v7vL+\nzB6+Rjz9MDZ8Yze44dtzydaGr8e+eMNvvM/+yrHesnF/tB/+xTyP3rOhXdI9kI/4mow+jA3f\n2A1u+N5cMrTh67Ev3/Db7rO/SzHWT3d7Js8399d6+Ofumw4nhD/39kwH+5YkP+7yl67Kz9jD\n2PCO3d6Gb8wlcxu+MfblG35TgV+uFgO/ZSvycO+th5/5ITlK7vnA0/G/u/SE/ysd7PDD2PCO\n3d6Gb8wlcxu+MfblG35TgV+SunqV0j+31sNP97nlcOaQjvbuHknx4jn8MFLGx25vwzfmkrkN\n3xj78g2/qcB/SVdg13p4d99vrzf6Ww4pkGfzJceNPYyTibHb2/DDcylOJsa+fMNvvdbFwK/Z\n69FP+qzx8J6/o79tPKYAPtMTIaMCT4zd3oZv/DW34Rt/l2/4nQT+cPdn8pe9E2g8dO7r9Xr1\nHu/53OOSnQGZFHh67NY2fNJ7amfDJ82nSzf8TgInl/SF5549azzMeMb5icCL5yV7qTQp8OTY\nixBDG77/1M6Gb/7NQxZs+L0Efr5O/T/yZ42H7ZjouOXb+VLvi+GHMTI59oJYxz4w+MZfcxu+\n+XfoWRB7CZzxV7/yNB7Guise19sje5BfUHzUV3K7D+PDM/YCQxs+pXUV2tCGT7Eu8MWlN6d8\npqvTexjprviuLjV8ZB/pfaefXA8/jA7f2O1t+JTqeoqxDZ/S8mDJht9J4Pfs5pRr+ha+9fA9\ne0v/vfGgJDzqS4Xm7sTyjt3ehk8p5pK5DZ9SebB0w+8k8DO7cpW98PQfxvhSmry5+rbVa33t\nf/hhZHjHbnDDJ/WJp7kNn3Q9WLDh93oP/Hit2/27+/D5fnHXOD/LcI198cy+WJI1Dz+MDNnY\nbW34pHFB1NqGT9pjX7Th47xsAQAiEBjAMAgMYBgEBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAY\nwDAIDGAYBAYwDAIDGAaBAQyDwACGQWAAwyAwgGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFg\nAMMgMIBhEBjAMAgMYBgEBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaB\nAQyDwACGQWAAwyAwgGEQGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgMYBgE\nBjAMAgMYBoEBDIPAAIZBYADDIDCAYRAYwDAIDGAYBAYwDAIDGAaBAQyDwACGQWAAwyAwgGEQ\nGMAwCAxgGAQGMAwCAxgGgQEMg8AAhkFgAMMgMIBhEBjAMAgMYBgEBjAMAgMYBoEBDIPAAIb5\nH3ScPKatMNr/AAAAAElFTkSuQmCC", "text/plain": "Plot with title \"Forecasts from ARIMA(3,0,1)(0,1,2)[12] with drift\""}, "output_type": "display_data", "metadata": {}}]}, {"source": "## Summary\n\nIn this lab you have learned to work with and analyze time series data. Specifically, you have done the following:\n\n- Examined the properties of time series objects.\n- Plotted time series data.\n- Decomposed time series data into its trend, seasonal, and remainder components.\n- Modeled the remainder components as AR, MA, ARMA and ARIMA models. \n- Created and evaluated difference series methods.\n- Constructed and evaluated a forecasting model. ", "cell_type": "markdown", "metadata": {"collapsed": true}}], "nbformat": 4, "metadata": {"language_info": {"version": "3.1.1", "name": "R", "file_extension": ".r", "mimetype": "text/x-r-source", "pygments_lexer": "r", "codemirror_mode": "r"}, "kernelspec": {"name": "r", "language": "R", "display_name": "R"}}}