Time Series Introduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploratory time series data analysis\n",
    "\n",
    "Many phenomena in our day-to-day lives, such as the movement of stock prices, are measured in intervals over a period of time. Time series analysis methods are extremely useful for analyzing these special data types."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploring raw time series\n",
    "The most common first step when conducting time series analysis is to display your time series dataset in a visually intuitive format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(warn = -1)\n",
    "\n",
    "library(tidytext)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df <- read.csv(\"datasets/timeseries/Nile.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>streamflow</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1120</td></tr>\n",
       "\t<tr><td>1160</td></tr>\n",
       "\t<tr><td> 963</td></tr>\n",
       "\t<tr><td>1210</td></tr>\n",
       "\t<tr><td>1160</td></tr>\n",
       "\t<tr><td>1160</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       " streamflow\\\\\n",
       "\\hline\n",
       "\t 1120\\\\\n",
       "\t 1160\\\\\n",
       "\t  963\\\\\n",
       "\t 1210\\\\\n",
       "\t 1160\\\\\n",
       "\t 1160\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "streamflow | \n",
       "|---|---|---|---|---|---|\n",
       "| 1120 | \n",
       "| 1160 | \n",
       "|  963 | \n",
       "| 1210 | \n",
       "| 1160 | \n",
       "| 1160 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  streamflow\n",
       "1 1120      \n",
       "2 1160      \n",
       "3  963      \n",
       "4 1210      \n",
       "5 1160      \n",
       "6 1160      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Nile <- ts(df[\"streamflow\"], start = 1871, end = 1970, frequency = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time Series:\n",
      "Start = 1871 \n",
      "End = 1970 \n",
      "Frequency = 1 \n",
      "       streamflow\n",
      "  [1,]       1120\n",
      "  [2,]       1160\n",
      "  [3,]        963\n",
      "  [4,]       1210\n",
      "  [5,]       1160\n",
      "  [6,]       1160\n",
      "  [7,]        813\n",
      "  [8,]       1230\n",
      "  [9,]       1370\n",
      " [10,]       1140\n",
      " [11,]        995\n",
      " [12,]        935\n",
      " [13,]       1110\n",
      " [14,]        994\n",
      " [15,]       1020\n",
      " [16,]        960\n",
      " [17,]       1180\n",
      " [18,]        799\n",
      " [19,]        958\n",
      " [20,]       1140\n",
      " [21,]       1100\n",
      " [22,]       1210\n",
      " [23,]       1150\n",
      " [24,]       1250\n",
      " [25,]       1260\n",
      " [26,]       1220\n",
      " [27,]       1030\n",
      " [28,]       1100\n",
      " [29,]        774\n",
      " [30,]        840\n",
      " [31,]        874\n",
      " [32,]        694\n",
      " [33,]        940\n",
      " [34,]        833\n",
      " [35,]        701\n",
      " [36,]        916\n",
      " [37,]        692\n",
      " [38,]       1020\n",
      " [39,]       1050\n",
      " [40,]        969\n",
      " [41,]        831\n",
      " [42,]        726\n",
      " [43,]        456\n",
      " [44,]        824\n",
      " [45,]        702\n",
      " [46,]       1120\n",
      " [47,]       1100\n",
      " [48,]        832\n",
      " [49,]        764\n",
      " [50,]        821\n",
      " [51,]        768\n",
      " [52,]        845\n",
      " [53,]        864\n",
      " [54,]        862\n",
      " [55,]        698\n",
      " [56,]        845\n",
      " [57,]        744\n",
      " [58,]        796\n",
      " [59,]       1040\n",
      " [60,]        759\n",
      " [61,]        781\n",
      " [62,]        865\n",
      " [63,]        845\n",
      " [64,]        944\n",
      " [65,]        984\n",
      " [66,]        897\n",
      " [67,]        822\n",
      " [68,]       1010\n",
      " [69,]        771\n",
      " [70,]        676\n",
      " [71,]        649\n",
      " [72,]        846\n",
      " [73,]        812\n",
      " [74,]        742\n",
      " [75,]        801\n",
      " [76,]       1040\n",
      " [77,]        860\n",
      " [78,]        874\n",
      " [79,]        848\n",
      " [80,]        890\n",
      " [81,]        744\n",
      " [82,]        749\n",
      " [83,]        838\n",
      " [84,]       1050\n",
      " [85,]        918\n",
      " [86,]        986\n",
      " [87,]        797\n",
      " [88,]        923\n",
      " [89,]        975\n",
      " [90,]        815\n",
      " [91,]       1020\n",
      " [92,]        906\n",
      " [93,]        901\n",
      " [94,]       1170\n",
      " [95,]        912\n",
      " [96,]        746\n",
      " [97,]        919\n",
      " [98,]        718\n",
      " [99,]        714\n",
      "[100,]        740\n"
     ]
    }
   ],
   "source": [
    "print(Nile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "100"
      ],
      "text/latex": [
       "100"
      ],
      "text/markdown": [
       "100"
      ],
      "text/plain": [
       "[1] 100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(Nile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nANNGZCKD+VFSAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(Nile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nBCAAIgEIgEgAAiASgACIBCAAIgEI8B/hvWlVi3jh0gAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Annual River Nile Volume at Aswan, 1871-1970\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# renaming the X and Y axis\n",
    "plot(Nile, xlab = \"Year\", ylab = \"River Volume (1e9 m^{3})\", \n",
    "         main = \"Annual River Nile Volume at Aswan, 1871-1970\", type = \"b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What does the time index tell us?\n",
    "Some data are naturally evenly spaced by time. The time series discrete_data shown has 20 observations, with one observation appearing at each of the discrete time indices 1 through 20. Discrete time indexing is appropriate for discrete_data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time Series:\n",
      "Start = 1 \n",
      "End = 20 \n",
      "Frequency = 1 \n",
      " [1]  0.47942554  0.84147098  0.99749499  0.90929743  0.59847214  0.14112001\n",
      " [7] -0.35078323 -0.75680250 -0.97753012 -0.95892427 -0.70554033 -0.27941550\n",
      "[13]  0.21511999  0.65698660  0.93799998  0.98935825  0.79848711  0.41211849\n",
      "[19] -0.07515112 -0.54402111\n"
     ]
    }
   ],
   "source": [
    "data <- c(0.47942554,0.84147098,0.99749499,0.90929743,0.59847214,0.14112001,-0.35078323,-0.75680250,-0.97753012,-0.95892427,-0.70554033,-0.27941550\n",
    ",0.21511999,0.65698660,0.93799998,0.98935825,0.79848711,0.41211849,-0.07515112,-0.54402111)\n",
    "\n",
    "discrete_data <- ts(data, start = 1, end = 20, frequency = 1)\n",
    "print(discrete_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nMECQAAMECTBAkAADBAkwQJAAA/8AynTU2A2hFnUAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"discrete_data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(discrete_data, type = \"b\", main = \"discrete_data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The time series continuous_series shown also has 20 observations, it is following the same periodic pattern as discrete_data, but its observations are not evenly spaced. Its first, second, and last observations were observed at times 1.210322, 1.746137, and 20.180524, respectively. Continuous time indexing is natural for continuous_series, however, the observations are approximately evenly spaced, with about 1 observation observed per time unit. Let's investigate using a discrete time indexing for continuous_series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1]  0.56889468  0.76630408  0.99207512  0.97481741  0.39912320  0.37660246\n",
      " [7] -0.38532033 -0.83635852 -0.99966983 -0.99831019 -0.64622280 -0.09386151\n",
      "[13]  0.40052909  0.68160578  0.95318159  0.99693803  0.83934194  0.37003754\n",
      "[19] -0.25509676 -0.61743983\n"
     ]
    }
   ],
   "source": [
    "data2 <- c(0.56889468,0.76630408,0.99207512,0.97481741,0.39912320,0.37660246\n",
    ",-0.38532033,-0.83635852,-0.99966983,-0.99831019,-0.64622280,-0.09386151\n",
    ",0.40052909,0.68160578,0.95318159,0.99693803,0.83934194,0.37003754\n",
    ",-0.25509676,-0.61743983)\n",
    "\n",
    "continuous_series <- data2\n",
    "print(continuous_series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\n/gMOcreAYtG89gAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"continuous_series\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(continuous_series, type = \"b\", main = \"continuous_series\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "continuous_time_index <- c(1.210322,1.746137,2.889634,3.591384,5.462065,5.510933,7.074295,8.264398,9.373382,9.541063,11.161122,12.378371,13.390559,14.066280,15.093547,15.864515,16.857413,18.091457,19.365451,20.180524)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\ngCABAgQJECBIgABBAgQIEiDwH0lhIeZ7Zg83AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the continuous_series using continuous time indexing\n",
    "par(mfrow=c(2,1))\n",
    "plot(continuous_time_index,continuous_series, type = \"b\")\n",
    "\n",
    "# Make a discrete time index using 1:20 \n",
    "discrete_time_index <- c(1:20)\n",
    "\n",
    "# Now plot the continuous_series using discrete time indexing\n",
    "plot(discrete_time_index,continuous_series, type = \"b\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the various differences between the resulting figures, but the approximation appears reasonable because the overall trend remained preserved"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Sampling Frequency (Exact): Some time series data is EXACTLY evenly spaced. example: hourly temperature measurements\n",
    "* Sampling Frequency (Approximate): Some time series data is APPROXIMATELY evenly spaced. example: temperature measurements everytime you check your email.\n",
    "* Sampling Frequency (Missing Values): Some time series data is evenly spaced but with missing values. example: hourly temperature measurements but only during the times you're awake.\n",
    "\n",
    "#### Basic assumptions\n",
    "Simplifying assumptions for time series:\n",
    "* Consecutive observations are equally spaced.\n",
    "* Apply a discrete-time observation index.\n",
    "* In practice, this may only hold approximately. \n",
    "\n",
    "Example: Daily log returns on stock may only be available for weekdays.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identifying the sampling frequency\n",
    "In addition to viewing your data and plotting over time, there are several additional operations that can be performed on time series datasets.\n",
    "\n",
    "The start() and end() functions return the time index of the first and last observations, respectively. The time() function calculates a vector of time indices, with one element for each time index on which the series was observed.\n",
    "\n",
    "The deltat() function returns the fixed time interval between observations and the frequency() function returns the number of observations per unit time. Finally, the cycle() function returns the position in the cycle of each observation.\n",
    "\n",
    "These commands provide considerable descriptive information about the structures and patterns in your time series data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## When is the sampling frequency exact?\n",
    "The sampling frequency is often only approximate and the interval between observations is not quite a fixed unit. For example, there are usually 365 days in a year based on the Gregorian calendar. However, (almost) every four years there are 366 days (leap years). This compensates for the fact that the Earth completes a rotation around Sol, the sun, in approximately 365.2422 days, on average.\n",
    "\n",
    "As a simplifying assumption, we often ignore these small discrepancies and proceed as though the sampling frequency and observation intervals are fixed constants. Typically, our results will not be sensitive to approximation when the underlying process is not changing too quickly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Missing values\n",
    "Sometimes there are missing values in time series data, denoted NA in R, and it is useful to know their locations. It is also important to know how missing values are handled by various R functions. Sometimes we may want to ignore any missingness, but other times we may wish to impute or estimate the missing values.\n",
    "\n",
    "Let's again consider the monthly AirPassengers dataset, but now the data for the year 1956 are missing. \n",
    "\n",
    "The mean() function calculates the sample mean, but it fails in the presence of any NA values. Use mean(___, na.rm = TRUE) to calculate the mean with all missing values removed. It is common to replace missing values with the mean of the observed values. Does this simple data imputation scheme appear adequate when applied the the AirPassengers dataset?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a time series object with ts()\n",
    "The function ts() can be applied to create time series objects. A time series object is a vector (univariate) or matrix (multivariate) with additional attributes, including time indices for each observation, the sampling frequency and time increment between observations, and the cycle length for periodic data. Such objects are of the ts class, and represent data that has been observed at (approximately) equally spaced time points. Now you will create time series objects yourself.\n",
    "\n",
    "The advantage of creating and working with time series objects of the ts class is that many methods are available for utilizing time series attributes, such as time index information. For example, as you've seen in earlier exercises, calling plot() on a ts object will automatically generate a plot over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2.0521941073</li>\n",
       "\t<li>4.2928852797</li>\n",
       "\t<li>3.3294132944</li>\n",
       "\t<li>3.508595067</li>\n",
       "\t<li>0.0009576938</li>\n",
       "\t<li>1.9217186345</li>\n",
       "\t<li>0.7978134128</li>\n",
       "\t<li>0.2999543435</li>\n",
       "\t<li>0.9435687536</li>\n",
       "\t<li>0.5748283388</li>\n",
       "\t<li>-0.0034005903</li>\n",
       "\t<li>0.3448649176</li>\n",
       "\t<li>2.2229761136</li>\n",
       "\t<li>0.1763144576</li>\n",
       "\t<li>2.709762277</li>\n",
       "\t<li>1.2501948965</li>\n",
       "\t<li>-0.4007164754</li>\n",
       "\t<li>0.8852732121</li>\n",
       "\t<li>-1.5852420266</li>\n",
       "\t<li>-2.2829278891</li>\n",
       "\t<li>-2.560953129</li>\n",
       "\t<li>-3.1259963754</li>\n",
       "\t<li>-2.8660295895</li>\n",
       "\t<li>-1.7847009207</li>\n",
       "\t<li>-1.8894912908</li>\n",
       "\t<li>-2.7255351194</li>\n",
       "\t<li>-2.10331418</li>\n",
       "\t<li>-0.0174256893</li>\n",
       "\t<li>-0.3613204151</li>\n",
       "\t<li>-2.9008403327</li>\n",
       "\t<li>-3.2847440927</li>\n",
       "\t<li>-2.8684594718</li>\n",
       "\t<li>-1.9505074437</li>\n",
       "\t<li>-4.8801892525</li>\n",
       "\t<li>-3.2634605353</li>\n",
       "\t<li>-1.6396062522</li>\n",
       "\t<li>-3.301257584</li>\n",
       "\t<li>-2.6331245433</li>\n",
       "\t<li>-1.7058354022</li>\n",
       "\t<li>-2.2119825061</li>\n",
       "\t<li>-0.5170595186</li>\n",
       "\t<li>0.0752508095</li>\n",
       "\t<li>-0.8406994716</li>\n",
       "\t<li>-1.4022683487</li>\n",
       "\t<li>-0.138211423</li>\n",
       "\t<li>-1.4065954703</li>\n",
       "\t<li>-2.3046941055</li>\n",
       "\t<li>1.5073891432</li>\n",
       "\t<li>0.7118679477</li>\n",
       "\t<li>-1.1300519022</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2.0521941073\n",
       "\\item 4.2928852797\n",
       "\\item 3.3294132944\n",
       "\\item 3.508595067\n",
       "\\item 0.0009576938\n",
       "\\item 1.9217186345\n",
       "\\item 0.7978134128\n",
       "\\item 0.2999543435\n",
       "\\item 0.9435687536\n",
       "\\item 0.5748283388\n",
       "\\item -0.0034005903\n",
       "\\item 0.3448649176\n",
       "\\item 2.2229761136\n",
       "\\item 0.1763144576\n",
       "\\item 2.709762277\n",
       "\\item 1.2501948965\n",
       "\\item -0.4007164754\n",
       "\\item 0.8852732121\n",
       "\\item -1.5852420266\n",
       "\\item -2.2829278891\n",
       "\\item -2.560953129\n",
       "\\item -3.1259963754\n",
       "\\item -2.8660295895\n",
       "\\item -1.7847009207\n",
       "\\item -1.8894912908\n",
       "\\item -2.7255351194\n",
       "\\item -2.10331418\n",
       "\\item -0.0174256893\n",
       "\\item -0.3613204151\n",
       "\\item -2.9008403327\n",
       "\\item -3.2847440927\n",
       "\\item -2.8684594718\n",
       "\\item -1.9505074437\n",
       "\\item -4.8801892525\n",
       "\\item -3.2634605353\n",
       "\\item -1.6396062522\n",
       "\\item -3.301257584\n",
       "\\item -2.6331245433\n",
       "\\item -1.7058354022\n",
       "\\item -2.2119825061\n",
       "\\item -0.5170595186\n",
       "\\item 0.0752508095\n",
       "\\item -0.8406994716\n",
       "\\item -1.4022683487\n",
       "\\item -0.138211423\n",
       "\\item -1.4065954703\n",
       "\\item -2.3046941055\n",
       "\\item 1.5073891432\n",
       "\\item 0.7118679477\n",
       "\\item -1.1300519022\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2.0521941073\n",
       "2. 4.2928852797\n",
       "3. 3.3294132944\n",
       "4. 3.508595067\n",
       "5. 0.0009576938\n",
       "6. 1.9217186345\n",
       "7. 0.7978134128\n",
       "8. 0.2999543435\n",
       "9. 0.9435687536\n",
       "10. 0.5748283388\n",
       "11. -0.0034005903\n",
       "12. 0.3448649176\n",
       "13. 2.2229761136\n",
       "14. 0.1763144576\n",
       "15. 2.709762277\n",
       "16. 1.2501948965\n",
       "17. -0.4007164754\n",
       "18. 0.8852732121\n",
       "19. -1.5852420266\n",
       "20. -2.2829278891\n",
       "21. -2.560953129\n",
       "22. -3.1259963754\n",
       "23. -2.8660295895\n",
       "24. -1.7847009207\n",
       "25. -1.8894912908\n",
       "26. -2.7255351194\n",
       "27. -2.10331418\n",
       "28. -0.0174256893\n",
       "29. -0.3613204151\n",
       "30. -2.9008403327\n",
       "31. -3.2847440927\n",
       "32. -2.8684594718\n",
       "33. -1.9505074437\n",
       "34. -4.8801892525\n",
       "35. -3.2634605353\n",
       "36. -1.6396062522\n",
       "37. -3.301257584\n",
       "38. -2.6331245433\n",
       "39. -1.7058354022\n",
       "40. -2.2119825061\n",
       "41. -0.5170595186\n",
       "42. 0.0752508095\n",
       "43. -0.8406994716\n",
       "44. -1.4022683487\n",
       "45. -0.138211423\n",
       "46. -1.4065954703\n",
       "47. -2.3046941055\n",
       "48. 1.5073891432\n",
       "49. 0.7118679477\n",
       "50. -1.1300519022\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  2.0521941073  4.2928852797  3.3294132944  3.5085950670  0.0009576938\n",
       " [6]  1.9217186345  0.7978134128  0.2999543435  0.9435687536  0.5748283388\n",
       "[11] -0.0034005903  0.3448649176  2.2229761136  0.1763144576  2.7097622770\n",
       "[16]  1.2501948965 -0.4007164754  0.8852732121 -1.5852420266 -2.2829278891\n",
       "[21] -2.5609531290 -3.1259963754 -2.8660295895 -1.7847009207 -1.8894912908\n",
       "[26] -2.7255351194 -2.1033141800 -0.0174256893 -0.3613204151 -2.9008403327\n",
       "[31] -3.2847440927 -2.8684594718 -1.9505074437 -4.8801892525 -3.2634605353\n",
       "[36] -1.6396062522 -3.3012575840 -2.6331245433 -1.7058354022 -2.2119825061\n",
       "[41] -0.5170595186  0.0752508095 -0.8406994716 -1.4022683487 -0.1382114230\n",
       "[46] -1.4065954703 -2.3046941055  1.5073891432  0.7118679477 -1.1300519022"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_vector <- c(2.0521941073,4.2928852797,3.3294132944,3.5085950670,0.0009576938,\n",
    "1.9217186345,0.7978134128,0.2999543435,0.9435687536,0.5748283388\n",
    ",-0.0034005903,0.3448649176,2.2229761136,0.1763144576,2.7097622770, 1.2501948965,-0.4007164754,0.8852732121,-1.5852420266,-2.2829278891,-2.5609531290,-3.1259963754,-2.8660295895,-1.7847009207,-1.8894912908\n",
    ",-2.7255351194,-2.1033141800,-0.0174256893,-0.3613204151,-2.9008403327\n",
    ",-3.2847440927,-2.8684594718,-1.9505074437,-4.8801892525,-3.2634605353,-1.6396062522,-3.3012575840,-2.6331245433,-1.7058354022,-2.2119825061\n",
    ",-0.5170595186,0.0752508095,-0.8406994716,-1.4022683487,-0.1382114230\n",
    ",-1.4065954703,-2.3046941055,1.5073891432,0.7118679477,-1.1300519022)\n",
    "\n",
    "data_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nIEBIECAkCBASBAgJAoQEAUKCACFBwH+YPz1qzwxgSwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              Qtr1          Qtr2          Qtr3          Qtr4\n",
      "2004  2.0521941073  4.2928852797  3.3294132944  3.5085950670\n",
      "2005  0.0009576938  1.9217186345  0.7978134128  0.2999543435\n",
      "2006  0.9435687536  0.5748283388 -0.0034005903  0.3448649176\n",
      "2007  2.2229761136  0.1763144576  2.7097622770  1.2501948965\n",
      "2008 -0.4007164754  0.8852732121 -1.5852420266 -2.2829278891\n",
      "2009 -2.5609531290 -3.1259963754 -2.8660295895 -1.7847009207\n",
      "2010 -1.8894912908 -2.7255351194 -2.1033141800 -0.0174256893\n",
      "2011 -0.3613204151 -2.9008403327 -3.2847440927 -2.8684594718\n",
      "2012 -1.9505074437 -4.8801892525 -3.2634605353 -1.6396062522\n",
      "2013 -3.3012575840 -2.6331245433 -1.7058354022 -2.2119825061\n",
      "2014 -0.5170595186  0.0752508095 -0.8406994716 -1.4022683487\n",
      "2015 -0.1382114230 -1.4065954703 -2.3046941055  1.5073891432\n",
      "2016  0.7118679477 -1.1300519022                            \n"
     ]
    }
   ],
   "source": [
    "# Convert data_vector to a ts object with start = 2004 and frequency = 4\n",
    "time_series <- ts(data_vector, start = 2004, frequency = 4)\n",
    "\n",
    "print(time_series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(time_series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, ts objects are treated differently by commands such as print() and plot(). For example, automatic use of the time-index in your calls to plot() requires a ts object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing whether an object is a time series\n",
    "When you work to create your own datasets, you can build them as ts objects. Recall the dataset data_vector from the previous exercise, which was just a vector of numbers, and time_series, the ts object you created from data_vector using the ts() function and information regarding the start time and the observation frequency.\n",
    "\n",
    "When you use datasets from others, such as those included in an R package, you can check whether they are ts objects using the is.ts() command. The result of the test is either TRUE when the data is of the ts class, or FALSE if it is not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is.ts(data_vector)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is.ts(time_series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is.ts(Nile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting a time series object\n",
    "It is often very useful to plot data we are analyzing, as is the case when conducting time series analysis. If the dataset under study is of the ts class, then the plot() function has methods that automatically incorporate time index information into a figure.\n",
    "\n",
    "Let's consider the eu_stocks dataset (available in R by default as EuStockMarkets). This dataset contains daily closing prices of major European stock indices from 1991-1998, specifically, from Germany (DAX), Switzerland (SMI), France (CAC), and the UK (FTSE). The data were observed when the markets were open, so there are no observations on weekends and holidays. We will proceed with the approximation that this dataset has evenly spaced observations and is a four dimensional time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "7440"
      ],
      "text/latex": [
       "7440"
      ],
      "text/markdown": [
       "7440"
      ],
      "text/plain": [
       "[1] 7440"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eu_stocks_data <- c(628.75,1613.63,1606.51,1621.04,1618.16,1610.61,1630.75,1640.17,1635.47,\n",
    "1645.89,1647.84,1638.35,1629.93,1621.49,1624.74,1627.63,1631.99,1621.18,\n",
    "1613.42,1604.95,1605.75,1616.67,1619.29,1620.49,1619.67,1623.07,1613.98,\n",
    "1631.87,1630.37,1633.47,1626.55,1650.43,1650.06,1654.11,1653.60,1501.82,\n",
    "1524.28,1603.65,1622.49,1636.68,1652.10,1645.81,1650.36,1651.55,1649.88,\n",
    "1653.52,1657.51,1649.55,1649.09,1646.41,1638.65,1625.80,1628.64,1632.22,\n",
    "1633.65,1631.17,1635.80,1621.27,1624.70,1616.13,1618.12,1627.80,1625.79,\n",
    "1614.80,1612.80,1605.47,1609.32,1607.48,1607.48,1604.89,1589.12,1582.27,\n",
    "1567.99,1568.16,1569.71,1571.74,1585.41,1570.01,1561.89,1565.18,1570.34,\n",
    "1577.00,1590.29,1572.72,1572.07,1579.19,1588.73,1586.01,1579.77,1572.58,\n",
    "1568.09,1578.21,1573.94,1582.06,1610.18,1605.16,1623.84,1615.26,1627.08,\n",
    "1626.97,1605.70,1589.70,1589.70,1603.26,1599.75,1590.86,1603.50,1589.86,\n",
    "1587.92,1571.06,1549.81,1549.36,1554.65,1557.52,1555.31,1559.76,1548.44,\n",
    "1543.99,1550.21,1557.03,1551.78,1562.89,1570.28,1559.26,1545.87,1542.77,\n",
    "1542.77,1542.77,1542.77,1564.27,1577.26,1577.26,1577.26,1598.19,1604.05,\n",
    "1604.69,1593.65,1581.68,1599.14,1613.82,1620.45,1629.51,1663.70,1664.09,\n",
    "1669.29,1685.14,1687.07,1680.13,1671.84,1669.52,1686.71,1685.51,1671.01,\n",
    "1683.06,1685.70,1685.66,1678.77,1685.85,1683.71,1686.59,1683.73,1679.14,\n",
    "1685.03,1680.81,1676.17,1688.46,1696.55,1690.24,1711.35,1711.29,1729.86,\n",
    "1716.63,1743.36,1745.17,1746.76,1749.29,1763.86,1762.27,1762.29,1746.77,\n",
    "1753.50,1753.21,1739.88,1723.92,1734.42,1723.13,1732.92,1729.89,1725.74,\n",
    "1730.90,1714.17,1716.20,1719.06,1718.21,1698.84,1714.76,1718.35,1706.69,\n",
    "1723.37,1716.18,1738.78,1737.41,1714.77,1724.24,1733.77,1729.96,1734.46,\n",
    "1744.35,1746.88,1746.88,1746.88,1747.47,1753.10,1745.17,1745.72,1742.92,\n",
    "1731.68,1731.18,1728.09,1728.09,1731.29,1733.82,1745.78,1752.57,1748.13,\n",
    "1750.70,1747.91,1745.79,1735.34,1719.92,1763.59,1766.76,1785.40,1783.56,\n",
    "1804.42,1812.33,1799.51,1792.80,1792.80,1806.36,1798.23,1800.62,1786.19,\n",
    "1791.35,1789.05,1789.05,1784.71,1789.45,1779.74,1786.97,1773.25,1781.62,\n",
    "1773.75,1773.75,1776.34,1770.72,1772.39,1762.55,1764.35,1752.83,1755.98,\n",
    "1754.95,1759.90,1759.84,1776.50,1769.98,1766.98,1752.29,1760.17,1750.32,\n",
    "1731.44,1735.51,1733.84,1730.78,1699.46,1652.71,1654.09,1636.81,1622.81,\n",
    "1613.36,1617.78,1617.18,1637.62,1622.20,1608.49,1605.11,1609.61,1624.94,\n",
    "1618.07,1611.96,1578.95,1561.39,1547.87,1548.63,1560.16,1554.76,1531.87,\n",
    "1526.14,1509.03,1530.03,1484.97,1464.03,1475.11,1516.12,1519.69,1529.97,\n",
    "1516.44,1515.53,1543.89,1534.72,1538.66,1536.71,1523.83,1527.10,1530.20,\n",
    "1601.50,1580.29,1595.09,1579.47,1600.59,1566.00,1557.01,1542.74,1536.30,\n",
    "1510.66,1481.03,1483.83,1470.09,1484.78,1475.41,1402.34,1421.49,1434.61,\n",
    "1446.32,1437.65,1441.57,1471.64,1453.95,1453.79,1458.02,1479.59,1504.89,\n",
    "1496.54,1511.00,1528.86,1534.02,1536.60,1508.19,1493.54,1489.68,1482.44,\n",
    "1483.34,1470.57,1484.84,1487.71,1508.63,1515.27,1509.84,1542.28,1541.79,\n",
    "1542.48,1550.27,1550.27,1543.37,1547.84,1523.62,1526.68,1513.42,1523.02,\n",
    "1529.69,1545.12,1546.82,1528.12,1530.65,1526.25,1519.48,1506.65,1504.30,\n",
    "1480.65,1476.70,1478.07,1479.62,1477.55,1472.59,1495.60,1517.45,1520.93,\n",
    "1527.06,1527.06,1527.06,1547.51,1545.82,1538.43,1538.43,1538.43,1538.04,\n",
    "1554.03,1551.17,1538.37,1529.10,1522.26,1533.79,1510.18,1526.91,1555.52,\n",
    "1581.49,1572.61,1572.69,1580.64,1593.35,1571.28,1575.59,1561.78,1572.68,\n",
    "1574.04,1590.33,1584.14,1605.91,1615.98,1643.83,1646.85,1639.12,1642.80,\n",
    "1659.07,1649.64,1674.93,1651.60,1656.35,1670.90,1683.30,1679.41,1658.09,\n",
    "1652.92,1661.96,1680.02,1691.37,1701.46,1690.48,1685.46,1686.15,1702.27,\n",
    "1711.91,1714.48,1708.65,1688.74,1705.05,1700.28,1689.71,1696.38,1686.57,\n",
    "1656.59,1653.20,1666.72,1663.27,1667.26,1675.18,1686.64,1676.84,1670.04,\n",
    "1657.06,1658.36,1667.64,1654.60,1658.13,1658.13,1658.13,1671.54,1674.95,\n",
    "1674.67,1678.65,1687.14,1680.06,1666.49,1680.01,1656.03,1643.53,1636.59,\n",
    "1630.88,1618.60,1626.83,1632.00,1619.92,1628.88,1617.74,1607.70,1616.45,\n",
    "1613.46,1632.99,1636.02,1632.35,1630.37,1619.26,1606.64,1606.64,1613.98,\n",
    "1608.58,1623.05,1617.18,1633.18,1627.21,1627.21,1625.59,1628.53,1630.56,\n",
    "1638.47,1660.88,1662.28,1679.69,1679.69,1685.85,1686.44,1684.57,1689.93,\n",
    "1681.47,1687.14,1697.26,1698.33,1690.96,1692.16,1699.52,1712.33,1703.05,\n",
    "1700.93,1698.36,1697.39,1694.83,1705.66,1739.48,1798.63,1798.36,1808.74,\n",
    "1806.52,1815.63,1807.12,1829.36,1835.09,1826.45,1821.28,1828.53,1830.61,\n",
    "1859.49,1846.02,1832.20,1823.40,1823.07,1818.10,1857.36,1861.22,1870.80,\n",
    "1878.94,1870.24,1864.51,1894.56,1908.69,1917.69,1903.44,1918.75,1930.29,\n",
    "1937.77,1909.53,1893.48,1907.65,1915.59,1890.58,1909.54,1929.56,1931.88,\n",
    "1923.67,1928.63,1920.43,1911.15,1878.77,1870.32,1870.46,1868.28,1874.38,\n",
    "1869.25,1852.81,1862.62,1884.67,1922.69,1922.05,1899.54,1902.14,1890.18,\n",
    "1914.40,1915.61,1908.97,1910.23,1920.46,1934.99,1973.45,1994.09,1991.95,\n",
    "2015.71,2009.28,2004.11,1999.60,1995.35,2023.26,2032.25,2036.93,2029.87,\n",
    "2048.05,2083.62,2061.18,2048.75,2040.97,2053.66,2064.98,2068.51,2086.40,\n",
    "2086.22,2057.10,2013.65,2007.50,2040.74,2020.11,2021.81,2023.06,2047.20,\n",
    "2070.17,2070.17,2075.99,2072.13,2020.36,2027.99,2036.45,2057.80,2045.25,\n",
    "2052.09,2052.92,2089.77,2099.76,2128.30,2118.01,2127.39,2165.95,2166.58,\n",
    "2165.50,2163.83,2128.07,2129.52,2144.03,2154.76,2188.18,2183.78,2209.17,\n",
    "2227.63,2227.63,2266.70,2236.91,2229.62,2255.29,2255.29,2274.62,2249.85,\n",
    "2233.61,2220.63,2224.95,2225.00,2228.10,2182.06,2142.37,2151.05,2115.56,\n",
    "2130.35,2132.52,2098.36,2073.94,2107.29,2090.78,2128.66,2123.31,2156.61,\n",
    "2192.60,2181.88,2184.05,2137.08,2143.90,2095.11,2099.57,2116.43,2119.69,\n",
    "2108.77,2101.93,2130.71,2135.25,2162.29,2133.85,2108.06,2113.64,2140.25,\n",
    "2082.90,2075.33,2103.24,2057.20,2018.69,2044.45,2076.76,2132.12,2125.47,\n",
    "2118.01,2124.51,2101.89,2169.40,2178.91,2168.11,2160.45,2140.39,2130.55,\n",
    "2141.70,2162.96,2144.36,2144.00,2167.72,2162.82,2151.84,2142.88,2142.88,\n",
    "2142.88,2177.09,2184.89,2202.57,2203.18,2224.85,2211.19,2215.19,2198.24,\n",
    "2211.92,2218.37,2193.89,2194.09,2194.41,2218.13,2208.68,2241.36,2256.98,\n",
    "2237.82,2252.51,2266.72,2261.71,2241.85,2249.78,2233.55,2218.77,2241.34,\n",
    "2248.02,2248.02,2257.33,2272.96,2268.11,2254.21,2245.79,2238.97,2238.97,\n",
    "2188.01,2137.56,2146.00,2112.80,2129.76,2137.34,2113.62,2120.23,2158.88,\n",
    "2163.59,2131.80,2143.93,2131.14,2143.58,2084.42,2088.44,2073.21,2047.29,\n",
    "2031.80,1986.42,1957.08,2004.93,2032.52,2005.07,2000.48,2022.25,2042.45,\n",
    "2020.85,2040.69,2061.70,2034.64,2031.33,2049.10,2047.83,2069.46,2048.57,\n",
    "2051.25,2070.71,2103.54,2116.96,2129.86,2120.97,2126.75,2148.23,2144.21,\n",
    "2163.32,2135.93,2134.12,2152.19,2161.50,2193.63,2190.83,2176.66,2188.81,\n",
    "2182.32,2160.56,2166.51,2156.31,2133.74,2134.34,2152.65,2166.56,2151.44,\n",
    "2143.84,2113.37,2121.25,2132.98,2153.48,2190.58,2215.72,2205.82,2207.09,\n",
    "2185.78,2197.38,2173.60,2158.07,2167.68,2178.10,2155.58,2155.81,2157.15,\n",
    "2118.17,2129.36,2097.45,2100.55,2059.15,2067.17,2072.81,2097.33,2057.83,\n",
    "2056.89,2070.36,2016.08,2002.30,2002.30,1988.67,1946.49,1965.41,1977.67,\n",
    "2048.56,2087.71,2072.68,2108.08,2118.52,2095.58,2069.58,2055.94,2048.15,\n",
    "2016.60,2022.64,1995.85,2009.45,2026.37,2064.86,2061.58,2066.18,2039.91,\n",
    "2061.37,2069.39,2043.30,2056.36,2090.78,2098.04,2073.67,2091.04,2112.21,\n",
    "2112.21,2091.94,2089.48,2097.20,2073.29,2040.05,2058.79,2056.27,2050.82,\n",
    "2036.24,2057.08,2045.54,2042.38,2067.26,2046.99,2044.04,2041.85,2024.19,\n",
    "2003.64,2019.13,2040.94,2054.23,2069.90,2066.59,2080.16,2095.50,2102.25,\n",
    "2100.98,2100.98,2110.77,2097.34,2074.68,2097.51,2079.19,2068.92,2072.90,\n",
    "2051.46,2058.20,2053.41,2062.08,2061.76,2059.68,2064.14,2088.25,2081.39,\n",
    "2085.62,2079.60,2050.86,2013.03,2027.67,2026.97,2040.79,2030.56,2026.68,\n",
    "2024.82,2047.44,2038.46,2077.94,2085.08,2093.01,2087.78,2117.80,2127.56,\n",
    "2118.96,2128.33,2135.49,2112.06,2119.29,2101.98,2101.82,2096.26,2126.44,\n",
    "2117.59,2106.05,2097.85,2127.21,2116.64,2094.16,2069.95,2041.26,2029.38,\n",
    "1989.20,2008.85,1974.14,2022.50,1995.22,2016.15,1979.52,1984.99,1984.15,\n",
    "1978.07,1935.08,1935.87,1928.82,1911.70,1918.85,1949.76,1914.69,1934.96,\n",
    "1965.68,1972.59,1976.52,1978.71,1980.81,1979.26,1991.08,1982.99,1982.99,\n",
    "1982.99,1954.62,1943.88,1955.33,1987.70,1978.97,2007.57,2028.52,2024.25,\n",
    "2017.95,2017.95,2036.47,2037.99,2034.15,2021.22,2030.65,2050.66,2064.41,\n",
    "2086.41,2102.40,2092.00,2109.36,2088.99,2083.80,2064.42,2096.87,2083.55,\n",
    "2105.88,2105.88,2065.71,2069.26,2081.46,2099.95,2119.24,2132.72,2132.72,\n",
    "2154.17,2136.72,2137.21,2107.16,2127.79,2124.25,2124.84,2130.78,2125.06,\n",
    "2154.13,2140.36,2144.88,2144.88,2144.88,2137.36,2128.99,2091.30,2094.68,\n",
    "2089.04,2099.68,2110.13,2117.63,2111.35,2163.37,2184.39,2194.15,2200.32,\n",
    "2193.72,2191.25,2201.36,2183.71,2195.31,2183.52,2196.54,2232.02,2232.23,\n",
    "2237.73,2239.36,2217.91,2222.51,2211.26,2249.60,2234.86,2236.68,2244.56,\n",
    "2236.89,2222.28,2236.72,2228.44,2208.41,2236.73,2251.64,2253.93,2265.86,\n",
    "2269.60,2258.97,2262.66,2253.91,2257.34,2240.31,2230.27,2251.30,2234.23,\n",
    "2242.76,2263.08,2266.57,2266.37,2263.27,2266.77,2268.26,2266.07,2300.72,\n",
    "2300.29,2305.58,2289.49,2306.66,2294.15,2275.72,2204.44,2212.97,2232.02,\n",
    "2190.90,2184.24,2201.27,2197.01,2197.01,2211.60,2191.54,2176.35,2157.41,\n",
    "2137.01,2153.56,2159.73,2206.11,2193.85,2185.52,2197.57,2176.09,2148.12,\n",
    "2116.86,2114.88,2140.74,2142.74,2112.01,2149.71,2165.76,2182.11,2180.49,\n",
    "2169.69,2168.57,2174.27,2184.05,2182.47,2174.78,2195.15,2197.34,2196.64,\n",
    "2199.29,2196.59,2204.01,2201.90,2194.53,2197.26,2210.92,2247.97,2242.91,\n",
    "2249.75,2254.95,2266.56,2261.08,2269.34,2274.94,2260.62,2277.70,2277.70,\n",
    "2278.64,2283.26,2286.21,2283.84,2240.24,2241.43,2268.07,2268.35,2280.81,\n",
    "2280.81,2280.81,2280.44,2273.90,2260.69,2260.69,2307.70,2326.18,2332.81,\n",
    "2315.66,2336.76,2351.47,2340.31,2330.98,2353.89,2361.38,2379.43,2375.63,\n",
    "2389.62,2400.58,2391.74,2393.12,2436.68,2437.02,2449.71,2437.70,2456.09,\n",
    "2463.00,2472.53,2459.81,2416.84,2437.98,2442.43,2411.49,2435.07,2428.59,\n",
    "2436.09,2427.77,2426.51,2423.60,2387.60,2373.01,2401.59,2421.93,2449.52,\n",
    "2438.73,2449.09,2486.95,2485.18,2488.85,2486.83,2472.52,2471.38,2479.38,\n",
    "2448.80,2419.72,2415.29,2417.00,2432.46,2458.00,2472.55,2484.74,2491.73,\n",
    "2505.32,2479.84,2514.80,2505.78,2523.81,2502.94,2489.35,2500.75,2508.11,\n",
    "2489.52,2498.75,2498.75,2498.75,2510.81,2525.59,2508.12,2526.74,2540.79,\n",
    "2547.32,2519.82,2524.18,2535.86,2549.27,2549.12,2524.84,2538.68,2539.88,\n",
    "2505.97,2492.63,2492.63,2465.49,2472.43,2473.52,2476.79,2466.21,2470.57,\n",
    "2499.02,2496.33,2528.20,2534.40,2534.40,2552.29,2541.98,2564.12,2548.79,\n",
    "2546.55,2549.53,2549.53,2559.15,2548.53,2535.78,2523.81,2543.99,2550.42,\n",
    "2551.03,2559.02,2536.03,2552.96,2571.10,2569.90,2566.13,2544.90,2549.71,\n",
    "2554.12,2546.04,2532.22,2547.78,2562.19,2578.36,2572.06,2551.80,2570.44,\n",
    "2573.44,2565.32,2566.32,2578.74,2568.79,2561.51,2562.24,2573.00,2561.95,\n",
    "2548.97,2529.50,2475.98,2497.69,2505.56,2498.35,2468.32,2488.82,2459.13,\n",
    "2464.51,2469.51,2472.25,2466.84,2491.50,2504.16,2520.26,2520.52,2527.73,\n",
    "2541.41,2534.63,2532.96,2529.14,2545.65,2544.61,2542.75,2567.96,2556.25,\n",
    "2562.12,2534.44,2559.42,2562.12,2554.42,2563.59,2556.64,2548.84,2534.49,\n",
    "2538.34,2528.73,2526.18,2532.55,2542.74,2549.71,2568.77,2568.70,2588.04,\n",
    "2614.50,2630.24,2626.43,2621.20,2625.46,2641.50,2624.18,2643.42,2663.10,\n",
    "2664.96,2659.86,2655.49,2654.34,2685.29,2685.29,2704.25,2705.21,2702.60,\n",
    "2685.23,2683.52,2692.69,2700.83,2718.73,2705.06,2717.50,2727.56,2733.67,\n",
    "2721.74,2678.89,2681.94,2690.79,2703.33,2675.50,2664.72,2671.40,2670.19,\n",
    "2678.73,2716.16,2735.28,2724.25,2732.29,2730.44,2764.00,2770.61,2784.39,\n",
    "2800.60,2768.68,2781.54,2766.08,2765.29,2769.47,2800.52,2808.62,2793.86,\n",
    "2829.68,2848.84,2853.46,2900.76,2880.89,2894.43,2832.53,2870.30,2890.95,\n",
    "2836.36,2846.94,2815.77,2841.16,2808.50,2814.23,2824.83,2835.54,2844.09,\n",
    "2844.09,2844.09,2844.09,2859.22,2880.07,2880.07,2880.07,2820.81,2863.26,\n",
    "2890.20,2876.34,2904.08,2936.69,2915.81,2956.78,2978.84,2976.56,2996.12,\n",
    "3006.87,2999.19,3000.66,3026.63,3037.28,2982.63,2992.55,3028.27,2997.95,\n",
    "3018.58,3037.70,3064.70,3067.48,3114.73,3124.78,3161.36,3185.72,3191.45,\n",
    "3211.01,3256.86,3249.17,3260.30,3230.83,3209.04,3197.09,3203.79,3180.63,\n",
    "3233.34,3245.02,3272.58,3261.04,3258.74,3345.09,3375.45,3396.55,3419.51,\n",
    "3426.77,3430.95,3382.40,3367.82,3404.29,3337.11,3289.59,3305.72,3247.03,\n",
    "3288.52,3302.57,3374.93,3439.22,3407.83,3407.83,3407.83,3281.46,3210.94,\n",
    "3212.82,3235.35,3342.77,3328.13,3364.76,3352.58,3319.24,3297.52,3369.26,\n",
    "3347.54,3361.80,3361.20,3328.41,3348.90,3366.87,3396.49,3357.57,3372.96,\n",
    "3425.86,3438.09,3438.09,3491.08,3565.69,3548.52,3537.45,3537.45,3533.21,\n",
    "3593.14,3559.29,3588.57,3564.85,3569.26,3569.26,3516.20,3600.40,3575.44,\n",
    "3621.72,3669.31,3665.43,3626.60,3635.38,3562.73,3596.40,3655.59,3651.59,\n",
    "3684.60,3700.53,3668.61,3671.16,3671.87,3737.16,3752.37,3750.02,3721.18,\n",
    "3730.56,3777.56,3788.54,3748.79,3761.07,3819.52,3820.16,3809.92,3766.89,\n",
    "3834.84,3867.53,3939.73,3946.73,4003.35,4030.10,4026.97,4000.65,4074.30,\n",
    "4142.19,4139.68,4223.69,4203.91,4131.94,4139.96,4297.64,4384.82,4320.52,\n",
    "4368.54,4400.30,4377.70,4458.66,4405.52,4336.98,4302.50,4325.86,4364.25,\n",
    "4428.08,4342.31,4333.15,4377.51,4237.06,4195.53,4077.59,4080.55,4190.45,\n",
    "4251.93,4204.81,4090.14,4076.75,3993.70,3992.03,3897.43,3919.79,4001.81,\n",
    "4127.28,4062.13,4093.43,4073.71,4131.26,4104.57,4028.00,3890.24,3796.61,\n",
    "3869.53,3995.69,3970.44,4004.04,3983.06,4096.85,4091.77,4150.95,4104.93,\n",
    "4135.09,4116.52,4154.89,4262.98,4266.17,4266.17,4326.35,4311.13,4267.40,\n",
    "4179.92,4164.62,4225.27,4215.23,4168.62,4149.92,4049.16,4069.25,4172.47,\n",
    "4124.86,3976.38,3981.44,3871.39,3645.69,3806.66,3748.88,3753.66,3847.73,\n",
    "3784.80,3841.39,3813.88,3715.38,3728.37,3734.79,3697.48,3701.94,3676.65,\n",
    "3816.71,3844.14,3876.90,3931.81,3941.91,3832.10,3850.14,3926.93,3961.97,\n",
    "3972.08,4125.92,4096.40,4074.55,4159.72,4191.81,4208.14,4187.13,4116.70,\n",
    "4016.70,4061.91,4029.08,4150.31,4154.57,4162.92,4055.35,4125.54,4132.79,\n",
    "4132.79,4132.79,4132.79,4266.02,4224.30,4224.30,4224.30,4364.32,4416.95,\n",
    "4360.05,4339.98,4293.64,4237.75,4134.64,4150.01,4145.41,4140.22,4216.24,\n",
    "4290.05,4310.83,4250.47,4238.77,4222.16,4266.34,4316.05,4385.29,4444.53,\n",
    "4442.53,4529.88,4529.18,4509.25,4494.72,4536.91,4519.56,4558.62,4552.46,\n",
    "4509.37,4522.42,4535.56,4627.42,4611.66,4581.08,4583.03,4610.66,4604.55,\n",
    "4704.58,4695.78,4693.86,4781.62,4759.62,4690.52,4676.42,4762.71,4828.89,\n",
    "4852.22,4862.41,4838.67,4872.24,4905.59,4945.91,4908.55,4949.91,5045.16,\n",
    "5014.13,5064.35,5114.13,5029.00,5066.90,5069.89,5097.25,5135.35,5179.04,\n",
    "5254.32,5345.89,5309.67,5267.35,5312.25,5312.25,5312.25,5367.98,5359.24,\n",
    "5292.97,5326.63,5407.93,5373.80,5312.28,5262.57,5144.42,5002.71,5110.88,\n",
    "5083.80,5241.23,5241.23,5337.75,5226.20,5264.62,5164.89,5270.61,5348.75,\n",
    "5307.82,5371.99,5374.11,5414.31,5343.66,5441.00,5514.51,5514.51,5530.19,\n",
    "5592.46,5639.89,5466.88,5507.36,5556.99,5556.99,5583.83,5640.42,5605.38,\n",
    "5724.75,5787.05,5773.77,5799.22,5799.22,5631.34,5581.24,5621.71,5742.83,\n",
    "5689.89,5644.22,5648.11,5748.34,5784.40,5886.72,5870.49,5933.73,5841.83,\n",
    "5910.51,5905.15,5961.45,5942.06,5975.88,6018.89,6000.84,6001.24,6023.31,\n",
    "6101.90,6106.10,6108.00,6162.86,6186.09,6184.10,6081.11,6043.82,6040.58,\n",
    "5854.35,5867.52,5828.74,5906.33,5861.19,5774.38,5718.70,5614.77,5528.12,\n",
    "5598.32,5460.43,5285.78,5386.94,5355.03,5473.72,1678.10,1688.50,1678.60,\n",
    "1684.10,1686.60,1671.60,1682.90,1703.60,1697.50,1716.30,1723.80,1730.50,\n",
    "1727.40,1733.30,1734.00,1728.30,1737.10,1723.10,1723.60,1719.00,1721.20,\n",
    "1725.30,1727.20,1727.20,1731.60,1724.10,1716.90,1723.40,1723.00,1728.40,\n",
    "1722.10,1724.50,1733.60,1739.00,1726.20,1587.40,1630.60,1685.50,1701.30,\n",
    "1718.00,1726.20,1716.60,1725.80,1737.40,1736.60,1732.40,1731.20,1726.90,\n",
    "1727.80,1720.20,1715.40,1708.70,1713.00,1713.50,1718.00,1701.70,1701.70,\n",
    "1684.90,1687.20,1690.60,1684.30,1679.90,1672.90,1663.10,1669.30,1664.70,\n",
    "1672.30,1687.70,1686.80,1686.60,1675.80,1677.40,1673.20,1665.00,1671.30,\n",
    "1672.40,1676.20,1692.60,1696.50,1716.10,1713.30,1705.10,1711.30,1709.80,\n",
    "1688.60,1698.90,1700.00,1693.00,1683.90,1679.20,1673.90,1683.90,1688.40,\n",
    "1693.90,1720.90,1717.90,1733.60,1729.70,1735.60,1734.10,1699.30,1678.60,\n",
    "1675.50,1670.10,1652.20,1635.00,1654.90,1642.00,1638.70,1622.60,1596.10,\n",
    "1612.40,1625.00,1610.50,1606.60,1610.70,1603.10,1591.50,1605.20,1621.40,\n",
    "1622.50,1626.60,1627.40,1614.90,1602.30,1598.30,1627.00,1627.00,1627.00,\n",
    "1655.70,1670.10,1670.10,1670.10,1670.10,1704.00,1711.80,1700.50,1690.30,\n",
    "1715.40,1723.50,1719.40,1734.40,1772.80,1760.30,1747.20,1750.20,1755.30,\n",
    "1754.60,1751.20,1752.50,1769.40,1767.60,1750.00,1747.10,1753.50,1752.80,\n",
    "1752.90,1764.70,1776.80,1779.30,1785.10,1798.20,1794.10,1795.20,1780.40,\n",
    "1789.50,1794.20,1784.40,1800.10,1804.00,1816.20,1810.50,1821.90,1828.20,\n",
    "1840.60,1841.10,1846.30,1850.00,1839.00,1820.20,1815.20,1820.60,1807.10,\n",
    "1791.40,1806.20,1798.70,1818.20,1820.50,1833.30,1837.10,1818.20,1824.10,\n",
    "1830.10,1835.60,1828.70,1839.20,1837.20,1826.70,1838.00,1829.10,1843.10,\n",
    "1850.50,1827.10,1829.10,1848.00,1840.50,1853.80,1874.10,1871.30,1871.30,\n",
    "1871.30,1860.50,1874.70,1880.10,1874.70,1875.60,1859.50,1874.20,1880.10,\n",
    "1880.10,1907.70,1920.50,1937.30,1936.80,1949.10,1963.70,1950.80,1953.50,\n",
    "1945.00,1921.10,1939.10,1928.00,1933.40,1925.70,1931.70,1928.70,1924.50,\n",
    "1914.20,1914.20,1920.60,1923.30,1930.40,1915.20,1916.90,1913.80,1913.80,\n",
    "1899.70,1888.00,1868.80,1879.90,1865.70,1881.30,1873.10,1862.50,1869.30,\n",
    "1846.90,1847.10,1838.30,1845.80,1835.50,1846.60,1854.80,1845.30,1854.50,\n",
    "1870.50,1862.60,1856.60,1837.60,1846.70,1856.50,1841.80,1835.00,1844.40,\n",
    "1838.90,1805.60,1756.60,1786.10,1757.10,1762.80,1756.80,1761.90,1778.50,\n",
    "1812.70,1806.10,1798.10,1794.90,1805.40,1820.30,1819.60,1809.60,1799.90,\n",
    "1800.30,1793.30,1784.80,1791.70,1800.20,1788.60,1775.70,1753.50,1768.20,\n",
    "1727.90,1709.60,1704.60,1740.60,1745.70,1751.70,1747.30,1757.80,1774.20,\n",
    "1774.40,1788.30,1788.00,1779.10,1792.80,1812.00,1872.10,1851.40,1873.40,\n",
    "1889.60,1897.50,1888.80,1900.40,1913.40,1909.90,1910.80,1879.20,1880.20,\n",
    "1878.30,1885.20,1867.60,1788.00,1820.50,1858.20,1870.30,1878.40,1881.50,\n",
    "1893.20,1889.30,1877.30,1884.00,1904.70,1922.70,1908.50,1911.40,1921.10,\n",
    "1930.80,1927.80,1908.30,1905.90,1911.10,1921.60,1933.60,1942.00,1951.50,\n",
    "1955.70,1957.40,1962.30,1946.10,1950.20,1929.70,1913.40,1889.50,1882.80,\n",
    "1895.40,1897.90,1891.50,1880.10,1887.00,1891.40,1914.60,1931.20,1929.20,\n",
    "1924.30,1927.00,1935.00,1955.40,1962.20,1980.70,1987.70,1993.70,2015.70,\n",
    "2005.00,2023.90,2028.50,2044.90,2045.80,2057.30,2061.70,2061.70,2061.70,\n",
    "2092.30,2090.10,2105.40,2105.40,2105.40,2117.70,2128.20,2124.70,2079.90,\n",
    "2074.90,2046.40,2079.80,2076.70,2104.50,2101.30,2084.00,2063.90,2062.70,\n",
    "2089.90,2102.90,2086.00,2085.90,2064.10,2072.70,2091.00,2120.20,2120.40,\n",
    "2117.60,2123.70,2132.20,2137.00,2134.80,2121.40,2127.50,2135.50,2144.80,\n",
    "2131.00,2112.90,2131.30,2117.80,2096.10,2051.50,2065.70,2061.00,2100.60,\n",
    "2120.50,2130.90,2142.40,2139.50,2134.60,2132.20,2150.10,2157.00,2165.00,\n",
    "2127.20,2157.20,2150.80,2139.10,2154.70,2182.40,2161.30,2166.30,2146.80,\n",
    "2135.70,2160.90,2175.70,2188.90,2190.30,2188.40,2190.30,2184.00,2196.00,\n",
    "2184.90,2188.30,2188.30,2188.30,2181.70,2165.70,2160.50,2162.90,2166.30,\n",
    "2170.80,2178.10,2177.30,2162.30,2140.40,2124.70,2138.20,2123.20,2129.70,\n",
    "2152.80,2160.00,2165.80,2165.40,2162.60,2179.10,2191.10,2191.50,2183.30,\n",
    "2186.30,2205.20,2227.20,2227.00,2227.00,2232.90,2237.40,2243.50,2247.50,\n",
    "2267.10,2271.60,2271.60,2253.80,2259.80,2269.00,2284.20,2309.70,2294.50,\n",
    "2312.50,2309.20,2308.60,2293.80,2274.00,2294.60,2323.40,2318.00,2329.50,\n",
    "2335.00,2323.90,2335.80,2347.30,2369.80,2371.90,2376.20,2375.50,2368.80,\n",
    "2364.40,2390.90,2372.00,2397.10,2403.00,2408.70,2418.10,2410.50,2399.90,\n",
    "2396.40,2381.80,2324.50,2313.70,2340.20,2350.50,2388.70,2398.00,2408.70,\n",
    "2401.50,2400.90,2400.70,2429.80,2431.50,2424.90,2423.30,2420.50,2384.50,\n",
    "2411.10,2449.50,2461.00,2478.70,2464.90,2488.00,2480.60,2474.50,2467.30,\n",
    "2472.40,2499.70,2475.20,2478.60,2481.00,2488.50,2470.40,2463.80,2438.80,\n",
    "2392.50,2403.40,2397.90,2382.10,2363.60,2365.60,2388.30,2361.80,2374.40,\n",
    "2385.20,2418.40,2431.80,2414.60,2425.80,2445.90,2482.40,2478.30,2485.40,\n",
    "2473.10,2481.60,2490.30,2521.30,2534.80,2528.00,2533.60,2548.50,2552.50,\n",
    "2571.00,2586.40,2612.60,2663.60,2660.70,2668.40,2690.10,2701.40,2685.00,\n",
    "2700.20,2715.90,2720.90,2723.20,2727.10,2742.90,2749.90,2706.60,2654.20,\n",
    "2675.30,2727.10,2742.10,2720.10,2721.10,2717.40,2712.30,2711.10,2727.10,\n",
    "2733.90,2696.50,2702.10,2717.80,2726.80,2741.90,2738.20,2738.50,2774.30,\n",
    "2787.20,2819.00,2836.40,2834.80,2843.80,2858.40,2861.20,2876.90,2867.80,\n",
    "2850.60,2867.70,2889.50,2909.00,2918.00,2942.40,2967.40,2967.40,2972.60,\n",
    "2930.90,2934.20,2957.60,2957.60,2996.20,2999.20,3009.40,3021.90,3042.90,\n",
    "3015.90,3026.60,2999.00,2949.90,2990.60,3011.10,3037.50,3049.40,3045.90,\n",
    "3039.30,3041.30,3066.50,3091.30,3095.20,3140.70,3178.40,3148.70,3169.10,\n",
    "3151.90,3166.60,3089.80,3097.20,3054.20,3012.20,3012.20,2947.10,2947.10,\n",
    "2947.10,3033.40,3025.90,2997.60,2982.80,3027.50,2958.40,2929.30,2888.20,\n",
    "2847.40,2768.50,2803.40,2865.20,2918.70,2902.40,2858.50,2861.20,2831.60,\n",
    "2870.50,2906.90,2887.10,2887.70,2843.50,2804.30,2824.70,2857.00,2850.80,\n",
    "2831.80,2862.40,2827.40,2814.50,2794.80,2794.80,2794.80,2807.30,2830.20,\n",
    "2860.90,2873.40,2884.00,2887.80,2877.70,2843.70,2872.90,2869.10,2837.10,\n",
    "2818.70,2781.60,2787.90,2763.50,2776.20,2791.30,2768.90,2736.30,2765.20,\n",
    "2755.90,2705.60,2682.20,2641.40,2569.50,2629.00,2633.00,2633.00,2678.70,\n",
    "2709.00,2727.10,2740.60,2725.80,2732.70,2732.70,2692.00,2673.10,2689.20,\n",
    "2711.90,2742.90,2722.90,2731.50,2725.90,2728.40,2781.40,2778.10,2801.10,\n",
    "2777.20,2763.80,2744.20,2740.00,2701.80,2666.60,2627.60,2545.00,2544.20,\n",
    "2595.70,2626.70,2577.20,2561.40,2604.40,2631.20,2608.80,2588.90,2636.40,\n",
    "2609.70,2598.90,2590.50,2560.30,2562.50,2508.00,2474.50,2528.30,2514.90,\n",
    "2494.70,2521.60,2562.30,2579.40,2599.20,2601.20,2604.40,2544.90,2559.30,\n",
    "2579.50,2579.50,2629.70,2620.70,2615.30,2600.80,2617.50,2585.50,2591.40,\n",
    "2588.80,2580.50,2570.60,2588.70,2599.30,2582.70,2557.00,2532.40,2530.90,\n",
    "2541.10,2551.10,2581.30,2635.20,2635.70,2645.60,2628.40,2672.00,2674.50,\n",
    "2652.40,2662.50,2664.10,2642.10,2643.00,2658.80,2637.70,2628.60,2603.30,\n",
    "2614.70,2593.00,2594.00,2602.90,2609.10,2586.10,2581.00,2590.00,2558.00,\n",
    "2534.40,2499.50,2522.50,2480.40,2484.80,2496.90,2553.40,2570.20,2562.70,\n",
    "2593.30,2585.30,2575.60,2542.50,2529.80,2530.90,2508.60,2525.20,2494.70,\n",
    "2477.20,2458.60,2490.50,2506.50,2503.90,2500.00,2534.80,2541.00,2557.90,\n",
    "2543.90,2590.40,2602.70,2597.80,2590.90,2591.90,2609.40,2600.90,2606.50,\n",
    "2607.00,2571.80,2546.10,2568.60,2572.50,2579.40,2584.70,2594.90,2576.00,\n",
    "2577.50,2611.00,2589.10,2584.30,2589.30,2576.00,2562.80,2566.00,2581.40,\n",
    "2598.00,2604.70,2600.70,2614.70,2636.10,2649.80,2651.00,2651.00,2673.50,\n",
    "2656.20,2628.80,2628.80,2628.80,2612.30,2632.40,2613.10,2622.30,2617.30,\n",
    "2600.40,2597.00,2600.50,2600.20,2591.60,2582.80,2593.60,2595.50,2574.60,\n",
    "2525.30,2534.80,2525.50,2554.70,2552.40,2540.20,2536.90,2560.80,2563.70,\n",
    "2589.40,2621.40,2628.00,2617.40,2636.90,2635.40,2636.00,2642.40,2636.00,\n",
    "2621.00,2601.00,2597.20,2609.60,2610.00,2632.10,2623.30,2607.50,2600.40,\n",
    "2619.20,2617.20,2586.50,2553.20,2543.10,2515.80,2461.50,2467.70,2450.30,\n",
    "2463.30,2475.00,2491.70,2497.50,2516.00,2505.50,2501.90,2480.70,2526.60,\n",
    "2518.10,2495.60,2495.00,2533.10,2508.90,2511.10,2536.20,2536.30,2556.10,\n",
    "2559.30,2561.20,2563.10,2562.40,2560.30,2560.30,2560.30,2547.10,2516.80,\n",
    "2544.20,2560.80,2554.80,2561.10,2574.40,2567.00,2597.20,2597.20,2621.40,\n",
    "2618.60,2641.70,2650.50,2658.80,2655.60,2661.40,2701.00,2728.20,2739.00,\n",
    "2746.60,2739.80,2727.70,2701.00,2751.20,2750.40,2778.50,2778.50,2751.70,\n",
    "2762.50,2779.40,2786.40,2807.80,2805.30,2805.30,2809.70,2819.60,2806.80,\n",
    "2795.30,2802.30,2800.90,2798.10,2800.20,2775.40,2803.00,2805.60,2816.80,\n",
    "2843.30,2837.70,2830.30,2845.10,2836.80,2845.60,2825.30,2827.50,2847.50,\n",
    "2843.70,2833.70,2848.40,2842.90,2847.30,2867.90,2869.70,2863.40,2892.30,\n",
    "2875.10,2856.20,2822.20,2830.20,2836.60,2833.20,2827.10,2824.70,2833.10,\n",
    "2826.80,2826.80,2852.30,2814.30,2807.10,2800.60,2797.40,2781.30,2802.60,\n",
    "2820.10,2807.20,2838.40,2880.60,2880.00,2889.50,2886.70,2900.80,2896.80,\n",
    "2887.10,2893.80,2883.30,2887.30,2915.70,2908.80,2918.30,2952.70,2971.10,\n",
    "2999.60,2989.10,2989.20,2986.30,2990.50,3016.80,3011.60,3025.40,3008.10,\n",
    "3033.50,3029.00,3039.10,2994.70,3015.30,3045.50,3009.80,3000.60,3014.80,\n",
    "3039.00,3049.00,3036.50,3036.60,3054.00,3064.00,3050.00,3073.00,3083.70,\n",
    "3109.20,3116.30,3112.30,3135.40,3124.50,3120.40,3041.70,3062.30,3078.90,\n",
    "3080.00,3026.60,3057.90,3108.20,3128.50,3123.40,3137.60,3123.20,3133.80,\n",
    "3132.60,3150.10,3130.40,3121.40,3133.00,3124.80,3148.40,3152.50,3182.20,\n",
    "3183.90,3201.00,3209.20,3220.10,3251.00,3229.50,3245.90,3251.60,3261.20,\n",
    "3278.40,3278.50,3281.50,3245.70,3246.60,3261.60,3280.90,3273.40,3272.20,\n",
    "3289.80,3251.60,3217.70,3254.30,3255.00,3277.90,3277.90,3277.90,3317.10,\n",
    "3297.70,3297.70,3297.70,3297.70,3384.50,3395.80,3376.10,3368.10,3361.50,\n",
    "3314.80,3284.10,3292.90,3233.90,3254.80,3219.30,3257.80,3253.10,3249.90,\n",
    "3219.00,3221.30,3211.20,3191.40,3198.20,3236.80,3248.70,3279.90,3270.00,\n",
    "3221.70,3253.80,3262.70,3245.60,3242.70,3253.10,3260.10,3266.10,3272.20,\n",
    "3280.30,3270.60,3243.50,3253.00,3264.40,3296.20,3298.60,3309.90,3360.50,\n",
    "3354.80,3385.50,3400.60,3383.40,3408.30,3581.90,3549.70,3506.20,3540.50,\n",
    "3558.30,3578.40,3561.10,3583.60,3605.10,3611.10,3629.30,3647.70,3677.00,\n",
    "3658.10,3671.00,3640.30,3646.50,3654.30,3648.30,3606.70,3611.10,3611.10,\n",
    "3611.10,3594.40,3601.50,3566.90,3575.50,3589.60,3607.50,3603.90,3601.20,\n",
    "3628.10,3673.20,3647.30,3668.40,3668.10,3696.00,3658.20,3651.00,3651.00,\n",
    "3635.80,3611.20,3591.60,3583.60,3534.10,3521.60,3556.90,3557.80,3582.40,\n",
    "3572.50,3572.50,3593.00,3584.00,3587.30,3550.00,3547.40,3572.20,3572.20,\n",
    "3583.80,3558.20,3537.70,3556.10,3544.60,3568.10,3572.00,3585.50,3547.90,\n",
    "3575.80,3575.60,3600.90,3607.40,3593.90,3600.10,3628.30,3643.60,3655.40,\n",
    "3687.30,3701.50,3699.60,3723.50,3703.00,3732.90,3728.20,3750.80,3757.00,\n",
    "3771.30,3731.20,3732.80,3773.40,3788.00,3810.00,3785.80,3755.40,3678.10,\n",
    "3656.20,3649.20,3661.50,3566.10,3585.20,3482.60,3537.40,3537.80,3549.50,\n",
    "3518.20,3494.40,3494.40,3604.60,3623.30,3629.00,3662.60,3653.40,3643.20,\n",
    "3623.10,3630.20,3650.70,3646.30,3670.50,3664.40,3698.20,3683.80,3713.00,\n",
    "3725.40,3714.60,3722.40,3692.60,3682.60,3646.30,3654.70,3623.90,3634.20,\n",
    "3627.10,3637.80,3684.40,3694.20,3678.90,3687.20,3716.80,3722.70,3690.00,\n",
    "3690.10,3694.90,3694.90,3635.50,3661.20,3697.70,3699.50,3696.60,3736.40,\n",
    "3737.50,3760.20,3771.60,3771.60,3813.70,3818.10,3807.90,3797.30,3805.20,\n",
    "3813.70,3822.20,3790.20,3793.20,3803.30,3788.20,3775.30,3742.90,3753.60,\n",
    "3758.70,3763.50,3732.00,3723.10,3725.30,3736.10,3749.20,3784.80,3815.40,\n",
    "3811.50,3812.00,3827.60,3829.80,3825.70,3856.40,3897.90,3888.30,3892.60,\n",
    "3883.30,3861.50,3882.80,3891.70,3878.20,3845.30,3884.10,3902.50,3874.00,\n",
    "3924.50,3910.60,3913.80,3835.50,3874.00,3885.40,3857.60,3860.00,3839.30,\n",
    "3869.20,3850.40,3874.00,3880.80,3890.10,3875.50,3869.80,3869.80,3869.80,\n",
    "3922.20,3948.30,3942.20,3942.20,3942.20,3940.10,3923.80,3922.90,3944.90,\n",
    "3966.20,3947.40,3975.50,3983.60,3979.60,4007.10,4019.90,4009.50,4023.10,\n",
    "4115.40,4161.00,4125.50,4127.30,4182.30,4169.70,4209.10,4272.20,4282.80,\n",
    "4296.50,4305.50,4309.80,4357.90,4384.30,4408.40,4444.10,4436.30,4464.20,\n",
    "4514.60,4490.70,4525.50,4530.80,4522.50,4463.20,4503.90,4539.00,4519.70,\n",
    "4487.60,4460.10,4513.70,4547.10,4605.20,4638.90,4684.40,4677.10,4676.20,\n",
    "4609.90,4636.20,4556.50,4519.90,4535.10,4442.90,4491.30,4497.30,4558.60,\n",
    "4620.50,4659.20,4659.20,4659.20,4501.70,4488.70,4463.90,4471.50,4588.00,\n",
    "4582.60,4634.90,4626.60,4604.20,4586.30,4643.40,4625.60,4665.70,4699.10,\n",
    "4740.10,4752.30,4781.10,4836.10,4772.30,4793.30,4855.10,4897.60,4897.60,\n",
    "4953.50,5029.60,4988.40,5016.00,5016.00,5004.70,5042.50,5084.20,5134.30,\n",
    "5141.70,5157.50,5157.50,5081.00,5178.60,5176.40,5181.00,5196.70,5190.00,\n",
    "5133.10,5132.10,5041.60,5150.00,5207.20,5238.50,5251.20,5320.00,5368.80,\n",
    "5361.90,5308.60,5364.20,5384.60,5362.00,5345.90,5405.00,5510.30,5561.80,\n",
    "5587.80,5576.10,5662.40,5669.90,5700.30,5620.60,5654.80,5674.30,5804.90,\n",
    "5846.50,5947.00,6012.60,5977.10,5885.40,5801.50,5845.80,5844.70,5927.50,\n",
    "5868.30,5737.10,5620.50,5677.10,5869.90,5849.20,5847.00,5888.00,5842.10,\n",
    "5929.50,5898.20,5898.20,5771.00,5765.20,5812.10,5922.10,5864.80,5825.60,\n",
    "5808.40,5682.10,5579.50,5498.50,5405.60,5580.10,5690.10,5668.80,5475.80,\n",
    "5473.90,5363.30,5409.60,5217.30,5216.70,5271.50,5447.50,5478.60,5478.10,\n",
    "5532.90,5505.30,5445.10,5356.70,5280.80,5281.90,5321.70,5417.80,5550.40,\n",
    "5629.00,5611.00,5705.10,5730.40,5732.50,5667.10,5716.60,5691.80,5673.60,\n",
    "5754.70,5825.00,5929.00,5897.40,5846.90,5822.30,5732.20,5699.50,5792.80,\n",
    "5836.30,5815.90,5806.80,5751.60,5777.20,5862.90,5803.20,5651.80,5689.50,\n",
    "5533.50,5279.70,5479.00,5370.90,5467.20,5581.60,5538.20,5601.60,5557.40,\n",
    "5438.60,5459.70,5483.90,5434.00,5418.20,5437.00,5565.00,5574.20,5571.70,\n",
    "5650.40,5725.50,5645.70,5666.30,5738.30,5772.40,5775.90,5875.10,5919.90,\n",
    "5922.70,5969.50,6009.00,6095.30,6103.20,6056.60,6021.80,6018.70,5986.60,\n",
    "6092.70,6122.10,6115.10,5989.90,6049.30,6044.70,6046.70,6046.70,6046.70,\n",
    "6190.40,6267.60,6265.50,6265.50,6265.50,6397.00,6375.70,6390.00,6330.20,\n",
    "6251.80,6062.10,6169.30,6149.80,6148.50,6274.00,6340.40,6397.50,6391.40,\n",
    "6356.10,6391.00,6411.00,6424.00,6508.70,6530.40,6582.60,6688.00,6720.70,\n",
    "6708.90,6772.00,6857.10,6828.40,6860.80,6931.60,6856.00,6898.90,6905.30,\n",
    "6990.50,6966.20,6953.20,6986.70,6986.10,6945.00,7065.40,7118.60,7153.10,\n",
    "7273.00,7259.50,7130.50,7077.30,7197.20,7187.50,7246.50,7276.70,7267.90,\n",
    "7328.00,7261.20,7236.50,7132.40,7143.80,7300.50,7341.00,7407.40,7472.10,\n",
    "7415.90,7530.30,7536.30,7585.50,7615.50,7638.80,7725.90,7827.70,7744.30,\n",
    "7588.10,7624.10,7624.10,7624.10,7662.90,7616.30,7500.10,7453.70,7500.10,\n",
    "7369.10,7308.90,7265.50,7232.30,7053.50,7180.10,7241.80,7401.40,7401.40,\n",
    "7640.80,7596.20,7610.80,7536.00,7587.10,7677.50,7627.30,7582.80,7550.60,\n",
    "7519.40,7371.40,7483.20,7495.80,7495.80,7542.70,7657.10,7731.90,7633.50,\n",
    "7605.00,7656.10,7656.10,7657.50,7676.30,7592.90,7699.50,7743.40,7716.80,\n",
    "7652.60,7498.40,7417.40,7342.70,7388.70,7562.70,7488.00,7518.60,7511.80,\n",
    "7624.80,7667.90,7794.70,7816.90,7881.90,7882.00,8038.20,8047.30,8099.00,\n",
    "8166.00,8160.00,8227.20,8205.00,8192.40,8141.90,8180.50,8158.10,8126.50,\n",
    "8288.20,8400.80,8412.00,8340.70,8229.20,8205.70,7998.70,8093.00,8102.70,\n",
    "8205.50,8239.50,8139.20,8170.20,7943.20,7846.20,7952.90,7721.30,7447.90,\n",
    "7607.50,7552.60,7676.30,1772.80,1750.50,1718.00,1708.10,1723.10,1714.30,\n",
    "1734.50,1757.40,1754.00,1754.30,1759.80,1755.50,1758.10,1757.50,1763.50,\n",
    "1762.80,1768.90,1778.10,1780.10,1767.70,1757.90,1756.60,1754.70,1766.80,\n",
    "1766.50,1762.20,1759.50,1782.40,1789.50,1783.50,1780.40,1808.80,1820.30,\n",
    "1820.30,1820.30,1687.50,1725.60,1792.90,1819.10,1833.50,1853.40,1849.70,\n",
    "1851.80,1857.70,1864.30,1863.50,1873.20,1860.80,1868.70,1860.40,1855.90,\n",
    "1840.50,1842.60,1861.20,1876.20,1878.30,1878.40,1869.40,1880.40,1885.50,\n",
    "1888.40,1885.20,1877.90,1876.50,1883.80,1880.60,1887.40,1878.30,1867.10,\n",
    "1851.90,1843.60,1848.10,1843.40,1843.60,1833.80,1833.40,1856.90,1863.40,\n",
    "1855.50,1864.20,1846.00,1836.80,1830.40,1831.60,1834.80,1852.10,1849.80,\n",
    "1861.80,1856.70,1856.70,1841.50,1846.90,1836.10,1838.60,1857.60,1857.60,\n",
    "1858.40,1846.80,1868.50,1863.20,1808.30,1765.10,1763.50,1766.00,1741.30,\n",
    "1743.30,1769.00,1757.90,1754.90,1739.70,1708.80,1722.20,1713.90,1703.20,\n",
    "1685.70,1663.40,1636.90,1645.60,1671.60,1688.30,1696.80,1711.70,1706.20,\n",
    "1684.20,1648.50,1633.60,1699.10,1699.10,1722.50,1720.70,1741.90,1765.70,\n",
    "1765.70,1749.90,1770.30,1787.60,1778.70,1785.60,1833.90,1837.40,1824.30,\n",
    "1843.80,1873.60,1860.20,1860.20,1865.90,1867.90,1841.30,1838.70,1849.90,\n",
    "1869.30,1890.60,1879.60,1873.90,1875.30,1857.00,1856.50,1865.80,1860.60,\n",
    "1861.60,1865.60,1864.10,1861.60,1876.50,1865.10,1882.10,1912.20,1915.40,\n",
    "1951.20,1962.40,1976.50,1953.50,1981.30,1985.10,1983.40,1979.70,1983.80,\n",
    "1988.10,1973.00,1966.90,1976.30,1993.90,1968.00,1941.80,1947.10,1929.20,\n",
    "1943.60,1928.20,1922.00,1919.10,1884.60,1896.30,1928.30,1934.80,1923.50,\n",
    "1943.80,1942.40,1928.10,1942.00,1942.70,1974.80,1975.40,1907.50,1943.60,\n",
    "1974.10,1963.30,1972.30,1990.70,1978.20,1978.20,1978.20,1980.40,1983.70,\n",
    "1978.10,1984.90,1995.70,2006.60,2036.70,2031.10,2031.10,2041.60,2046.90,\n",
    "2047.20,2063.40,2063.40,2077.50,2063.60,2053.20,2017.00,2024.00,2051.60,\n",
    "2023.10,2030.80,2016.80,2045.10,2046.30,2029.60,2014.10,2014.10,2033.30,\n",
    "2017.40,2024.90,1992.60,1994.90,1981.60,1981.60,1962.20,1953.70,1928.80,\n",
    "1928.30,1918.10,1931.40,1908.80,1891.80,1913.90,1885.80,1895.80,1899.60,\n",
    "1920.30,1915.30,1907.30,1900.60,1880.90,1873.50,1883.60,1868.50,1879.10,\n",
    "1847.80,1861.80,1859.40,1859.40,1859.40,1853.30,1851.20,1801.80,1767.90,\n",
    "1762.70,1727.50,1734.60,1734.60,1755.40,1769.00,1801.60,1782.60,1754.70,\n",
    "1784.40,1787.60,1798.00,1793.80,1777.30,1755.20,1737.80,1730.10,1722.40,\n",
    "1753.50,1757.30,1736.70,1734.20,1724.20,1744.20,1689.70,1667.70,1667.80,\n",
    "1687.60,1687.50,1684.90,1674.20,1711.40,1780.50,1779.00,1779.30,1763.70,\n",
    "1756.80,1774.20,1802.00,1873.60,1836.20,1859.80,1852.70,1882.90,1826.10,\n",
    "1832.80,1828.90,1829.50,1843.50,1770.30,1731.90,1736.70,1724.00,1683.30,\n",
    "1611.00,1612.50,1654.20,1673.90,1657.30,1655.10,1685.10,1667.90,1650.00,\n",
    "1664.20,1679.10,1731.30,1722.20,1730.70,1766.40,1770.70,1774.50,1749.90,\n",
    "1730.90,1742.40,1742.40,1786.90,1804.10,1804.70,1793.60,1786.70,1798.50,\n",
    "1798.50,1821.50,1796.80,1772.70,1764.40,1759.20,1722.30,1724.20,1674.80,\n",
    "1720.60,1721.00,1739.70,1749.70,1771.40,1792.30,1783.30,1799.40,1781.70,\n",
    "1788.60,1765.90,1791.20,1769.50,1758.70,1738.30,1744.80,1736.70,1735.20,\n",
    "1760.10,1786.30,1824.40,1821.10,1854.60,1854.60,1857.50,1870.30,1858.80,\n",
    "1857.80,1857.80,1843.10,1850.80,1859.60,1844.50,1852.60,1814.60,1796.80,\n",
    "1782.50,1803.50,1827.10,1837.50,1837.70,1818.80,1812.20,1820.40,1779.90,\n",
    "1792.60,1777.40,1780.60,1772.20,1785.90,1787.30,1824.10,1854.40,1908.20,\n",
    "1904.70,1894.10,1893.30,1905.60,1912.00,1899.50,1878.20,1905.00,1926.50,\n",
    "1937.20,1959.20,1944.10,1953.40,1944.60,1983.70,1998.80,2001.50,1995.20,\n",
    "1986.80,1995.10,2004.30,2009.70,1992.40,1988.90,1965.20,1986.00,1975.30,\n",
    "1967.30,1963.50,1962.70,1939.30,1952.20,1954.60,2001.40,2025.80,2033.90,\n",
    "2035.90,2031.40,2005.90,1990.80,1974.70,1995.30,1984.00,1986.90,1986.90,\n",
    "1986.90,2018.10,2015.40,1988.60,1986.70,1968.90,1949.30,1931.90,1944.50,\n",
    "1916.60,1911.60,1927.40,1942.50,1920.60,1939.00,1937.00,1923.60,1926.30,\n",
    "1920.50,1878.60,1877.20,1854.50,1872.70,1879.90,1851.70,1835.70,1846.40,\n",
    "1836.80,1836.80,1836.80,1861.40,1891.10,1890.40,1904.60,1888.70,1888.70,\n",
    "1872.80,1875.80,1867.90,1859.70,1887.90,1893.70,1915.20,1911.20,1920.40,\n",
    "1916.80,1897.90,1918.80,1900.30,1910.30,1929.20,1935.30,1942.40,1963.30,\n",
    "1960.80,1991.00,1977.50,1971.90,1960.20,1941.20,1925.40,1935.10,1943.70,\n",
    "1980.40,1985.70,1992.20,1991.20,1991.20,1963.10,1974.90,1981.70,1968.40,\n",
    "1947.50,1965.70,1995.00,2006.20,1998.10,1989.50,2036.00,2085.90,2129.00,\n",
    "2110.60,2101.40,2115.30,2149.80,2138.50,2139.80,2167.40,2161.90,2148.00,\n",
    "2148.00,2136.30,2160.80,2139.20,2128.20,2111.40,2123.40,2159.30,2173.60,\n",
    "2183.90,2205.70,2216.50,2191.90,2185.10,2156.10,2158.00,2137.30,2129.40,\n",
    "2108.80,2108.40,2119.10,2134.10,2078.50,2075.60,2099.50,2107.40,2094.40,\n",
    "2080.00,2057.50,2092.60,2108.60,2120.00,2126.80,2114.60,2116.70,2128.70,\n",
    "2158.80,2164.50,2147.40,2156.40,2138.70,2126.90,2127.30,2113.90,2139.30,\n",
    "2145.00,2147.30,2149.70,2199.70,2231.90,2227.70,2210.40,2192.00,2196.00,\n",
    "2182.00,2182.00,2169.70,2171.20,2136.00,2081.00,2084.80,2112.90,2087.30,\n",
    "2087.30,2096.90,2117.90,2115.90,2148.00,2149.70,2145.20,2082.60,2071.50,\n",
    "2070.60,2118.40,2120.60,2119.30,2110.10,2154.00,2160.50,2188.40,2186.70,\n",
    "2176.10,2205.30,2211.40,2198.10,2196.30,2156.50,2162.60,2160.30,2196.40,\n",
    "2223.50,2215.90,2225.80,2243.00,2251.50,2276.60,2264.60,2281.90,2281.20,\n",
    "2268.20,2290.60,2274.30,2249.60,2275.10,2307.60,2317.30,2331.30,2281.90,\n",
    "2252.20,2262.30,2234.80,2247.40,2274.70,2257.80,2244.00,2274.50,2278.30,\n",
    "2282.40,2281.00,2313.20,2334.40,2331.30,2355.90,2322.00,2329.20,2287.10,\n",
    "2299.90,2302.10,2296.80,2275.10,2281.60,2258.00,2258.00,2281.20,2251.80,\n",
    "2215.20,2226.70,2252.00,2208.30,2199.00,2238.10,2183.10,2144.70,2144.70,\n",
    "2178.70,2219.90,2216.40,2199.70,2184.60,2175.00,2215.00,2258.50,2242.70,\n",
    "2247.80,2221.30,2202.70,2200.70,2200.20,2152.60,2136.60,2144.50,2123.40,\n",
    "2083.90,2081.90,2081.90,2081.90,2100.30,2128.20,2119.60,2114.80,2145.30,\n",
    "2148.60,2152.40,2139.10,2159.60,2160.10,2136.00,2102.70,2092.00,2135.20,\n",
    "2116.30,2130.90,2147.30,2150.30,2166.00,2186.20,2179.00,2141.60,2162.60,\n",
    "2158.20,2139.40,2165.00,2176.70,2176.70,2187.00,2187.80,2195.20,2184.00,\n",
    "2165.40,2155.40,2155.40,2133.30,2084.40,2091.90,2050.70,2052.50,2029.90,\n",
    "1979.70,2007.40,2041.70,2037.20,2023.70,2046.80,2028.40,2020.70,1977.70,\n",
    "1992.00,1966.40,1942.80,1936.00,1903.00,1890.80,1917.00,1939.00,1907.00,\n",
    "1911.60,1925.80,1936.30,1892.00,1872.90,1866.20,1878.70,1889.00,1920.80,\n",
    "1920.80,1949.80,1942.10,1974.60,1974.60,1974.60,2025.10,2052.30,2043.70,\n",
    "2053.80,2041.40,2059.80,2076.80,2055.70,2053.40,2075.00,2069.60,2117.20,\n",
    "2115.00,2096.50,2107.10,2106.30,2074.50,2064.20,2038.90,2007.00,2007.00,\n",
    "2012.40,2035.00,2010.50,2001.30,1972.60,2000.60,2006.30,2026.50,2062.70,\n",
    "2075.30,2060.40,2069.10,2034.90,2020.40,1998.20,1961.50,1964.20,1983.40,\n",
    "1948.80,1966.80,1969.40,1952.90,1977.30,1924.60,1922.90,1919.30,1897.20,\n",
    "1899.40,1927.40,1902.70,1901.30,1905.00,1876.20,1879.30,1852.80,1876.10,\n",
    "1833.70,1843.40,1856.40,1898.30,1919.00,1918.10,1955.60,1933.00,1906.40,\n",
    "1898.60,1876.30,1867.40,1842.10,1841.60,1824.40,1831.50,1858.10,1905.70,\n",
    "1905.70,1905.70,1873.60,1911.10,1931.70,1906.10,1921.50,1943.90,1948.40,\n",
    "1948.40,1941.10,1954.50,1950.20,1927.50,1926.50,1927.80,1911.40,1893.10,\n",
    "1934.70,1945.90,1952.40,1940.00,1975.90,1964.00,1982.70,1973.70,1969.00,\n",
    "1969.80,1954.10,1937.00,1919.30,1917.10,1930.20,1931.10,1924.20,1928.10,\n",
    "1924.70,1940.90,1952.10,1949.90,1966.60,1956.00,1927.80,1894.20,1881.20,\n",
    "1881.20,1885.90,1901.80,1871.50,1886.40,1864.20,1859.20,1849.10,1844.10,\n",
    "1854.00,1872.80,1856.90,1860.30,1837.10,1813.30,1772.80,1780.20,1802.50,\n",
    "1826.30,1814.10,1813.40,1797.90,1827.80,1816.10,1842.40,1872.10,1870.40,\n",
    "1850.90,1874.40,1869.40,1850.10,1856.10,1861.90,1835.00,1822.50,1802.20,\n",
    "1805.60,1804.40,1827.00,1805.70,1802.20,1776.90,1808.40,1807.40,1795.20,\n",
    "1773.30,1748.60,1756.80,1727.10,1743.10,1721.80,1769.00,1738.60,1785.80,\n",
    "1788.80,1811.60,1813.80,1818.00,1795.70,1817.30,1836.10,1837.20,1852.40,\n",
    "1893.00,1859.50,1864.00,1882.80,1872.90,1890.20,1900.40,1880.90,1869.30,\n",
    "1871.90,1881.10,1881.10,1881.10,1855.70,1874.90,1882.00,1928.40,1918.50,\n",
    "1945.90,1942.30,1931.00,1918.50,1918.50,1936.90,1971.10,1946.20,1927.40,\n",
    "1927.40,1988.70,1996.70,2003.60,2017.30,1991.50,2001.30,2004.70,1989.80,\n",
    "1965.50,1979.50,1965.30,1960.70,1960.70,1919.10,1927.80,1927.30,1948.00,\n",
    "1960.80,1971.30,1971.30,1965.90,1974.70,1951.20,1897.00,1907.80,1922.80,\n",
    "1893.70,1920.70,1905.00,1918.40,1896.10,1902.80,1925.20,1895.10,1902.40,\n",
    "1877.70,1865.50,1861.90,1858.80,1879.70,1889.40,1907.80,1889.50,1950.80,\n",
    "1949.40,1961.30,1961.70,1948.30,1948.30,1951.50,1929.00,1931.20,1905.90,\n",
    "1908.90,1926.60,1941.30,1942.50,1947.90,1932.80,1920.00,1917.80,1960.00,\n",
    "1950.80,1957.10,1950.40,1954.70,1943.70,1949.20,1946.20,1946.20,1946.20,\n",
    "1970.40,1967.30,1971.60,1984.40,1963.30,1957.40,1939.20,1937.80,1890.10,\n",
    "1899.50,1921.40,1883.40,1881.70,1900.50,1902.50,1884.80,1861.70,1854.90,\n",
    "1869.70,1873.60,1898.20,1892.40,1880.00,1871.70,1882.50,1863.80,1853.90,\n",
    "1790.70,1800.60,1816.30,1791.80,1767.60,1788.40,1780.70,1800.70,1803.90,\n",
    "1800.30,1809.60,1785.70,1778.00,1794.40,1803.80,1817.00,1790.50,1779.70,\n",
    "1770.70,1757.30,1740.70,1721.10,1724.20,1764.10,1754.10,1742.40,1795.30,\n",
    "1814.00,1814.00,1828.70,1832.10,1822.60,1857.40,1866.30,1852.60,1839.80,\n",
    "1838.20,1838.20,1875.20,1905.10,1890.50,1881.40,1872.90,1875.50,1867.10,\n",
    "1891.00,1889.80,1870.30,1857.30,1828.30,1820.90,1774.90,1814.90,1834.80,\n",
    "1846.80,1856.30,1849.60,1848.90,1833.80,1875.00,1859.30,1820.50,1810.20,\n",
    "1831.20,1834.40,1873.40,1873.40,1866.70,1877.00,1879.10,1872.00,1872.00,\n",
    "1908.40,1943.00,1931.20,1917.70,1916.60,1916.30,1910.10,1897.90,1907.60,\n",
    "1924.40,1952.10,1966.00,1960.10,1964.30,1954.40,1934.10,1946.00,1950.20,\n",
    "1966.70,1980.70,2003.10,2021.00,2024.10,2022.20,1985.60,1988.50,1983.30,\n",
    "1956.20,1960.70,1967.70,1983.30,1956.40,1964.20,1952.50,1939.70,1932.40,\n",
    "1936.90,1953.30,1976.90,1960.90,1974.50,1996.90,1990.80,2017.20,2015.30,\n",
    "2001.90,2005.90,2008.00,1975.50,1948.90,1932.10,1944.30,1962.40,1950.10,\n",
    "1965.00,1967.20,1969.80,1976.90,1974.40,2003.80,2008.00,2030.50,2020.00,\n",
    "2044.80,2055.60,2070.40,2064.00,2075.00,2075.00,2075.00,2081.70,2093.90,\n",
    "2072.50,2074.70,2080.60,2097.30,2075.10,2086.00,2092.50,2116.50,2112.00,\n",
    "2122.10,2116.40,2138.40,2130.80,2146.80,2146.80,2136.80,2115.40,2090.40,\n",
    "2083.70,2083.70,2085.40,2114.80,2100.90,2122.10,2124.60,2124.60,2136.90,\n",
    "2120.60,2129.70,2103.50,2114.50,2117.70,2117.70,2132.90,2117.10,2108.40,\n",
    "2110.10,2121.10,2111.00,2115.40,2133.20,2102.00,2120.80,2137.50,2137.30,\n",
    "2126.20,2111.80,2113.00,2107.90,2100.70,2077.10,2084.20,2097.60,2118.40,\n",
    "2113.30,2112.90,2123.70,2118.80,2111.80,2114.00,2126.80,2098.80,2079.10,\n",
    "2076.60,2081.90,2073.40,2050.60,2029.50,1989.50,1995.10,2007.30,1992.80,\n",
    "1960.30,1982.20,1954.10,1974.70,1962.90,1961.10,1968.50,1995.90,2009.90,\n",
    "2023.40,2013.20,1999.30,1996.70,1997.40,1985.40,1978.20,1980.60,1979.50,\n",
    "1979.50,1979.50,1986.20,2019.30,2000.60,2017.80,2020.80,2020.40,2018.00,\n",
    "2002.90,1977.60,1970.60,1977.00,1971.40,1984.80,1996.20,2004.80,2020.30,\n",
    "2042.10,2038.10,2065.40,2080.40,2086.20,2080.90,2072.70,2082.30,2079.50,\n",
    "2067.10,2081.50,2103.40,2104.10,2107.10,2132.80,2123.20,2141.80,2136.10,\n",
    "2152.70,2151.60,2161.50,2146.70,2135.60,2147.10,2143.60,2168.30,2158.50,\n",
    "2165.30,2185.20,2180.20,2175.60,2148.90,2151.60,2162.40,2150.40,2125.70,\n",
    "2124.80,2140.50,2140.50,2142.20,2187.30,2213.40,2211.80,2205.20,2205.20,\n",
    "2229.10,2217.20,2218.20,2240.30,2228.80,2240.10,2233.40,2233.60,2255.50,\n",
    "2277.10,2275.10,2270.80,2290.30,2315.70,2318.60,2349.10,2308.70,2292.50,\n",
    "2240.70,2255.80,2251.40,2213.30,2212.10,2203.40,2222.60,2193.70,2218.90,\n",
    "2248.70,2278.50,2287.40,2289.60,2289.60,2303.80,2307.00,2318.60,2315.70,\n",
    "2315.70,2257.00,2282.80,2306.70,2301.70,2331.60,2349.10,2327.50,2361.30,\n",
    "2402.10,2388.00,2407.80,2425.10,2406.10,2409.90,2442.50,2461.30,2430.30,\n",
    "2435.20,2482.80,2465.00,2503.10,2516.60,2508.60,2503.10,2541.30,2558.40,\n",
    "2597.50,2595.40,2582.10,2599.30,2628.40,2627.40,2634.50,2617.50,2594.80,\n",
    "2575.20,2562.80,2567.90,2607.70,2602.20,2629.40,2607.80,2600.30,2651.70,\n",
    "2666.20,2698.90,2708.30,2709.20,2686.20,2641.70,2632.10,2645.60,2588.40,\n",
    "2574.00,2596.80,2553.70,2587.10,2579.30,2624.30,2648.70,2656.70,2656.70,\n",
    "2656.70,2581.80,2530.30,2514.50,2518.00,2572.30,2579.00,2617.60,2608.00,\n",
    "2574.60,2566.10,2620.60,2621.00,2615.20,2547.60,2522.70,2514.70,2533.60,\n",
    "2539.80,2536.30,2550.30,2602.90,2639.50,2639.50,2655.30,2672.80,2651.90,\n",
    "2643.30,2643.30,2633.90,2693.10,2719.60,2774.60,2776.00,2784.30,2784.30,\n",
    "2751.10,2786.40,2741.70,2762.90,2654.70,2680.30,2583.20,2579.20,2583.90,\n",
    "2601.50,2624.50,2635.40,2690.90,2719.30,2686.20,2664.20,2696.20,2760.30,\n",
    "2808.50,2795.90,2762.60,2751.70,2739.70,2757.10,2762.20,2784.80,2867.40,\n",
    "2893.60,2891.00,2858.30,2944.00,2909.50,2937.00,2934.50,2947.70,2929.80,\n",
    "2950.60,2929.10,2941.60,2941.60,2950.70,2988.00,2958.60,2876.70,2874.10,\n",
    "2921.10,3003.50,2973.50,3025.90,3022.20,3023.60,3069.30,3075.70,3049.50,\n",
    "2992.40,2984.10,3037.10,3056.30,2996.30,2983.40,2998.60,2924.00,2921.80,\n",
    "2921.80,2870.10,2936.20,2979.30,2957.20,2904.20,2898.60,2869.30,2871.70,\n",
    "2828.40,2770.50,2805.80,2921.20,2918.00,2927.00,2924.50,2940.90,2919.70,\n",
    "2874.60,2843.60,2834.10,2898.60,2940.60,2944.00,2978.40,2977.20,3017.50,\n",
    "2997.20,3023.70,3005.40,2985.60,2989.00,3008.30,3054.90,3052.10,3094.00,\n",
    "3078.00,3064.40,3024.10,2960.70,2955.10,3002.90,3002.50,2992.20,2992.90,\n",
    "2958.00,2946.70,2989.90,2958.10,2856.90,2849.00,2769.60,2651.30,2818.00,\n",
    "2739.50,2739.30,2788.00,2774.90,2822.40,2781.80,2707.10,2707.10,2707.10,\n",
    "2694.50,2700.70,2698.90,2773.00,2782.60,2790.60,2821.20,2861.70,2802.50,\n",
    "2786.30,2811.70,2829.00,2854.40,2918.50,2913.10,2902.40,2914.50,2910.10,\n",
    "2932.50,2959.40,2932.20,2828.50,2830.30,2838.30,2912.20,2893.30,2894.50,\n",
    "2822.90,2869.70,2858.10,2874.10,2874.10,2875.10,2939.50,2975.50,2998.90,\n",
    "2998.90,3038.70,3072.80,3037.70,3006.70,2954.90,2919.80,2862.50,2902.90,\n",
    "2919.80,2932.80,2976.10,2987.00,3008.30,2998.10,2988.60,2966.20,3000.50,\n",
    "3052.00,3088.30,3133.80,3172.10,3187.50,3188.40,3166.30,3189.60,3216.70,\n",
    "3220.90,3235.80,3240.00,3178.70,3187.70,3225.10,3280.50,3281.70,3250.60,\n",
    "3262.50,3273.50,3262.30,3348.20,3397.00,3421.90,3446.70,3414.90,3381.30,\n",
    "3395.80,3483.20,3525.90,3521.50,3539.40,3526.60,3540.20,3598.30,3661.30,\n",
    "3652.50,3688.70,3688.90,3680.10,3738.50,3818.70,3783.80,3810.20,3800.20,\n",
    "3875.30,3883.30,3935.90,3932.00,3986.80,3903.30,3873.90,3894.50,3894.50,\n",
    "3894.50,3867.70,3884.60,3845.90,3861.60,3885.70,3860.40,3835.10,3822.10,\n",
    "3788.70,3689.40,3777.20,3726.20,3867.90,3867.90,3979.30,3945.50,3947.50,\n",
    "3912.80,3912.80,4007.30,3986.10,4018.50,4012.00,3990.20,3945.30,3980.80,\n",
    "4047.90,4047.90,4049.80,4108.70,4115.90,4017.40,4014.90,4041.20,4041.20,\n",
    "4087.00,4149.40,4119.00,4185.10,4204.60,4201.90,4208.60,4141.60,4050.80,\n",
    "4005.30,4013.30,4092.90,4052.30,4027.30,4018.60,4065.00,4126.30,4203.80,\n",
    "4215.70,4248.20,4203.50,4260.70,4252.10,4304.40,4311.10,4333.10,4339.90,\n",
    "4319.20,4256.40,4256.40,4256.40,4344.30,4358.10,4388.50,4368.90,4322.10,\n",
    "4220.10,4235.90,4205.40,4139.50,4122.40,4139.20,4197.60,4177.30,4095.00,\n",
    "4047.90,3976.40,3968.60,4041.90,3939.50,3846.00,3945.70,3951.70,3995.00,\n",
    "2443.60,2460.20,2448.20,2470.40,2484.70,2466.80,2487.90,2508.40,2510.50,\n",
    "2497.40,2532.50,2556.80,2561.00,2547.30,2541.50,2558.50,2587.90,2580.50,\n",
    "2579.60,2589.30,2595.00,2595.60,2588.80,2591.70,2601.70,2585.40,2573.30,\n",
    "2597.40,2600.60,2570.60,2569.40,2584.90,2608.80,2617.20,2621.00,2540.50,\n",
    "2554.50,2601.90,2623.00,2640.70,2640.70,2619.80,2624.20,2638.20,2645.70,\n",
    "2679.60,2669.00,2664.60,2663.30,2667.40,2653.20,2630.80,2626.60,2641.90,\n",
    "2625.80,2606.00,2594.40,2583.60,2588.70,2600.30,2579.50,2576.60,2597.80,\n",
    "2595.60,2599.00,2621.70,2645.60,2644.20,2625.60,2624.60,2596.20,2599.50,\n",
    "2584.10,2570.80,2555.00,2574.50,2576.70,2579.00,2588.70,2601.10,2575.70,\n",
    "2559.50,2561.10,2528.30,2514.70,2558.50,2553.30,2577.10,2566.00,2549.50,\n",
    "2527.80,2540.90,2534.20,2538.00,2559.00,2554.90,2575.50,2546.50,2561.60,\n",
    "2546.60,2502.90,2463.10,2472.60,2463.50,2446.30,2456.20,2471.50,2447.50,\n",
    "2428.60,2420.20,2414.90,2420.20,2423.80,2407.00,2388.70,2409.60,2392.00,\n",
    "2380.20,2423.30,2451.60,2440.80,2432.90,2413.60,2391.60,2358.10,2345.40,\n",
    "2384.40,2384.40,2384.40,2418.70,2420.00,2493.10,2493.10,2492.80,2504.10,\n",
    "2493.20,2482.90,2467.10,2497.90,2477.90,2490.10,2516.30,2537.10,2541.60,\n",
    "2536.70,2544.90,2543.40,2522.00,2525.30,2510.40,2539.90,2552.00,2546.50,\n",
    "2550.80,2571.20,2560.20,2556.80,2547.10,2534.30,2517.20,2538.40,2537.10,\n",
    "2523.70,2522.60,2513.90,2541.00,2555.90,2536.70,2543.40,2542.30,2559.70,\n",
    "2546.80,2565.00,2562.00,2562.10,2554.30,2565.40,2558.40,2538.30,2533.10,\n",
    "2550.70,2574.80,2522.40,2493.30,2476.00,2470.70,2491.20,2464.70,2467.60,\n",
    "2456.60,2441.00,2458.70,2464.90,2472.20,2447.90,2452.90,2440.10,2408.60,\n",
    "2405.40,2382.70,2400.90,2404.20,2393.20,2436.40,2572.60,2591.00,2600.50,\n",
    "2640.20,2638.60,2638.60,2638.60,2625.80,2607.80,2609.80,2643.00,2658.20,\n",
    "2651.00,2664.90,2654.10,2659.80,2659.80,2662.20,2698.70,2701.90,2725.70,\n",
    "2737.80,2722.40,2720.50,2694.70,2682.60,2703.60,2700.60,2711.90,2702.00,\n",
    "2715.00,2715.00,2704.60,2698.60,2694.20,2707.60,2697.60,2705.90,2680.90,\n",
    "2681.90,2668.50,2645.80,2635.40,2636.10,2614.10,2603.70,2593.60,2616.30,\n",
    "2598.40,2562.70,2584.80,2550.30,2560.60,2532.60,2557.30,2534.10,2515.80,\n",
    "2521.20,2493.90,2476.10,2497.10,2469.00,2493.70,2472.60,2497.90,2490.80,\n",
    "2478.30,2484.00,2486.40,2483.40,2431.90,2403.70,2415.60,2387.90,2399.50,\n",
    "2377.20,2348.00,2373.40,2423.20,2411.60,2399.60,2420.20,2407.50,2392.80,\n",
    "2377.60,2350.10,2325.70,2309.60,2303.10,2318.00,2356.80,2376.10,2354.70,\n",
    "2363.50,2359.40,2365.70,2311.10,2281.00,2285.00,2311.60,2312.60,2312.60,\n",
    "2298.40,2313.00,2381.90,2362.20,2372.20,2337.70,2327.50,2340.60,2370.90,\n",
    "2422.10,2370.00,2378.30,2483.90,2567.00,2560.10,2586.00,2580.50,2621.20,\n",
    "2601.00,2560.00,2565.50,2553.00,2572.30,2549.70,2446.30,2488.40,2517.10,\n",
    "2538.80,2541.20,2557.20,2584.70,2574.70,2546.60,2563.90,2562.20,2617.00,\n",
    "2645.70,2658.10,2669.70,2661.60,2669.80,2650.40,2642.30,2658.30,2687.80,\n",
    "2705.60,2691.70,2711.10,2702.70,2695.40,2714.60,2696.80,2726.40,2697.50,\n",
    "2679.60,2679.20,2704.00,2706.20,2732.40,2722.90,2727.10,2709.60,2741.80,\n",
    "2760.10,2778.80,2792.00,2764.10,2771.00,2759.40,2754.50,2769.80,2750.70,\n",
    "2726.50,2716.20,2721.80,2717.90,2732.80,2740.30,2789.70,2807.70,2842.00,\n",
    "2827.40,2827.50,2827.50,2827.50,2847.80,2832.50,2846.50,2846.50,2861.50,\n",
    "2833.60,2826.00,2816.50,2799.20,2773.40,2757.90,2745.30,2759.20,2765.10,\n",
    "2763.10,2737.60,2748.70,2773.30,2781.20,2771.90,2835.70,2832.50,2816.90,\n",
    "2807.20,2851.60,2834.40,2873.80,2865.90,2862.90,2870.00,2831.30,2816.40,\n",
    "2834.30,2843.00,2845.90,2812.20,2814.00,2837.70,2840.00,2838.30,2818.00,\n",
    "2817.00,2828.70,2868.00,2882.60,2882.30,2918.60,2904.80,2916.60,2957.30,\n",
    "2949.90,2956.70,2953.40,2915.90,2922.40,2919.30,2889.90,2883.30,2900.10,\n",
    "2863.90,2861.10,2860.60,2852.80,2852.90,2846.50,2861.00,2878.70,2878.40,\n",
    "2869.90,2838.80,2832.20,2822.10,2821.80,2821.80,2821.80,2846.80,2842.10,\n",
    "2839.70,2824.40,2830.00,2856.10,2869.60,2881.10,2843.80,2822.30,2832.70,\n",
    "2797.30,2786.80,2813.10,2813.10,2812.60,2796.50,2786.30,2793.70,2829.70,\n",
    "2836.10,2860.80,2849.30,2847.00,2858.10,2847.30,2819.70,2816.80,2812.20,\n",
    "2825.60,2837.70,2846.90,2855.30,2840.70,2840.70,2849.20,2863.00,2852.80,\n",
    "2829.90,2844.80,2844.40,2866.90,2860.00,2861.80,2885.50,2870.00,2883.00,\n",
    "2875.70,2879.40,2903.40,2907.60,2900.70,2894.70,2887.50,2897.00,2886.00,\n",
    "2900.00,2888.80,2857.70,2838.50,2848.10,2848.30,2845.90,2843.20,2830.90,\n",
    "2837.10,2832.30,2831.70,2833.00,2842.90,2823.90,2814.10,2820.10,2827.70,\n",
    "2844.20,2879.40,2884.20,2917.60,2926.50,2941.70,2945.00,2941.30,2943.40,\n",
    "2969.80,2986.40,2971.60,3006.10,3009.10,3010.10,3008.30,3025.00,3073.60,\n",
    "3065.50,3057.60,3042.00,3049.30,3079.20,3079.20,3100.60,3100.60,3100.00,\n",
    "3085.10,3072.60,3057.30,3055.40,3038.60,3035.40,3031.20,3037.00,3024.80,\n",
    "3028.00,2989.40,3003.90,3005.50,3004.50,3001.60,3007.50,3001.30,3005.20,\n",
    "3026.30,3036.90,3030.10,3037.50,3039.30,3067.70,3085.20,3100.80,3092.40,\n",
    "3108.60,3102.20,3094.70,3080.90,3086.30,3120.80,3137.60,3129.60,3156.30,\n",
    "3188.30,3199.00,3184.80,3165.30,3154.30,3163.00,3171.00,3164.40,3164.10,\n",
    "3162.30,3149.00,3085.60,3077.60,3096.00,3098.50,3099.70,3099.10,3093.30,\n",
    "3097.50,3120.00,3125.50,3108.00,3070.60,3069.30,3067.20,3093.10,3111.40,\n",
    "3135.80,3166.90,3233.20,3223.90,3234.20,3237.30,3237.30,3277.40,3271.60,\n",
    "3261.30,3254.60,3248.40,3278.80,3311.20,3337.10,3364.90,3342.40,3355.70,\n",
    "3396.50,3412.30,3412.30,3412.30,3462.00,3428.80,3418.40,3418.40,3408.50,\n",
    "3379.20,3403.00,3446.00,3440.60,3413.80,3372.00,3360.00,3400.60,3407.80,\n",
    "3437.00,3475.10,3470.00,3484.20,3481.40,3444.00,3436.10,3427.30,3447.40,\n",
    "3491.80,3481.50,3520.30,3491.50,3475.40,3419.10,3440.20,3429.10,3407.00,\n",
    "3378.90,3363.50,3393.20,3417.70,3425.30,3382.60,3350.30,3333.70,3341.90,\n",
    "3267.50,3281.20,3328.10,3270.60,3248.10,3246.50,3278.00,3305.90,3264.40,\n",
    "3246.70,3233.90,3191.90,3233.40,3267.40,3242.90,3255.70,3218.10,3198.00,\n",
    "3201.50,3155.30,3121.70,3129.00,3129.50,3123.40,3092.40,3086.40,3086.40,\n",
    "3086.40,3116.20,3131.50,3129.00,3120.80,3149.40,3159.10,3145.80,3131.70,\n",
    "3168.30,3138.20,3128.00,3098.30,3101.20,3133.70,3106.10,3125.30,3150.00,\n",
    "3129.90,3125.30,3125.30,3100.00,3070.50,3106.00,3106.00,3097.80,3136.30,\n",
    "3130.50,3137.80,3119.20,3115.60,3123.50,3116.50,3122.80,3127.30,3108.40,\n",
    "3089.10,3020.70,3019.70,2966.40,2966.40,2970.50,2931.90,2980.80,2997.80,\n",
    "3009.40,3004.80,3038.20,3028.90,3055.90,3016.30,3039.60,3045.80,3030.10,\n",
    "3022.90,2971.10,2940.20,2960.40,2942.40,2876.60,2899.90,2909.00,2946.30,\n",
    "2919.20,2936.40,2970.40,2965.00,2946.70,2964.40,2962.40,2983.80,2963.90,\n",
    "3005.30,3050.40,3074.80,3082.00,3091.30,3077.20,3095.10,3114.70,3106.10,\n",
    "3117.20,3082.30,3095.90,3082.60,3097.40,3157.50,3160.40,3150.50,3167.50,\n",
    "3171.90,3168.60,3167.00,3138.20,3142.30,3142.20,3147.30,3190.30,3182.60,\n",
    "3191.40,3171.30,3175.10,3205.20,3234.20,3265.10,3265.10,3249.60,3251.30,\n",
    "3216.50,3222.70,3241.50,3205.40,3203.90,3180.00,3139.30,3128.80,3121.40,\n",
    "3079.80,3112.70,3065.10,3079.10,3037.30,3014.80,3021.20,3028.20,2999.80,\n",
    "3008.50,3038.70,2992.50,3026.30,2983.50,3001.80,2956.30,2984.40,2998.70,\n",
    "3032.30,3073.00,3100.50,3141.90,3106.70,3120.20,3085.30,3060.80,3063.20,\n",
    "3032.80,3029.10,3000.90,2999.90,3029.60,3083.80,3097.40,3096.30,3081.30,\n",
    "3104.40,3097.60,3065.80,3063.80,3099.60,3103.50,3075.90,3095.30,3135.40,\n",
    "3146.50,3127.50,3131.00,3121.00,3078.70,3027.50,3036.60,3033.50,3047.10,\n",
    "3061.10,3081.40,3039.60,3017.30,3033.50,3016.10,3012.50,3013.80,2977.30,\n",
    "2943.40,2946.40,2980.60,2973.40,3013.60,3034.40,3058.10,3070.40,3091.70,\n",
    "3083.40,3083.40,3083.40,3095.80,3065.60,3065.50,3065.50,3065.70,3051.60,\n",
    "3032.30,3065.00,3055.80,3060.40,3049.40,3033.20,3048.30,3076.70,3054.00,\n",
    "3054.90,3028.60,2995.90,2954.20,2969.00,2982.20,3007.30,3022.20,2995.90,\n",
    "2991.60,3017.30,3034.70,3059.70,3062.00,3072.70,3072.50,3099.00,3109.90,\n",
    "3081.10,3071.30,3074.90,3051.10,3044.20,3018.60,3023.40,3019.50,3049.30,\n",
    "3037.70,3025.30,3009.30,3041.20,3038.20,3025.10,3001.90,2977.00,2992.10,\n",
    "2986.90,3021.10,3011.80,3050.60,3047.00,3094.10,3089.30,3124.20,3135.00,\n",
    "3139.70,3136.40,3153.40,3149.80,3128.30,3142.30,3176.20,3137.90,3143.10,\n",
    "3188.10,3190.20,3200.90,3210.90,3204.20,3190.90,3209.80,3208.80,3208.80,\n",
    "3208.80,3194.50,3170.10,3174.70,3199.90,3209.30,3214.90,3226.20,3217.60,\n",
    "3216.70,3220.40,3248.20,3262.60,3264.30,3251.70,3251.70,3261.20,3290.10,\n",
    "3317.90,3310.30,3310.70,3300.80,3297.40,3285.80,3261.00,3284.50,3291.80,\n",
    "3327.30,3328.20,3311.10,3311.10,3309.90,3319.40,3340.60,3345.00,3376.60,\n",
    "3380.00,3370.80,3380.80,3337.70,3344.60,3348.00,3339.80,3370.40,3366.10,\n",
    "3381.30,3377.20,3378.30,3403.80,3379.40,3309.20,3313.20,3282.70,3294.00,\n",
    "3314.60,3323.70,3349.20,3394.90,3388.30,3462.90,3455.00,3464.00,3450.60,\n",
    "3447.20,3429.20,3442.60,3420.70,3405.30,3400.40,3413.10,3431.60,3432.90,\n",
    "3454.30,3458.30,3468.90,3463.30,3449.90,3499.90,3475.60,3482.40,3483.50,\n",
    "3468.80,3468.30,3474.70,3467.50,3441.40,3444.40,3465.10,3470.60,3509.80,\n",
    "3535.70,3530.20,3515.90,3520.00,3524.90,3524.90,3502.60,3504.00,3477.80,\n",
    "3509.40,3522.70,3532.40,3557.70,3545.60,3554.50,3549.30,3535.90,3570.80,\n",
    "3565.40,3564.60,3533.30,3541.40,3561.50,3557.90,3514.80,3507.00,3523.30,\n",
    "3485.00,3479.00,3508.20,3520.20,3524.20,3544.10,3544.40,3526.50,3510.30,\n",
    "3460.10,3474.30,3523.80,3568.00,3557.30,3562.20,3593.00,3578.60,3551.40,\n",
    "3531.50,3535.30,3537.80,3519.60,3497.90,3510.00,3529.10,3518.70,3523.00,\n",
    "3500.40,3514.80,3522.40,3537.10,3541.60,3523.40,3536.80,3547.90,3571.40,\n",
    "3610.80,3609.20,3628.80,3604.10,3632.40,3602.50,3624.00,3649.00,3648.80,\n",
    "3655.50,3664.30,3664.30,3669.70,3664.20,3662.80,3639.50,3630.00,3652.10,\n",
    "3654.90,3662.40,3671.60,3642.60,3596.10,3576.90,3613.70,3633.30,3658.30,\n",
    "3658.30,3658.30,3676.40,3676.70,3689.30,3689.30,3687.90,3715.60,3714.10,\n",
    "3704.50,3720.60,3720.60,3671.50,3654.90,3657.30,3662.70,3710.60,3704.20,\n",
    "3748.70,3748.40,3754.20,3735.00,3758.20,3734.20,3734.70,3734.60,3735.30,\n",
    "3759.30,3752.80,3781.30,3746.60,3747.50,3726.10,3708.40,3716.30,3726.60,\n",
    "3747.60,3745.00,3779.80,3770.90,3744.30,3714.60,3725.60,3740.00,3740.30,\n",
    "3704.20,3715.90,3738.20,3727.60,3752.70,3768.60,3777.10,3758.90,3758.20,\n",
    "3710.30,3674.50,3639.50,3640.30,3681.80,3644.80,3669.60,3693.00,3685.40,\n",
    "3698.30,3707.00,3681.90,3660.90,3672.40,3672.60,3699.70,3718.40,3728.50,\n",
    "3725.10,3755.60,3755.60,3755.60,3758.60,3767.40,3744.20,3766.80,3790.50,\n",
    "3825.30,3805.60,3820.70,3857.10,3852.70,3833.00,3817.60,3819.30,3832.80,\n",
    "3809.20,3817.90,3806.00,3776.40,3751.60,3751.60,3723.00,3707.30,3728.30,\n",
    "3754.40,3739.20,3759.70,3776.20,3753.60,3789.60,3778.20,3789.40,3764.20,\n",
    "3747.00,3752.10,3752.10,3760.20,3775.70,3746.70,3747.80,3739.20,3755.20,\n",
    "3753.40,3760.30,3706.80,3728.80,3755.70,3769.20,3761.70,3753.60,3761.50,\n",
    "3756.40,3753.20,3727.50,3722.30,3710.80,3679.50,3695.50,3678.80,3711.00,\n",
    "3725.60,3725.70,3714.10,3760.60,3743.20,3741.50,3752.30,3765.80,3749.00,\n",
    "3728.30,3698.30,3632.30,3658.20,3693.40,3710.50,3681.30,3708.40,3668.80,\n",
    "3684.70,3673.30,3678.80,3668.50,3703.20,3734.40,3770.60,3788.30,3788.40,\n",
    "3811.10,3811.40,3810.70,3803.30,3823.40,3830.30,3837.40,3872.90,3863.70,\n",
    "3883.20,3872.10,3891.10,3907.50,3907.50,3905.70,3918.70,3885.00,3867.60,\n",
    "3884.40,3855.90,3872.70,3887.20,3893.00,3910.80,3916.10,3905.60,3932.60,\n",
    "3967.90,3977.20,3972.30,3955.70,3974.30,3964.10,3919.70,3910.50,3935.70,\n",
    "3933.20,3946.40,3953.70,3992.20,4015.10,4000.00,4024.80,4031.50,4035.60,\n",
    "4009.30,3994.70,4028.10,4038.70,4050.80,4024.40,4042.10,4053.10,4073.10,\n",
    "4057.20,4028.40,3999.40,4022.40,4025.30,3993.50,3963.90,3979.10,3948.50,\n",
    "3928.10,3921.10,3935.70,3900.40,3910.80,3914.40,3934.30,3926.90,3926.10,\n",
    "3958.20,3962.10,3978.10,3962.80,3953.80,4018.70,4054.60,4068.40,4049.20,\n",
    "4050.20,4058.00,4038.50,4061.50,4045.20,4051.20,3963.00,4011.60,4035.70,\n",
    "3982.50,3990.70,3972.40,3993.80,3979.60,4018.20,4051.30,4077.60,4087.20,\n",
    "4092.50,4092.50,4092.50,4091.00,4115.70,4118.50,4118.50,4057.40,4089.50,\n",
    "4106.50,4078.80,4087.50,4087.00,4056.60,4107.30,4168.20,4158.90,4197.50,\n",
    "4207.70,4194.00,4195.50,4219.10,4219.10,4218.80,4212.00,4237.40,4207.50,\n",
    "4228.40,4275.80,4257.80,4260.90,4281.50,4265.90,4307.80,4307.70,4304.30,\n",
    "4304.30,4327.10,4341.00,4337.80,4332.30,4357.40,4356.10,4336.80,4331.10,\n",
    "4344.70,4329.30,4339.20,4308.30,4307.10,4357.70,4360.10,4399.30,4420.30,\n",
    "4437.40,4444.30,4422.50,4397.70,4424.30,4373.30,4356.80,4332.20,4258.10,\n",
    "4254.80,4214.80,4270.70,4301.50,4312.90,4312.90,4312.90,4248.10,4236.60,\n",
    "4214.60,4236.60,4271.70,4269.30,4292.30,4313.20,4270.70,4251.70,4286.80,\n",
    "4294.60,4298.90,4310.50,4328.70,4346.10,4387.70,4388.50,4369.70,4389.70,\n",
    "4433.20,4436.00,4445.00,4455.60,4455.60,4519.30,4537.50,4580.40,4630.90,\n",
    "4669.60,4691.00,4686.90,4681.20,4693.90,4645.20,4607.50,4642.00,4651.80,\n",
    "4661.80,4661.80,4681.60,4677.50,4672.30,4621.30,4562.80,4557.80,4557.10,\n",
    "4576.20,4645.00,4686.70,4739.60,4724.80,4757.40,4783.10,4745.10,4682.20,\n",
    "4657.00,4653.70,4593.90,4575.80,4596.30,4640.00,4657.90,4640.30,4604.60,\n",
    "4728.30,4751.40,4831.70,4812.80,4810.70,4758.50,4762.40,4767.80,4799.50,\n",
    "4857.40,4899.30,4964.20,4949.00,4877.20,4805.70,4846.70,4874.50,4862.90,\n",
    "4851.50,4862.60,4876.60,4927.30,4907.50,4899.30,4895.70,4960.60,5026.20,\n",
    "5086.80,5031.30,5031.90,5075.80,5003.60,4991.30,4865.80,4835.00,4914.20,\n",
    "4958.40,4978.00,4901.10,4901.10,4886.30,4906.90,4845.40,4817.50,4870.20,\n",
    "4952.20,4976.90,4991.30,4994.20,4985.20,4950.50,4905.20,4854.80,4848.20,\n",
    "4902.90,4976.40,5013.10,5046.20,5023.80,5075.70,5027.50,5077.20,5065.50,\n",
    "5226.30,5220.30,5244.20,5317.10,5296.10,5330.80,5300.00,5305.60,5262.10,\n",
    "5217.80,5227.30,5300.10,5298.90,5263.70,5287.90,5271.10,5211.00,5225.90,\n",
    "5148.80,4991.50,4970.20,4840.70,4755.40,4871.80,4801.90,4842.30,4906.40,\n",
    "4897.40,4908.30,4863.80,4764.30,4806.80,4793.70,4720.40,4711.00,4741.80,\n",
    "4867.00,4845.40,4830.10,4908.40,4985.80,4898.60,4863.50,4891.20,4889.00,\n",
    "4831.80,4921.80,4977.60,4970.70,5082.30,5142.90,5187.40,5177.10,5130.70,\n",
    "5035.90,5045.20,5121.80,5203.40,5190.80,5168.30,5020.20,5018.20,5049.80,\n",
    "5013.90,5013.90,5013.90,5112.40,5132.30,5135.50,5135.50,5193.50,5262.50,\n",
    "5264.40,5224.10,5237.10,5138.30,5068.80,5083.90,5106.90,5165.80,5263.10,\n",
    "5273.60,5278.20,5272.30,5253.10,5181.40,5237.20,5326.30,5372.60,5422.40,\n",
    "5458.50,5599.00,5612.80,5595.80,5606.40,5629.70,5600.90,5613.30,5607.90,\n",
    "5552.50,5582.30,5619.90,5709.50,5723.40,5718.50,5718.50,5702.80,5651.00,\n",
    "5745.10,5764.80,5767.30,5820.60,5807.70,5733.10,5695.60,5782.90,5818.90,\n",
    "5828.50,5829.80,5794.80,5782.30,5785.10,5834.90,5903.60,5997.90,5956.30,\n",
    "5947.00,5983.70,5967.80,5905.60,5939.30,5911.90,5932.20,6017.60,6052.80,\n",
    "6064.20,6105.80,6094.00,6055.20,6105.50,6105.50,6105.50,6104.10,6074.10,\n",
    "6002.00,5922.20,5954.10,5955.00,5931.10,5898.10,5863.90,5722.40,5806.60,\n",
    "5833.10,5928.30,6011.30,6011.30,5986.50,5992.40,5938.00,5969.80,6028.30,\n",
    "5956.70,5972.90,5948.50,5917.80,5826.20,5877.80,5907.40,5935.60,5955.60,\n",
    "5955.60,5970.70,5870.20,5862.30,5870.70,5837.90,5842.30,5898.40,5860.80,\n",
    "5947.30,6037.80,6019.80,5987.40,5852.50,5769.80,5715.70,5729.70,5832.70,\n",
    "5812.10,5748.10,5712.40,5772.00,5804.90,5858.90,5877.40,5884.50,5832.50,\n",
    "5919.90,5960.20,5988.40,5990.30,6003.40,6009.60,5969.70,5927.90,5958.20,\n",
    "6100.20,6151.50,6116.80,6174.00,6179.00,6132.70,5989.60,5976.20,5892.30,\n",
    "5836.10,5835.80,5844.10,5910.70,5837.00,5809.70,5736.10,5632.50,5594.10,\n",
    "5680.40,5587.60,5432.80,5462.20,5399.50,5455.00)\n",
    "\n",
    "length(eu_stocks_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is.ts(eu_stocks_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eu_stocks <- ts(eu_stocks_data, start = c(1991, 130), end = c(1998, 169), frequency = 260)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is.ts(eu_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1991</li>\n",
       "\t<li>130</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1991\n",
       "\\item 130\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1991\n",
       "2. 130\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1991  130"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start(eu_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1998</li>\n",
       "\t<li>169</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1998\n",
       "\\item 169\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1998\n",
       "2. 169\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1998  169"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "end(eu_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "260"
      ],
      "text/latex": [
       "260"
      ],
      "text/markdown": [
       "260"
      ],
      "text/plain": [
       "[1] 260"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "frequency(eu_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nKCAkQAEhAQoICVDwHy2OQlNctj2hAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(eu_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////QFLu4AAAACXBIWXMAABJ0AAAS\ndAHeZh94AAAgAElEQVR4nO3diXayOhSG4Y0gDlW4/7st8yQyZRMTeJ+z1vmxlSTFfAIhoqQA\njMmvGwAcAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAk\nQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIU\nECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEDB8YIkuXex+C6Wx56xtJya\nchunPK+ByCV+1Y+vs2us/xur35r+YVGz/uuatfk+9qD3tJXrPrMnSfQ0aqMtBw3So1h8eBik\nuK7yVjz8C+br/lWQns36z7LJ4eeD3tNWrnuttkRs0khbDhqk8pUI/QvSva3zr2rF7Do/CtKz\n2TCvusnR8EHvaSvXbTfFfbi6gw4aJBkubipHr1GLXbI34CQ7KA2rjrhrkEy8o3bjZruOKElf\nWdtfgwe9p61cN/v/NUmT/FjPtLEWHDJI2euUH1g/i6XyL3zkS5f4XT2jfOozP3i4Ppv13pfO\nYcTw5e+kc/D0YTHpPe8D5WlamsSBBHH1YNiKZ5aX62uslqRY6O4Pe7VkxWZ1hM/OOtlfG7yH\n5QwreWcnYNkpyGCP1C2s1+Dklu/Uo8f4Zg7r9bOTuiz8+f7kNnjQe9rKdQcb3HE+tHGd/FAg\n6zlp8f52r16FsHu8VL8y9Q+jer1L58h+QZCqp38UU77flr36HbT1frSiOh/qJikrM/rr1lkH\nqV9LXWzctOjdy1Gnld1K/srlUHpB6hXWbXC93NkqnQqij65etK73oPe0lesGzYPgs3rnHDNI\nUbHtA4mqIGX/hElxIl++uMVfHdXdujmIknqUIk2XBKl8+mgxueKApO6KwVgrKt1xueLEILg+\n3mmnsM/G1sUWe978GVmf7+ao38qmkqB93HlSr7Bug6/FH5iEY2cp+Q6ss0nyHUmzF20f9J62\nct1bc2jHOdIvZC/C656/o2Zvv/dX+XpdqgHx8pHUh0Jyz16oW9sd827eLWes13W6aPH0kWKC\n7N38GRQPy+wkZY/8aEXwLIemus2vE3PpHrYNa8mKDV5FD7+Uz0mC/o6t08pOJY/yUd62zp/U\nK6zXYCkbnHw7S6mbfi1XKnd0vQe9p61dt78Tdtwxg/TOD7KzTvd+9V/EbpCad7q4fLuugtB9\n7kyQiqePFFPs1Z7Fw6h8i017vaFpRV5AMuxmz0tVaXvY9lFLdRKYXG7vtD7l6J/I9FtZVVKt\n1ow9935aFtZrcB6468RlnLrpr+6W6j3oPW31umWSRo4rHXTMIGVd4JLtAIK0DdL7EYfSDZJU\nXaa4bNt93JYzE6QkHS+mXv/SLSQYb8VYN3s/rsUB1v2ztqqWj7cHGV5tGW10p20y8tP+Xx0U\nB1cylaVmzeryT9Ds6psHg0bIsAlT69bvKD4M2h01SNk7eLFLqIP0qF+UXpDaNdLPDv3t8Xiu\nPoupe3yn4pFWfHm/LkaIL5+1tcX2Wyby+Tbw2cpVQcp/WF8d7p1+jW2ifEJC9LqUbxe9B/1G\njATp67pxc47kwxXZgwbpUYypPeog5VMcLtf6jKn5f/MmH6TfgzN8/NlFh8Uk7fOCbiFjrRjU\nE7R56D1rUMtHkILboLttDVLQ/6uTx9Th1ecmisYezATp27qM2v1WEaRylt07bQcbntXvmv9H\nnyc3w3KGj/O+/DfooiPFFI+fRWeIuideY60Y1HNtxvD6R4qDWsLhOdJfXvhgqKRbePMnFw14\n9H4bDs6Rhgdyz+F4yMcmiiKpxl3ugwejW3LhutO7bNf40MZ1igAVx9eXYXfs7QtGhtuG5fQe\nB8V7/l8w6KIjxeTn/fnI2L0cJ/sr/gnHWzGoJy+tuJSbr1/HO5kftSue0d0ljQbpXo7aPSZG\n7XoNvjTngeP7hM6bybVscjJ4MLolF657aQYQfRhuOGSQ0vLoPk47b7pxO+xbvYbN5dFyJzAS\npFbaTqEcdNGRYipF52uu0fx9acWg3vZ6UTn0HFR/x6CWpth2QCLsDYCPBmnuOtJ90OAsnOG7\nGHOIR+PQfTMp3IYPRv7Cxesy1+63pNnftPuZv7pvF/2jfg3rznntrNcrp9ftyqPFYqJA/+kf\nxZSn6OUJet014q+tGNTbJCaoR9fLN+R+LX8fMxvyHd3HEPuwkqoFUf+3vcK6DW4GG8KR7dP9\nURX/6PPB2JZdum7cbYrrjhqk/MpJ0jwqBoOCa359qTMRpfzoT3eS3KCcXpCKMsLHsIuOFfO4\nSBBXBzbFPLbqMzWjrRjWW5Qm0a1aP6qz06ulmBFXFyvNeVS7SxoPUvrO/4aRuXZtYb0Gl+dH\n4X2snb0f3Tvr9B+Mr7ls3b9rIHweyV2jL6wXhf/UYf8wFSfcOKMfNFNz2CAlfkzV+ZWDvurf\nxf3jd3WHDdJd/uafdF4HfdW/K05ndzzsPmyQInI05aCv+nf51JuxD6ppOWyQMIlXHVBAkAAF\nBAlQQJAABQQJUECQAAUECVBAkAAFBAlQQJAABQQJUECQAAUECVBAkAAFBAlQQJAABQQJUECQ\nAAUECVBAkAAFBAlQQJAABQQJUECQAAUECVBAkAAFBAlQQJAABQQJUECQAAUECVBAkAAFBAlQ\nQJAABRaCJIBnNvRy/eD8oApAE0ECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEAB\nQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAwRmCVH6m/hIn9Q8CCcqFq4TFv6FcVWvE6VgN\n0t8tKvp0FP/tVcVoaZXgXT5+ZsvPcjGQe/b/ex0sYCOLQUounXuuhLtU8aW0orh3WFd6lbje\nA/2JvNMkkJlgAzMsBimW4PEqlt7PQOI9qvhSWlXcpdoPZfufoK4hP7iLOLDDnLkuaTFIgbya\n5df0wdQ+QXqWgXlkIY7l0bTqxoEdZjkUpN499KZvqLdPkBK55P+E2YHcX3NsmR3ccWCHWQ4F\nyWyPZHC/y+anxUJSVB1IPYZ35cAO8xwKUnaO9CzHzX50jlQuPIqqu8d2HNlhlkNByo6pWpdk\n6pl7BulSHMm9ysO8fIfEWANmzd7b2+51pLi4jhREN8vXkcp/3/mJ0bvJcrF3/Mv2R5wkYY7M\n9clzzGwo/y0O6m5NkG75z4LsEI/rsZhDkNLudaS//H/VeVpxbJcd2KXMEMIst4L0sylC+f/L\nmQ2vIjm5UF752Hd+rvbm4A7TXArSD6cItXPt4nqWXfrMDvTKqXZMtsMcl4L0wylCRXTLc6I2\nMUFwbfLMwR0muRSkn00RAky5FKSfTRECDMlsn2SPBMxyKkg/myIEGHIqSD+bIgQYcitIv5oi\nBJgRx4LkUhXAYl4FafZjRcCPuBakH00RAsxI6lKQfjZFCDDjVpB+NkUIMONWkLggCz+JW0Fi\nihD85FiQ2CPBT+W7/nSnZIoQMK06enImSEwRgpecCxJThOAj94LkUhXAMvVEG/XxMYKEM6kD\n5E6QkjgfqrtdRMLH9DMJEpzhXJDeQdaUJGCKELziXJCuEiX5dz+8s0xdGf6GJ5wLUnEzxvKO\njNV3q6hXAahzMEhp2nznJFOE4AnngnTNpwjdynlCyfRJEkGCM+rO6EyQXhLErzQKsiQ9L82d\ng1WrANQ5F6T0GbRThG77VAFok4+FyWdtKHi9x7X4lGx0e+9WBaDLxSA5VAUwr3fXE4IEbEOQ\nAAUECVAg3a9zIUjAJpISJMAYQQIUSPOpvurh1FM3lL47ggQXECRAAUECFBAkQAFBAhQQJEAB\nQQIUECRAAUECFBAkwJgQJMBcGaTeD6aevKH83REk/B5BAszldxchSIChMkj9n0w8e0MF61dx\nsApgmvQ+Z17+ZOLZGypYv4qDVQDTCBKgQD5yQ5CA1QgSoIAgAQoIEqCAIAEKPmNDkIC1ZKQX\nEiRgJYIEKCBIgAKCBCgYDdL3jkmQgDEECVAw1gcJErASQQIUECRAAUECzI1mhiABS5WdjyAB\nRggSoEA6/x/+iiABCxEkwFg1oWE8MgQJWKb6XCxBAkwQJMCY1LeFJEjAdm2Qvvx6Ys0Nle2O\nIOEnCBKgQKQM0pdjOIIELFF9I9K3cyGCBCxBkAAFRYK+jdkRJGCZmSBNrbmhsvWrOFgF8Ikg\nAQrKWQ0ECTBSTQ8iSIAJggQoIEiAueZT5o4H6e8WFXMwovhvryqA7fwIUnKRVrhLFYAJP4IU\nS/B4FUvvZyDxHlUAJvwIUiCvZvklwR5VACb8CFJvKGR6XIQg4Rf8CBJ7JDiuCdLWVfdepZCd\nIz3fxRLnSHCSH0FKw86o3SXZpQrAgCdBSv/i4jpSEN24jgQH+RIkl6oABoQgAeb8CRJThOAw\nX4LEFCE4zZcgMUUITqsD5HqQuCALp/kSJKYIwWm+BIk9EpzWBGnTylZWKTBFCC4TX4LEFCG4\nzJ8gMUUIDmtOjdwPkktVAH1HCZJ07VMF8J18LGxae9dVKkwRgrvMOh1ThICCN0FiihBc5k2Q\nuCALl3kTJKYIwWXeBIk9EhxmOFTMFCEg50+QmCIEh3kUJKYIwV0+BcmlKoAeggQoMOxz9oN0\nv4hEz12rAFbzJ0jlvrMacZgctCNIsM6zIMUSJ2n6juW+RxXARqafOLAdpECKce9ELntUAWxk\n2uVsB2nZnVoIEizzLUjXOkhMEYJDjD9LajVI0e3+lEe2mMRMEYJLjHuc1SA1HyMXCZgiBIf4\nFKT09brfo6gYcognc0SQYJlXQXKqCqCDIAEKCBJgzvwGcAQJIEiABoIEKCBIgAKCBJhTuNs8\nQQIIEqCAIAHmNL5IiCDh9AgSoEAYtQPMCXPtAHMa3Y0g4fQIEqCAIAEKCBJgTAgSYE7hIlJK\nkHB6BAlQoJIjgoSzI0iAAp3ORpBwcgQJMKdzZEeQcHIECTCnM/hNkHBuGp/pKwuysoqDVQCp\n3g6JIOHUCBKgQCtHBAmnptbTCBJOTK+jESScGEECxq3qOwQJGEeQ7FaBgyJIdqvAQa26BQNB\nAsYtDJJ0/q9TrY1VHKwCB0WQ7FaBYxKCZLcKHNPCIAlBAr7LJ6EumT9HkIAJBMl2FTikIkcE\nyWIVOCSCZLsKHJIs/Kxe+RzFfkaQcCSy8EISQQImfAZpvC8RJGDCSJBGO5OUB4GqFVtYxcEq\ncEhrgqR245OqYgurOFgFDunziI0gAasRJNtV4JAIku0qcEgfQRpPixAkYEIVJOn8gCABaxEk\n21XgkAiS7SpwQDIapJHeVAaJmQ3AmGZO92yQFk7JW1G1lVUqf7co/2InieK/varAmdWZkYkg\n1eN6/gYpuUgr3KUKnNs5ghRL8HgVS+9nIPEeVeDcvgTpcza410EK5NUsvyTYowqc2zmC1Pt7\npkceCRK2GA1SP0nif5DYI2Fn40FKB0Eqb33nb5Cyc6Tnu1jiHAm7+AySfASpvGPXt0l426u2\nskop7IzaXZJdqsCptUGS7k/k45zJ6z1Smv7FxXWkILpxHQk7aILUjHoPg1Terkt3Z1RVaWMV\nB6vAATX7oTpIMh6kHavedxUHq8AB9YMkzRjd0YLEFCHsqY3LoYPEFCHsayRI5cNjBYkpQtjX\nSYLEBVns6+Ny0TGDxBQh7KsfpLQNUndf5X+Q2CNhXycJElOEsK9vQUoHQdq57h1XKTFFCHuS\nswSJKULY09Ig7VO5lVUcrAKHQ5DKYrv2qQKH9hkkGQvSTpVbWaXCFCHsqH955bhBYooQdtXr\nNQcOElOEsKuRIH386ghB4oIsdrUgSPt1LKYI4Shk+ECOGST2SNjVfJB2HA5mihAOQj4eHTRI\nTBHCnkaCNPzdQYLEFCHsaCpI9TRwh4P0jPLWRW+l9oxVASwwH6Q9p8yYBiksJ/RIoJokgoTV\nvA7SXcIkb91drmtKmKuVIGG1z07jUZACST5vrzxfAkGCOq+D1Nw7bEETpU+5VTg7r4N0qfZI\nL7nMrvcXECTsx+sgVedIz0Du8ysmkYTFmASHdtA3HaTysMnZIKXRoo9F1B4ij5QgYQ8zQZJF\n5x+Kta9cJb+OJNFj4brvUKKEIGEHngdprZsET4IEbWOHbR9B2rN+K6t0vS7zh6oECSudL0hp\neiVI0DbWpzwK0k43/iFIWGeuAxIkYAHfg1T5CyPzpkxXAUw4SJDSZNWk1U1VAN/NHRH5EiTl\nIXqChDXmTy36NxXaowk6q9ynb2aiUQXwzaILKvveCFttsOGm1qSUIGGd4wTpsmDO6sYqgDnz\nGXE9SDshSFhjwYfhCBIwY8mnStOde5VBkFZ84tVCq3BaSzofQQJm+B6kHREkLCUE6adV4CBk\n0SjC7j1KK0h/qpPtCBKWWjZhwfkgxZwj4ZfkGEFqc/RUa1JKkLCY9nv4VoZBCuSRhvJ+hzLz\n/RLbqwAmOJIjjTut3rK90Wvh/bg2VAFM2HdO93IKQXrmN4fkHAk/cZAgRdmh3Vsu6R9Bgn1y\nmCAVt6grviOJT8jCut0/rrec6fD3LX90lenvVjarAvjiGEFSHfAerwKYUF6/dKOzmExaDWLd\nb479rAKY4Mo1pJxBkPJbD4f77Jac2TxwmTO7o9TsHOkd518dFr802zOoAvjuKEHK/F2LGzYk\nau35rAIY585IQ6ox+/uRj35fdQ/xnNk8cNjunzFaQ+NjFMktO13ivnawzKleovR5pPnvDjOu\nAuhzqpewR4KvnOolnCPBV071EtO5doza4Vec6iUmQfrLryMFXEfCbzjVS5jZAF851UuM5trd\ntA/phlUAH9oblP60GQMGQVK9S8N4FUBP9xqsW52EG0TCH0KQnKsCHiqDVPUOtzoJQYI/yq9U\nJkguVQEPdYPk1lgDQYJHCJJ7VcBDbZCWfQeFRYZButZXkt7caRW7Kz7IV946yLEcGd9pNXgU\n/975GAV2J2kdJJdue1Iy/ah5INE72x1JwE30sbdekH7dmAHjc6SbSCxyU2rOaBVAQer7NLh0\n15OK+WBDdlSX30VflWtbCU44dJDKPZLuHYud20pwQjdIrjE/Rwqzc6SIcyTsr5ogdMQg1Ud1\nj4BRO+ztwEEK67t/J3ytC/ZWB8nF7sHMBvhCDh2kZ5T/XZHu91K4uKXwa/WnkQ4ZpLC8NiaB\napJc3FL4qXpPdNAg3SVM8r/rzldfYlf1paODBimQpP+xRR0ubin8VPcarIvdw3j4OyVIsODg\nQbpUe6SXXNSalLq5pfBTBw9SdY70DHSn27m4pfBT3fneLnYP01G7SEqLPtf3dyufHsUzE4pc\n3FL4JXG9U6hcR5LosWC95CKt6eC5vc1g3/GDtFwswaO84f47OxScnC/u9jaDfQSpFUj7vRWv\n6S8mc3ubwT7ne4RBkKRvfr3huLlqq3BozvcIi0Fij4TNnO8RxqN2Qf4NSX/BghlC2TnSs5yR\nxzkS1nG/QxgGKa72Mq8lHzYPO/uvy+RXK7m/3WCV+x1CYYpQf2HKX1xcRwqiG9eRsIb7HcJ4\n0mq9R5o85zGpAvCgQxgf2hV3PcnOeVTvbOf+doNV7ncIlQ/25XMblqzJFCFs436HML4g+yim\nCC35cnOmCGEjD/oDU4TgPg/6A1OE4D4P+oPFIDFFCBt50B9Mg3RrTnxm12OPhI086A+GQbqt\nmGvHFCFs4t5XT4wwviC74iPmTBHCBu59qdgYrSlCizBFCOudIkiRTO5ZtvJhy8EOB7/mcoxh\nkN5BqPXFSOs+3ISz8KQ7GB/aren7TBHCal4MNVgNElOEsJ4Xu6OUKUJwnC9dgSlCcJovXYEp\nQnCaL12BuwjBZb6cItkMElOEsNoZgrQaU4SwFkEawxQhrORNT7AaJJeqgMva27z9tBkrECQ4\nqD7n9ubI7hdBugdymfnwhTebD/uoguTHNLuCzSC9Ignu1WcBmSKECVJ9w7c/HcFikF5FgmK5\nJuk7mv5AoD/bD7sgSBOu+bWjuLwSm0x/C7o/2w97EII0tV552Bt1HmhXgWOQ6mq/Rx3BepAe\n5TEdU4TwnTT7pF+3ZDGrh3bXejpDcmWKEL4rj+tSnzqCxSAlQefblKa/Bcaf7YcdSBMkf1i9\njhTX8Qlmvt/Pr20IVeJbhgrMbIBjCJIeDzcktPg06N0iSHCLJ7ffGiJIcItPF486CBLc4ulr\nT5DgFF9feoIEV3h49ahFkOCKPEQESZWvWxMGitE6b195ggQnSHkh1ttXniDBBVId13n7yhMk\nuKCIEEHS5u3mxEb1vU68feUJEn7Pv9vYfSBI+D1/d0QNgoTfO8DrTZDwc0d4uQkSfu0AB3YE\nCT93iBwRJPzaMV5sgoQfO8aLTZDwY8d4sQkSLBqb332MF5sgwRapbundPK5/egQECRaUH5KQ\nKkv1D/3+BFIfQcJ+pNnrNNLm1fXuCycmESTspz6Qk97nX5twlTuq3zVPE0HCburjuOZmDP0g\npZ7enXgUQcIuJG1PiOq9Uvur473EBAm76IZIhr/6/Jn3CBL2IL3To4/fHe8lJkjQVe+I6viM\nDCccZ6yuRZCgS6rrRc1jgqS3ioNVQF09JtfPycgNTXy+yck3BAlamsHtfpDGXk2CtG0VB6uA\ntmpwYRikkyBI0CGDi68nQ5Cgo7r8WofpbAgSdEh78Ygg7bWKg1VAWT0nqFo+G4IEFXKoj+mt\nR5CgQQiSjVUcrAKqZPDv6RAkaCBIVlZxsApo4gUjSDB32jOjFkGCOYJEkGDugJO5VyNIMHbG\nSapDBAmm2B+lBAlLfY8Lr1ZKkLDQxHkQr1ZKkLDQlyCN3G3rnAiSY1z90798YlwYsisRJKfM\njH/95P2//ITRWMuG39NyZgTJKdO9cnCjK0vqWsduBlTd6wQEyS0LgmR143T3OcN6T/sZvlEE\nySmzQbK6A5C6RoI0iyA5ZfrYzfKRVDOUUH9o76M1aBAkl0zcOURk9pREe6tJKr3mEKQJBMkl\nEwdLneGxb1tnlyCl0n/8NVcnZzVIf7eo6A9R/LdXFX77HqTuMPOXraM8Dv1ZXO8wj1HvPotB\nSi6d7+QNd6nCd9L/X/8334NUn/ZrbraxpJTfTd4sosNikGIJHq9i6f0MJN6jCt91giQjP+z+\noLdaHSTF7TZWWjuKx+5oyGKQAnk1yy8J9qjCc53Bsbanft6V3lKQRn9aDUAQpCGLQept/OlX\n4pQvk8ggSPXZyPB0RYY7qPo/zSRNBkmtluNgj+SM3qhcN0jDHcAwSJK2t683b8XM2CFBGmf3\nHOn5LpY4RxrR/dbVNh3Vz2X4zM4PumctxhuuGZj7NjTIcd04m8PfYWfU7pLsUoXHOkFqDtSa\nY7b+M3t9uf4mlc5x4WxV359V73K+X6siR6PsXkeKi+tIQXTjOtKHTjSq/Hz9tE93FzUYFJfu\ng281TUxEqudPTBRAkMZYDZJLVbhGBkGqpt3NB6m/MAjSYBC9XhwPkjRnSARpNYLkiP7wQR2k\n0c/T9Z4/+HX/SyH6g+idVcfy2fnYEVlZze6hHVOEvvoMUjre3wfP/whSM3reu94j/UyNXm7t\nzOY74QtgyGKQmCL0qR1LHg5oVwtrg1QNuTVxakoXaX85uuKS6Xz4yu7wN1OEBqrTkuG1GaMg\nSTdI7anTcGD7Y0UGtk1YDBIXZD+JfL0jQvX7r2tWq4+UmLaj51VUmwtSk0FiZNuAxSAxRehT\ndano63D01BWfdFmQ2gGL/rSEkSBhO/ZIP1XPSvh+Wef7qumXY7HmcLEJUmegYXjdqbcatrN7\njsQUob5mZODbHzw5B+FL/Nog1SV0R+y+BImDOkM2h7+ZIjQ0H6Spdb8dDjZjC71qmrVGfsrZ\nkTGbQWKKUF93n/H1Kd/X3hakXgGzZWEpq0FyqQoHrJlnOrb29/R1Bue+19A7dYIhd4IkXftU\n4RbDP3NFkGYLOMX23pfdQzumCHUYvl1MXWJaVHL9hjVxiobFLAaJKUJ9hn+kcZDaC03n2N77\nsjv8zRShDtM/8nuQFpcs00MdWI4Lsj+zW5CWl1yF6BSbe2cWg8QUob79/sgVQRKCpIM9kl2z\ng9JWnWWA1AKmCFnVmZ7qxN9IkLQwRcim5iKZK7sCR5pxAEwRsknqDzW4EiQmq2pxZ2aD5Sp+\nQqpPC7EnOByCZFPzYViugR6NzSAlV5HwWRVyxuHvdpbqQf/AE7M5RSgoJ9qVhZwwSO3Nro75\n952a1eHve5ame1BMsztdkITZ1odm9YJs8c87uLzPGaTuAxzMD6YIJWF4xiBxPHdoFoN0kfoi\n7CU8W5BO82nF07IYpLtcq6W3hKcLEpc+j83m8Hfc9KXnzPuzvT5npyZCdHhWL8i+onrpfXUl\nSDb6OId1x3f2mQ1W7rVCjo7v5EGqbxm8cy37Fg8HnD1I1T/7DgYQpOM7U5BGotKZa7Djfokg\nHd+5gtSWW366Lu3+gCBhuxMFqff1JuXBXD87BAmbnSlIzQfrvtwYcbddEkE6vvMEqSizE6SR\njwURJGx1miB1Pgz09eMM26ud2pnxadgzOE+QmoXJPr+x8IkhP26tfQonDJJ+vVPTI5j2fQ6H\nD9Kqr1zaVK/UQarPvPq1bykS3jlHkJYOyG2pt/maobQzkNGUR45O4uhBWjcn1ShI1V6pHySc\nhMdBkiVPXNfYDQdi0gapHl03KQ6e8jBIzTj2khP5vYM08n13MrKEo/MvSNIJUjp7Or+ysatP\nar5NhB0ZeMCReRiktDfDZ7hLGPTs1blYt1MafbKMjTvg2LwLkrQdtXraYKDMOEhrVvkSJNn1\nUxlwkG9Baoaae5HpTvqZSNWSmhWC1EQd5+FdkDqLMvLj/p2BN/XmRZOJPpuDUztIkIo9UXW8\n18Zn5yCx20HjMEHqzgTqj+ttrnxuQJBpdGh4HKT0I0idLyAymJ7z5Xzr83nkCI2jBGkw9tBO\nIt1Se71Hm7swTI5QO06Qur/YJ0htkeWo4cbicUSHDFI6GL3bVP1HFNsffM5OxdkdNUhm1Wel\ncMEAAAjWSURBVEt9BtQOW7QDg2k1o2Kv2uEjgjReSz0BqXos/SkVKUFCH0Ear6U7/tcEqToz\n6v0KyBGk8WqaUYXy/52jPCKEET4HyUIDmiBJ5ycECR8I0mQ17a0kF08cwikRpOlqmoFugoQp\nBGmmGmamYgmCNIMgYQmCNIOZqViCIM0gR1iCIM0gR1iCIM0gSFiCIM0gSFiCIAEKCBKggCAB\nCggSoIAgAQoIEqCAIAEKCBKggCABCggSoIAgAQoIEqCAIAEKCBKggCABCggSoIAgAQoIEqCA\nIAEKCBKgwGqQ/m5R8e2uUfy3tQqCBCdZDFJykVa4sQqCBCdZDFIsweNVLL2fgcTbqiBIcJLF\nIAXyapZfEmyrgiDBSRaD1LuL9vQttQkSPMMeCVBg9xzp+S6WOEfC0dgc/g47o3aXZFsVBAlO\nsnsdKS6uIwXRjetIOBbPZjaQI7iJIAEKPJsiRJDgJs+mCBEkuMmzKUIECW7y7IIsQYKbPJsi\nRJDgJvZIgALPpggRJLjJsylCBAlu8myKEEGCm5jZAChwJ0jSZbluwBBThAAFTBECFDBFCFDA\nBVlAAVOEAAXskQAFTBECFDBFCFDAFCFAgTszGxZVQZDgJoIEKCBIgAKCBCggSIACqzMbFn1S\nYrIKggQ3WQzSnSDhsGwe2r2C6Q9PLKiCIMFNVs+RXtMTgxZUQZDgJruDDffOvNVNVRAkuIlR\nO0ABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUEC\nFBAkQAFBAhQQJECBZ0EC3ESQAAUECVBAkAAFBAlQQJAABQQJUECQAAUECVBAkAAFBAlQQJAA\nBQQJUECQAAUECVBAkAAFBAlQQJAABQQJUECQAAUECVBAkAAFjgYJ8MyGXq4fnJ3s1tL9NgFN\ntlCwI13YjVYswUtsoWCavJUbrViCl9hCwTR5KzdasQQvsYWCafJWbrRiCV5iCwXT5K3caMUS\nvMQWCqbJW7nRiiV4iS0UTJO3cqMVS/ASWyiYJm/lRiuW4CW2UDBN3sqNVizBS2yhYJq8lRut\nWIKX2ELBNHkrN1qxBC+xhYJp8lZutALwHEECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFB\nAhQQJEABQQIUECRAAUECFBAkQAFBAhQ4G6R73bI4kPD5sXi/SBAn+gUnV5Hra5cmZ/62be7p\ngjff93225PSVb423esEG96qfff2yxY0dw4yrQXrVWzkstvhtsBgXi8GGDTZTcFAsbkrSTMmZ\nJNi0uacLfhl0ypkmP3faynWOAvUmv8vXL9gUfiOOBukVVNvrLmGS7yZevcWXXJP8B1ftguO8\nyFgi/Sbnok3dfXZbbGntoiYHwStNIonVCy485U+9ydeisfGGjmHKzSBlm6baXmGxtd/59uks\nRuUv1/fLuYIDSTaVO19y5rFpvzFX8L3Z4WmX/CjanazfcSzYFvnuecMbwFzJsrVjGHMzSNk2\n6W8SCXuL9dNWt35ZwVuOOeZLfjedQLXgu9zXF7qo5Ou2Q9yFWzmSDYeMcyVXx86bDhrNuBmk\n1/C9Jf/n490m6WRKs+B4S9ecLzmU95YgzRUcyfOanV+vL3i25Iukt6A4iFYuuHjOhiPG+ZJv\n1aHd1p30dm4GKW22zkXy88a/8nVtFkt3eX5Z2aTg7ABsy0s8W/JNHlsPOSYLjsoT99XvKfMl\ni0RbhwTmX75NO6T5ku/5aEOwdR9twPUg3SRK0ldYvts0i4X3loPs+YLvUbDxDW2y5GJMwCxI\n4wVLFtA02bQXnS05H2y4btoac1v5tXk8YLrkW2+Y1CLXg1SOR5fDXZ3FND9ZNXoT/l5wfnJg\n0ivHS77ko8hmQZpqciIX9ZLLywDvTSXPNTnedDQxW/I9P5pINr5+RpwPUrZVglv5qLOYCTf1\nnAUFbxqomiv5WnQcwyBNNHlj0ZMlf5yUKjZ52xW12ZIvxQHjxncVI84HqfBqt0y1+L6EGy+6\nzRT8+RyVkk2+ef5HTd5+kWGuYKOLX5Mlm2TfjOtBKi/s3PPt3llMnxtPrucKLhe3Hc1MlqwR\npOkmm5wwjpd8K/ai702bevrlMxizn9sY+e82HlEYcT1IxUXqv0t+Qt1Z3PbiLii4WEwio3Ok\n8ZK7z1BuclwMNmw655jZypdixsBjppDVBec7u42XqOY3RlJtEstcD1JSTp6K+otX87f38YKr\nuXZGwxhfSu48Q7XganFb15lu8m37xpjZFpetg99zJYcGr58R14OUvrPQRM/BosYJx2jBxUTi\ny8bDjpmSU9MgfSk42a/Jz3Dbpd7Zgg1OYuZfv41NNuNskACfECRAAUECFBAkQAFBAhQQJEAB\nQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAk\nQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkH1zbb8+M8i9MhXMI\nkhcu9ddD37d94Tr2RpC88BJ55/++ZfvXgWNPBMkPt/KbukO5/bolGEWQPFFE6FZ/8f39IkF5\nsPeMpPoab5Hk0p5LwS6C5InsoC5NqgO8NAtPJg/VrViSPEkiUbmAHyBIvrjLLa6GHJ4SJmkS\nyjNPzyNNH5K/jJL/FD9CkLwRSn1gF0memKQ9jquC9PebhiElSB7JDuyqPY7U8gfv5y2sgvTD\nxp0eG98fTVK6QQqbJYL0S2x8f3SC1PzsKpf7802Qfo6N748mKVE+zND5GUH6PTa+P5qkPCR4\n5cN4UTnC8OIc6ffY+P5ok1KeGAXvNI2rs6U/gvRbbHx/dJJyv4hci4uzV5Hw71nunH7WMhAk\nQANBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIU\nECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQAFBAhQQJEABQQIUECRAAUECFBAkQME/\nXjJ75LEkVU8AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Major European Stock Indices, 1991-1998\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use ts.plot with eu_stocks\n",
    "ts.plot(eu_stocks, col = 1:4, xlab = \"Year\", ylab = \"Index Value\", main = \"Major European Stock Indices, 1991-1998\")\n",
    "\n",
    "# Add a legend to your ts.plot\n",
    "legend(\"topleft\", legend = c(\"DAX\"), lty = 1, col = 1:4, bty = \"n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting the future\n",
    "We'll conduct some trend spotting, and learn the white noise (WN) model, the random walk (RW) model, and the definition of stationary processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Removing/filtering common trends in a time-series\n",
    "\n",
    "- log() can linearize a rapid growth trend. It can also stablize a time series with increasing variance. The downside to log transformations is that it is only applicable for positive values. \n",
    "- diff () can remove a linear trend. The diff() method can include a seasional difference transformation. It can remove periodic trends. \n",
    "\n",
    "Common types of trends in time series data include persistent growth or decay over time, increasing variability over time, and periodic or seasonal patterns, that is regularly spaced peaks and troughs appearing throughout the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Removing trends in variability via the logarithmic transformation\n",
    "The logarithmic function log() is a data transformation that can be applied to positively valued time series data. It slightly shrinks observations that are greater than one towards zero, while greatly shrinking very large observations. This property can stabilize variability when a series exhibits increasing variability over time. It may also be used to linearize a rapid growth pattern over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "rapid_growth <- c(505.9547,447.3556,542.5831,516.0634,506.9599,535.0162,496.9291,\n",
    "497.5626,577.2483,536.8560,541.2459,473.4978,550.9890,569.4106,\n",
    "522.9152,487.2002,594.6108,591.1740,615.9868,621.3175,607.1250,\n",
    "587.0367,554.1554,644.1172,509.7000,607.0943,603.5512,613.6216,\n",
    "544.9143,670.8118,687.1316,615.5817,711.1873,694.2979,681.9293,\n",
    "659.1403,642.7021,601.5301,666.7623,650.9657,606.0913,696.6788,\n",
    "641.6025,855.7719,667.3291,573.4914,791.7333,751.5914,610.7948,\n",
    "624.6503,833.2990,639.8867,736.8283,772.2923,686.8865,667.7631,\n",
    "712.9415,918.1838,656.1089,700.4972,683.4933,781.7380,715.6843,\n",
    "808.2875,820.7795,656.8856,733.3400,773.5387,641.2027,932.2119,\n",
    "680.6766,988.2828,664.8986,813.5283,883.4088,924.2749,969.4321,\n",
    "777.3293,880.9984,971.3583,902.9584,1020.7457,1075.1483,886.1707,\n",
    "889.6322,950.3908,878.0395,1043.7676,901.1090,1079.6584,933.9054,\n",
    "921.9433,870.8071,811.1398,1004.2677,1008.1758,1189.4893,751.9706,\n",
    "947.4753,886.5153,1074.8943,1101.1307,1130.1855,975.8495,948.1610,\n",
    "1177.8227,1227.1271,976.9957,836.7089,1323.6047,852.3532,1200.8262,\n",
    "1274.4788,1349.2614,1102.6334,1324.8566,1268.7187,1058.2289,1204.0872,\n",
    "1084.6503,1284.4305,1195.2843,1058.4262,1188.0577,1166.5934,1064.6946,\n",
    "1429.0685,1070.8528,1539.3305,1467.1571,1127.7058,1296.0717,1555.2741,\n",
    "1332.9037,1315.4236,1189.2462,1482.4339,1240.9287,1237.7720,1468.6083,\n",
    "1328.5457,1589.5078,1373.1630,1503.5563,1659.9376,1704.6137,1550.4638,\n",
    "1625.8026,1873.8582,1370.6209,1439.7114,1447.4369,1579.9158,1681.2571,\n",
    "1661.6059,1311.8468,1326.0308,1323.0995,1550.4863,1606.2042,1768.5401,\n",
    "1509.8368,1592.1086,1627.6188,1544.6329,1439.5234,1682.3518,1850.7097,\n",
    "1673.3801,1832.4272,1672.2672,1781.5768,1659.2899,1970.0389,2044.7124,\n",
    "1929.0902,1891.7042,1487.1577,2013.8722,1796.7886,1977.0183,1516.9552,\n",
    "1650.6039,1523.2834,1696.6181,1627.2609,1787.2968,1567.2874,1881.9963,\n",
    "2318.9833,1941.9879,1820.2797,2154.8123,2261.5471,2052.2214,2079.1710,\n",
    "2010.0609,2145.2606,1775.3008,2013.4070)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot(rapid_growth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nEBIgQEiAACEBAoQECBASIPAfId2rh94yuf8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_growth <- log(rapid_growth)\n",
    "ts.plot(linear_growth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logarithmic transformation helps stabilize your data by inducing linear growth over time. Remember to adjust your interpetation of the data accordingly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Removing trends in level by differencing\n",
    "The first difference transformation of a time series z[t] consists of the differences (changes) between successive observations over time, that is z[t]−z[t−1].\n",
    "\n",
    "Differencing a time series can remove a time trend. The function diff() will calculate the first difference or change series. A difference series lets you examine the increments or changes in a given time series. It always has one fewer observations than the original series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "z <- c(6.226447,6.103354,6.296341,6.246230,6.228432,6.282297,6.208447,6.209721,\n",
    "6.358273,6.285730,6.293874,6.160147,6.311715,6.344602,6.259419,6.188675,\n",
    "6.387907,6.382110,6.423225,6.431842,6.408735,6.375087,6.317445,6.467881,\n",
    "6.233822,6.408684,6.402831,6.419378,6.300629,6.508489,6.532526,6.422568,\n",
    "6.566936,6.542901,6.524926,6.490936,6.465681,6.399477,6.502434,6.478457,\n",
    "6.407031,6.546325,6.463969,6.752004,6.503283,6.351743,6.674225,6.622193,\n",
    "6.414761,6.437192,6.725393,6.461291,6.602355,6.649363,6.532169,6.503933,\n",
    "6.569399,6.822398,6.486327,6.551790,6.527217,6.661520,6.573239,6.694918,\n",
    "6.710255,6.487510,6.597609,6.650976,6.463346,6.837560,6.523087,6.895969,\n",
    "6.499635,6.701381,6.783788,6.829010,6.876710,6.655864,6.781056,6.878695,\n",
    "6.805677,6.928289,6.980214,6.786910,6.790808,6.856873,6.777692,6.950592,\n",
    "6.803626,6.984400,6.839375,6.826484,6.769420,6.698440,6.912014,6.915898,\n",
    "7.081279,6.622697,6.853801,6.787298,6.979978,7.004093,7.030137,6.883308,\n",
    "6.854524,7.071423,7.112431,6.884482,6.729476,7.188114,6.748001,7.090765,\n",
    "7.150293,7.207313,7.005457,7.189060,7.145763,6.964352,7.093477,6.989013,\n",
    "7.158071,7.086139,6.964538,7.080075,7.061843,6.970443,7.264778,6.976211,\n",
    "7.339103,7.291082,7.027941,7.167093,7.349407,7.195115,7.181914,7.081075,\n",
    "7.301441,7.123615,7.121068,7.292071,7.191840,7.371180,7.224872,7.315588,\n",
    "7.414535,7.441094,7.346309,7.393757,7.535755,7.223019,7.272198,7.277550,\n",
    "7.365127,7.427297,7.415540,7.179191,7.189945,7.187732,7.346324,7.381629,\n",
    "7.477910,7.319757,7.372815,7.394873,7.342542,7.272067,7.427948,7.523324,\n",
    "7.422601,7.513397,7.421936,7.485254,7.414145,7.585809,7.623012,7.564804,\n",
    "7.545233,7.304622,7.607815,7.493756,7.589345,7.324460,7.408897,7.328623,\n",
    "7.436392,7.394653,7.488460,7.357102,7.540088,7.748884,7.571467,7.506745,\n",
    "7.675459,7.723804,7.626678,7.639725,7.605920,7.671016,7.481725,7.607584)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nEiBASIAAIQEChAQIEBIgQEiAACEBAv8D7TbLKY+uBVwAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dz <- diff(z)\n",
    "\n",
    "ts.plot(dz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "200"
      ],
      "text/latex": [
       "200"
      ],
      "text/markdown": [
       "200"
      ],
      "text/plain": [
       "[1] 200"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "199"
      ],
      "text/latex": [
       "199"
      ],
      "text/markdown": [
       "199"
      ],
      "text/plain": [
       "[1] 199"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(dz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By removing the long-term time trend, you can view the amount of change from one observation to the next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Removing seasonal trends with seasonal differencing\n",
    "For time series exhibiting seasonal trends, seasonal differencing can be applied to remove these periodic patterns. For example, monthly data may exhibit a strong twelve month pattern. In such situations, changes in behavior from year to year may be of more interest than changes from month to month, which may largely follow the overall seasonal pattern.\n",
    "\n",
    "The function diff(..., lag = s) will calculate the lag s difference or length s seasonal change series. For monthly or quarterly data, an appropriate value of s would be 12 or 4, respectively. The diff() function has lag = 1 as its default for first differencing. Similar to before, a seasonally differenced series will have s fewer observations than the original series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- c(-4.198033,9.569009,5.175143,-9.691646,-3.215294,10.843669\n",
    ",6.452159,-10.833559,-2.235351,10.119833,6.579646,-8.656565\n",
    ",-2.515001,9.837434,7.386194,-8.243504,-4.264033,8.898861\n",
    ",8.544336,-8.066913,-4.023025,9.822679,7.772852,-6.587777\n",
    ",-3.459171,10.613851,7.374450,-5.798715,-1.204711,11.429236\n",
    ",7.570047,-4.968384,-2.003787,11.941348,9.406672,-4.396585\n",
    ",-1.555579,12.599877,8.502916,-3.728968,-2.827000,13.375981\n",
    ",8.128941,-3.149249,-2.799473,13.710570,6.755217,-3.779744\n",
    ",-3.768274,13.625336,6.537931,-3.249098,-5.024191,13.355373)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM\njIyampqnp6eysrK9vb3Hx8fQ0NDZ2dnh4eHp6enw8PD////QFLu4AAAACXBIWXMAABJ0AAAS\ndAHeZh94AAAgAElEQVR4nO2di1bjOBAFFciEDI/k//92SWBYHsHqK13Jsl11zi4Z1K2rOCpi\nG2ZIZwCoJs29AIA1gEgABhAJwAAiARhAJAADiARgAJEADCASgAFEAjCASAAGEAnAACIBGEAk\nAAOIBGAAkQAMIBKAAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAi\nARhAJAADiARgAJEADCASgAFEAjCASAAGEAnAACIBGEAkAAOIBGAAkQAMIBKAAUQCMIBIAAYQ\nCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhAJAADiARgAJEADCASgAFEAjCA\nSAAGEAnAACIBGEAkAAOIBGAAkQAMIBKAAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoAB\nRAIwgEgABhAJwAAiARhAJAADiARgAJEADCASgAFEAjCASAAGEAnAACIBGEAkAAOIBGAAkQAM\nIBKAAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIw0EGkBLAwCna5X5wZIgCcIBKA\nAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhAJAADiARgAJEA\nDCASgAFEAjCASAAGEAnAACIBGEAkWBHzbRxEghWBSN0jYI2oG8e30RAJVgQidY+ANYJI3SNg\njSBS9whYI4jUPQLWiPpLIRAJNoH8DtNYpN/rEQkGprlINvEQCQYGkepAJLiCSHUgElxBpDoQ\nCa4gUh2IBFeai4FIsAUQqQ5EgiuIVAciwRVxoyd15yASbAJEqgOR4EpjkXTxCkacLQNGwBJA\npDoQCa7IImlbB5FgGyBSHYgEV5qLJJ8L6iPOlgEjYAG0FgORYBMgUiWItE7kn0EdTKSJYkSC\nfiBSZcuAETADiFTZMmAEzAAiVbYMGAEzUPCjbYhUAyKtE0SqbBkwAmYAkSpbBoyAGUCkypYB\nI2AGSv76j9JSUI9IsDwQqbJlwAiYAUSqbBkwAmZgQJHken3I2DJgBMyA/jdYEakKRFoniFTZ\nMmAE9Ee9JEGkWhBpGTT+thAi1YJIywCRIkPGlgEjwAAiRYaMLQNGgIHG/zbJW7XQgkj9I8AA\nIkWGjC0DRoABXaSCnyRApHIQaRkgUmTI2DJgBBgYUaTW4ulDxpYBI8CA+JMKrUVKn/7fZEGI\nBE1ApMiQsWXACDCwBpHkennI2DJgBBhApMiQsWXACLiBetwXLlKZePKQsWXACLiBLpJ+iaFf\nk4Q7EGmGCLiBeNyLrtURqaJlwAi4wWAipS8fovWI1DUCbtD4G6yIVNsyYATcAJFCCxKHjC0D\nRsANCkTqcLcZkYpBpHlApNCCxCFjy4ARcINViNROPESCGD1Ekt8xxhFpqhKR4H8QKTK/POZr\nGTACblAiUsNrkvTtY7C+sXj6mK9lwAi4QcHPziGSOElVy4AR8JMkHnlEio35WsaIQM8MiBRb\njzrmaxkjApEyNBZJ3beIVA0izUKZSM32OSJVg0iz0EckfeMiUimINAuIFFuPOuZrGSNC/cWL\ni0d9vknsQaTYmK9ljAhECtQXiBTtQaTqljEiEClQj0j59ahjvpYxIhApUD+iSK0CEKlw1s2J\nJD5hRAquRxzztbzz9LBPF/aHp1YRk7MiUqb+jEih9YhjvpYrp7v0P/dNIqZBpFz9uUykYJPq\nRS+R9PWIY76WK4e0+/t8ffTyuEuHFhHTIFKu/oxIofWIY76WK7v0/PH4Oe1aREwj/iWB5VMi\nknKMECk25mt560u//cEWMZ3f5T7JSGxMpOL5FybS3O9IGxRJfMKiSOnGo1A9IpW2XHm9Rnp8\nuT6a5xoJkfL15zKRYk2IVN3yxv2nu3Z3pyYRmUkL9tWSQaRYw9JEOj8drt9H2u0f5vg+EiLl\n689jitR4/sWJNG/E5kQqe8IdRFLvwiGSNO1nmgQgUr7hLPS0Fqn1O17FO6Q25msZIkLfVws3\nKZ3FZ1wuUqipm0itr6nUMV/LEBH6vkKkQPnPx/l6RCpsGSKiuUijeac+4fTlQ7g+3IRI1S1v\nfSl8GYRIjgBECtYvTKQjIlWCSI3mV+9OiGO+ljeed9N/ecIQkZu0rUitTRpYpEgXIlW3vPM8\n/YNBjojMpAsXSQsYVyRVDET6xvHTz602ipieVBNJXMeIIilPIX37GK0PNqlngh1PHRcn0qwR\nBV+gESlSH2xCpPqWNhEl9wK0faVu3MaHBpGC9YgkRWxPJPXU9NxPpHzX4kWarEKkqXpEitQH\nuxCpvqVNBCLlys+I1KReHbS1tIlApFz5//+P1yNSZD3aoK2lTUSHa29147Y9NmJAqUhl196S\nSKIYcr0oKiLJkzYUSRZPBpGi9YikRCBStvyMSJF6RJInXbJIJQtai0iRBkQqjCgRSdxX8r5t\neXBKvhIgUpN6cdDW0iYCkQL1QgciCeuRBm0tbSI0kdRtVbZvESlWjkiI5KqXGUykNPnHTD0i\njSNSKrn0XrxI+jWPLlLRvtJEEsVApDKWK1LLo4NI4XpEEiKWL5J4JBEpXI9IQsQKRNIOJSKF\nyxFJiCgTSdxXjd+RJJVEMdKPB9GGsn2Va0Kk+pYmEV1EavgG8FYqm9pMpNp91VYk8R0v8gwQ\n6aNoBSK1C0CkeAMi6XOOJlL89K6fSOo+DPUgUn1Lk4i1iCTvdFWMIUUSL3oQqYjw82q3a3uK\nFOzZmEhV9eoTKHnC8UFbS5OIxiLJXsimfqoMnd6ViiR6Gu1AJDWwvqVJxJpEkq4ZEClfr16C\nIZI8pyiSeirYQSRZDERy1CPStznFL+iIFKgP9KjeIZKBRYtU0BFrQqR4PSLFIxYvUvEr314k\neSPmW2pF0k4dESkesV2R4sensB6RIguKD9pamkSkcOXXORuJpL4BIJJ3fkQqjRhWJDUh2oNI\n8XpEikd0EqlAC0SqL68UKfAEEOlz0TZFUl93RMrVI1LBnLEeRFLq8y2IZGhpErE1kdIvj10L\nqtqI+Q5EMrQ0iRhXJDUh1lIhUsE+aS6SKEZjkUregtV+Q0uTiC2LpL7uiOSu10ZdLS0iUrjy\n+5yIlJ8fkbLrUUZdLS0iUrz0W526zXUtEClfjkiIlAtQzk3jHYOJpIqBSIaWFhErE0ndudoL\nj0juem3U1dIiApHMC0IkbT3KqKulRUS5SOo234ZIdfs234BIhpYWEYhkLa8XSd1piKS3tIgY\nWqT2FyXbE0l8y2t+gMQ4S0uLiH4iNXl/0TsQSapHpGBE+vZRmFLd5YgUqEckFUTKNownkly/\nOJHU9SPSt5oxRYr0IJKzAZEKIxDJu56Ni6QfILHd0tIiokIkdZcjUqAekVS2J1LBFQ8iZUcR\nSW9pEYFI3vU0Fkn1rlpURApGDCaS/DpWvpCIlBlFpGAEIrWcHpEq4wMMJlJwPWsTSd3oiJRp\nQCREajE9ItXFB0CkbH2oBZGc81evH5E6iKRrsXyRzBu9u0jq/IhUIJK8zREpX6+KJO9MRGoS\ngUhNp0ekyvg8Y4iUbjyKT7lAkSqvARApM4xIiNSkHpHq4vOMJlJsQYgk1m9NJP0ASd2elgYR\niNS4HpHq4vMsUiT1iqH6EgORsoOI1JwViCR3zCxS9b5tL5IYgEgdRLJvc0RCJBVEigQgUl09\nIjlApHwAImUGEWkEkWrFm12k6n1VsHGmOhDJ0dIgApG860Ek+QApw6aWBhHpl8fBGccTSX2l\nECkziEiI1KAckdz10rCppUEEInnXg0iIhEiG9axPJHV+REIkw3oQCZFGEEl9GfUIREKkFhGI\nJC4IkTKjiLRMkWpfSERyz68/4fiwqaVBRPr1D6EZESk7bBVJ9Q6RLCBS9YoQCZEQybAiwyWA\neEmCSCKbFMn9Bd2QIL7u44kkByBSgwhEWrdI6lsYIhVGIBIiZcYQSRYDkaoXhEiIhEiGBSES\nIpWIZN627UWqf92XL5IYgEi6GNkGREKk3CgiIVKLekQSRhGpVf3CRFIvSRYvkkE8ZdjU4o8Q\nRZL3OSIhkjKKSNEGRMqPIZLEFkSqFw+RquoRyQIiVQcgkjw/Ig0pkvnkEZH0AESSRXK/YSBS\npuH22O8diGRp8UcgkvcSAJEy9Yj0yzAiZQcRKTyISKZ6RMp0IJKl5TPHu5T2j7URg4kkvyyI\nVBKASNe+a+N9unKojEAkRMoOrVmkQzqczueXQzrWRSASImWH1izSLp0uj0/pri5i8SLV73RE\nyg2tWaSUPv3h2/An5EUgknt6RBIG+4v0559Iu7oIREKk7NBqRdo/HB/T39eHp8P03QZEql2R\nQyR13040/DKgBswoUm5LdhXp47Qtpd2pLgKRECk7tFKRzs/Px+N+f2nfHSY9QqTqFSHSdPmi\nRXJGIFKHa57hRBIvwhApG/GjYIMitd8nCxJJXT8i/VKASHULQqSCemXc02KP6C+S90wKkXoE\nIBIi1dYj0vT0iPRLwdpFcrzuvm3bXiS1AZHKIma45kGkioZ5RFKfACJlWxBpuh6RiuqFcU+L\nPaKxSLIXiDTdgEieFnsEInnrEamoXhj3tNgj6sVApPxQ632OSK1BpNoARJqeH5F+K7Duc0TK\nNCCSOu5psUcgkrcekYrqhXFPiz0Ckbz1JpHUz88nkkc8YdzTYo8YTCT1y9vt0dZiIFJ5PSL9\nOohI2SFECg2Fxj0t9ogliCQvCZHKGxCpLAKRpusRqWh+REKkwBAildcj0q+D84rUeEWIVDQ/\nIiFSYEjfJuK+9X0ekTwgUmX9WkUSP49IegEi1SwIkTL1iPTrICLlRxApMhQa97S4I26MI1LN\nghqLJM+DSB4QqbIekcrml49QeNzT4o5Yp0iqGYhkD0YkRKpaECJl6hHp18Hli2S8BECkTD0i\n/TqISPkBRAqMxMY9Le4IRMrUI1LZ/IhkFUnd5e1F8pyqIVJxPSL9OqiKZG1ApD4BNpGymx6R\nwkOIVNyASKYWd0Tjax5EMjcgkqnFHYFI3npEKl1PvMDS4o5wiIFI+YHZ9qcrAJH0cUQqr0ek\nwnqhwNLijhhMJPVV+W0MkdwBiKSPI1J5PSIV1gsFlhZ3BCJ5620itQ5GJG8EInnrEamwXiiw\ntLgjEGm6vvUZFiLpBZYWdwQiTdevVyQxAJH0cUQqX5BtovaHrq1IBWZHCywt7giHSHPuhpmu\neRCpuAGRfh9qvhuaJ7TfJksXyXYkEOn3IUQqnmjxIhkv2qIFlhZ3BCJN1yNS6fzbEunmMCKV\nLwiRcgOI9PsQIhVPhEh6gaXFHIFImfrBRJJfGkQygUh19YhUOj8iIVL5glqfeSGSq8UcgUiZ\nekQqnR+RjCK5thsiZcsRqS2IFBsxXQshUnYAkX4fWpBIJmEQqbQekSaGxhOptTCIVFqPSBND\niJQrR6TAgqIFlhZzBCJ5P49I2QFE+n3IdzARaXoEkVwt5ojBRJInQiT3ihCpKGKwg7k5kVQx\nFiSS3hAtsLSYIxDJ+/nFi9T6LRWRpgYQKVc+okg3hxCpLAKRvJ83iiTu8+Yiyc8AkRCp+PMz\niiS/hSGSMQKRvJ9HpPL6eIWjxRyBSGXTmE6kEKmowtFijli8SMt5h0Gk7IKiFY4WcwQiTX8e\nkXJDiDQxjEjZXETKNswk0p/T+4OXe32iWER4GJGyuYiUbZhJpLT7e/14TNb3qenJTGIgUr4e\nkfILilZMtjzt0v7l9e0o7Z70iWIR4VFEyuYiUrZhtmukh5QOKT3o08QjgqPjidRaGETK1y9G\npMtZXTrqsygRsVFEKl0QIpXXxysyLW/vSAd9mnhEcHSuE6nFizTnPkekN16vke5fr5H2S7xG\nai4kIuXLEen98ftZ3d9dwUSxiPAoIhUuCJEq6uMVky2vb0dvnP7oE8UiwqOIVLig7YlkFC9e\n4WjxRiBS5vOIVD4/IiFS6YIQqaohWuFo8UZsTiTfGT0iFc2PSJMDiJQrR6RAQ7TC0eKNGEwk\n+YQbkdwrQqSiCETKjKxaJDVBFA+REKm0HpHqFhSscLR4IxApM4JImTFEmhpdgUgeMRApN4ZI\nU6OmXWvctisVybnN2ycgkjza/B0GkbL1iBQHkaL1KxDJIQYi2Vq8EYjkXREiZccQaWoyRMqW\nI1JgQcEKR4s3YvEiNT5V25xI6hNApOlRRMouCJGyDdsRySYGIuXrESmfEKxwtFgjECkzsniR\nrAGIJA8iUnZBiJRtQCREyi8IkbINiIRI+QUhUoOGYIWjxRrRWCTZi6WLNO8+X4RIgS2PSEI2\nIhU1IJKtxRqBSJkRRMoNItLkICJlFzSHSJn9gkg6Tw/7dGF/yPxL4WsRySMGImVGvc9geJFO\nd+l/pn9TJiLV1CNSVcDwIh3S7u/z9dHL4276F8EgUk39ykVSE1Yn0i49fzx+TrviiMFEKlgr\nItUEbF6kL7+v+ecvb06fKcpfq0jOFSFStmF4kYZ7R2q/bWd5h0GkuoDhRXq9Rnp8+3VKg1wj\nIVK2HJEiCwqWGFreuP907nZ3Ko5ApMwYIlUFjC/S+elw/T7Sbv8wxPeREClb3kGkG+OtRTI/\n42iJocUagUiZMUSqmh+REKloRYiUHUWk6bkQKVtuuOZBJF+LNQKRMmOIVDU/IiFS0Ypai4FI\nvhZrxIzXPIZtO92CSP4V1c+PSJm5ZhJpsBUhUm1DsMTQ4oyY81StuUhyAiJl6xFJHkOk7IIQ\nqWB+RDLXI1KgHpGiIFK4HpEK6hHJx4wiyV4sXSR5nyNSrKlFizMCkTJjmxPJ/QwQCZGyC0Ik\nfX5EKqlHJHfD4gIQCZGyC1qDSN8LEKkoApEyY4hUGYBIiJRdECLlGxBpDpHEbZtrWZ9IqhaI\nZASRKuoRqTIAkRCpYEWIlB9GJL3eK5JDDESqTEAkdWydIjV+j0Sk/DAi6fWIZG7Ib5fvFcOJ\nFNnxiCREDyiS/OUTkfQGRCqoX7tI8i5BJEQqqUek2gZECoJI4XpEQiRrizMCkTKj2or8+xyR\ngixLJHUqRKptQKQg6xFJ3raIhEjRkCYtzojFi+RNGE+kbxWIZGwxRsx6qoZISxSp9ioPkXL1\niLRJkeziRWvqW4wR84pRu23HW1FrkQK7BZGaMZ9IshfDiSSetyCSYUHBmvoWYwQiZUYRyV2P\nSAX1WxNJ3+cDiKQ+B0RS0xEJkfIBiJRNX75IcgIiIVJRBCJlRscSqWQPIpINRCqvR6RcACJl\n0/uLpG3bQAsiIZIPRCqvR6RcgDo/IhXUI1IuYTiRGniBSNX1iGRtCO0VRGoGIpXXSyvSt0h7\nkVS3EakoApGcKxpCpMo3SUQqikAk54oQydOASFL5LCK5V/SlAJE8DYgklW9TJPk9DJFiIFK8\nfnUiaXsquFUQqRXrEanzNY+6IkTyNCCSVI5IyxRJDkCk6npEqm9ApBiIFK8fXKTYS4lI+YTF\niSTuQlUkddci0mQ9IplbfBGqSI13bYFI7ve8riJpp4LRnYJIrUCkeMJ4In1UIZK7xReBSLnx\nLYiknm3WiaS9DcdBpHg9IokBwS5Eqo1ApNz4xkRK+nkXIuXDxW2ISBFKG8IbRb3k+VQkP4NY\nT8WK4qxIJHkXji+StCJ1GwZf+n4iaQuKNyFSZb3y5TxUP7RI8jbsIJLidui07uekiJQPR6QN\niRTfiIikhiPSwkUSEoR9iEhqOCItW6T4uVr4tO7HtJFGRKqsR6SpBu2SpOTMK5ygbUJEUsMR\nadEiFV1VqeWIFAhHpCWL1GxnIZIavnyR5CWtQCT5okoFkdTwziIFDsV4Isli9BKp3cZCJDW8\nUiT1DWbZImleqA3KNmkt0pepZS8QSa5HJEd9oUgt9xUiieGI1EAk+RKmSKSm2wqRxPD1iSRe\ntSHSrwG3HrdpCLIkkexfzhEpWi+K1HZXyV58rkIkRJrsGEmkxpsKkcRwRBpFJGmXIFIjEEmI\nSL/+IdMgihR/3XWRWu8pXaRPZWsUSdyFiDTVgEixFkQaQaTOSxJWpInRViSluAREErPHF8l/\nzbMCkZqTPhPt+fEgVC0sSm+xRYwlUskRRqSlgEjl9Yg00SC87s3vwvUAkcrrFy+SsiJRJOVl\nR6RGLbYIRJpuQCQj6dvHUHHB/A1BJCEDkRqBSOHybwWBZ4ZIsQZEatJii0Ck6YZRRFqDR9qB\nWplIqhkbFkl4GZNWjkjS9C1BJCEj3XyYbUCkLIjUqry/SNqSEMnKikUSO/27tviKJNyDSOMg\nHClEEmMRKdKwJpGUg6rP3pZliFR0hAcQSb4Lp4ukFA8MIoXnka95NiqS9oqsRSThSwgiibEj\nixQ9bIgUBZGi8/QWSVzRGCKd1/GTCgUgUnSezYokXvMgUqCyYPLGIFLRihDJTvisdtUiaVfq\niDTRgEj5woK5W4NIRStqJ9JWPRpZpONdSvvHVhHLF+lLibSi8FFDpDjRN+OOIr29Gvdv/5LL\noUkEIoVApDijinRIh9P5/HJIxxYRdSKFUhFpW4wq0i6dLo9P6a5FxPAiie95iDQ/wefeW6R/\ny5pe3iJECi6yuUgfRYjUgkFF+vNPpF2LiLWJpL2GikjaEd6wR0OKtH84Pqa/rw9Ph+m7DYik\nRKQvH2INiBRlRJE+/unllHanFhGIFG1ApDDDiXR+fj4e9/vrLYfDT49K/p3zzOKGEKn85sE4\nIm2a8UTqEYFIsQZEMoNIYioiwS3mECl/5uYRqem95iKRxAREWg6IJKYOK5JwzBDJDyKJqT1F\nku4LItKsIJKYug6R8MgNIompiAS3WJtI6rYtFym8xvFE2vTPzjVibbe/ESnUgUhuEElMHVUk\n6ZAhkh1EUkPTt49ChHI3W10RIs0LIqmhiAQ3QCQ1tJ9I0m1BRJoXRFJDEQlusGKRxCv7TYmk\nFEMERFJDxxRJO2KIZAeR1FBEghsgkhpaLpIYgEhLYusiFd5sjpcj0jZAJDU0SdXnIUUCO4ik\nhnYTSXrLQ6SZQSQ1dEiR8GhuEEkNRSS4ASKpoc1FKklApLlBJDUUkeAGiKSGFouk3i9HpCWB\nSGooIsEN1itSy+/aCOVdRMKj2UEkNbOXSMIxQKT5QSQ1E5HgBoikZsoiyR2ItEAQSc2Utzki\nbQFEUjMRCW6ASGpmqUjqRZV+7ggzgkhqJiLBDRBJzUQkuMHqRFLvNo8qUsFFGMwIIqmZA4oE\n84NIaiYiwQ1WK5L4/VVEgioQSc4svIRBpFWDSHJmmUjqTThEWhaIJGciEvwEkeTIJFWfEWkT\nIJIc2UUkPFoYiCRHIhL8BJHkSESCnyCSHIlI8BNEkiOLRFLv8iHSwkAkORKR4CeIJEciEvxk\n8yLJ9YgEN1irSJoXckNrkfBoaSASIoEBREIkMIBIJSJp6yswD5GWBiJ1EUltQKSlgUiIBAYQ\nCZHAACIhEhhAJLW+4KaaKgb/lvfyQCREAgOIhEhgAJEQCQysVCTNC7lBFalxPczP+kRSf5AA\nkcAAIiESGECkApHU5SHS+kGkEUUS54f5QSREAgOIJIukn3kh0vpBJEQCA4jUQySxHpYHIiES\nGEAkRAIDiIRIYACROogE62edIklayIGIBD9AJEQCA4hUIJK0HNgEiIRIYACREAkMIBIigQFE\nQiQwgEiIBAYQSf0GLsANEAmRwAAiIRIYQCREAgOIhEhgYJUiae2IBPUgEiKBAURCJDCASIgE\nBlYokvr3hdSbEwA/QSREAgOIhEhgAJEQCQwgEiKBAURCJDCASIgEBhAJkcDAKkWSyxEJKukq\n0tPDPl3YH55aRRR0IxLU01Gk0136n/smEUXdiAT1dBTpkHZ/n6+PXh536dAioqgbkaCejiLt\n0vPH4+e0axFR1I1IUE9Hkb7cTJu+s4ZIsDB4R0IkMND3Gunx5fqo8TWSCCJBPT1vf99/umt3\nd2oSUYL6FwEBftL3+0iH6/eRdvuHpt9HEkEkqGeNP9kghyES1IJIiAQGEAmRwAAiIRIYGEek\n9Jk2Eb8EIxJU0/UnG8KuIBIsjI4iHREJVkvPU7vn3fRfnjBEFNH3TBJWSddrpOfpHwxyRJSA\nSFBN35sNx08/t9ooogBEgmrGuWvXOeJzGiJBLYiESGAAkRAJDMwhUn7jIhIsDERCJDCASPz9\nWDCASIgEBhAJkcAAIiESGOD2NyKBAURCJDCASIgEBhAJkcAAIiESGEAkAAOIBGAAkQAMIBKA\nAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhAJAADiARgAJEA\nDCASgAFEAjCASAAGBhUJYGEU7HK/OEPlEbyZ3HlPfRCJ4JXkIhLBqwre3BOeJXx7R3lzwZt7\nwrOEb+8oby54c094lvDtHeXNBW/uCc8Svr2jvLngzT3hWcK3d5Q3F7y5JzxL+PaO8uaCN/eE\nZwnf3lHeXPDmnvAs4ds7ypsL3twTniV8e0d5c8Gbe8LzhwOsBUQCMIBIAAYQCcAAIgEYQCQA\nA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhAJAADiARgAJEADHQV6bBLu8OpZ+KF47/n2Df+\nePeR1jX49CelP8/n/sGvPKUZcj//u/fz7LDrKjpm3V+f8F3HxAvP/363QN/4wzVtd+oevLum\nXU3qfcBPu7dD3TX3+ZNI8+ywKx1Fekq75/PzLj31i3zlNTDNEP+c/pwub4Z/egcfLpGHtD/P\ncMD3b4e695He/3s4zw57o6NIh/T4+v+/6aFf5GUr3/971+8av38LvWT3Dd6l03tu9wP+9/19\noW/u8f+cWXbYOx1F2qeX85cvID1Ih/O7SPPEp3mC0+7cPfjl39esvrnHdPz3cJaX+J2OIqX0\n+UMnnr/ndo0/pftZgg/XzdU5+D69vEX1zd2nxz9pd+gf/JW1i/Qjt2v88XKu0T349RRrhn31\nkP6e5xHpyn334K8gUkNedvs5go/73fUyoWvw9YRqDpHSq8Dn0/U9GJE65naMP+3u5wk+n/sA\nBdoAAAK7SURBVP9031d3lzv9c4j0xuly03sjIu3mFal//P3dTMGXfbXrG/znesPsLWqWF/qS\nNtcOu4b2i3q7p/LS/Z7Kl7t2/eJf7u5fZgm+8v/twj7B6YONPOEf+f2iHq5ftB7fLoQ78i5S\n5/jH6+Vv/+C37yO9XM50egZ/FmmeJ7yfb4ddWP1PNnyI1Df+5cOjOX6y4bS/XCP1P+Bz/GTD\n4eLN6fq92I38ZMP57uM+ZVf+nTJ3jf/z/xfozs97939a9wP+fqi75p7envChe/BXul4BX382\nt2PgG/9E6hr/6Uyn9/N+Tbt7+2Z/9wP+fqj75p5mfML/w99HAjCASAAGEAnAACIBGEAkAAOI\nBGAAkQAMIBKAAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhA\nJAADiARgAJEADCASgAFEAjCASAAGEAnAACIBGEAkAAOIBGAAkQAMIBKAAUQCMIBISyB94uM3\nEMJI8KIsAUQaHl6UxYBAI8OLsxgQaWR4cRbDP5EuH1//e0i7h/P5kNLbb/E+3qXdccbVbR1E\nWgxfRXq4XC893l/+fzFpf71+up91gZsGkRbDV5HuT+fj+/935/Pj5dHpPj3Ou8QNg0iL4atI\nT9dHL+9/3qfT66NT2s+4vm2DSIvh2zXS+fP//785DvPAkV8MiDQyHPnFMC3SfOuCC7wAi2FK\npD23GWYGkRbDlEh/0+75fD5ys2E2EGkxTIl0vn5DKe1eZlvd1kGkxTAp0uUnG9IfPJoNRAIw\ngEgABhAJwAAiARhAJAADiARgAJEADCASgAFEAjCASAAGEAnAACIBGEAkAAOIBGAAkQAMIBKA\nAUQCMIBIAAYQCcAAIgEYQCQAA4gEYACRAAwgEoABRAIwgEgABhAJwAAiARhAJAADiARgAJEA\nDPwHH7IR+e1fxlEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx <- diff(x, lag = 4)\n",
    "\n",
    "ts.plot(dx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again differencing allows you to remove the longer-term time trend - in this case, seasonal volatility - and focus on the change from one period to another."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## White Noise (WN) model\n",
    "\n",
    "White Noise (WN) is the simplest example of a stationary process. A weak white noise process has:\n",
    "\n",
    "* A fixed, constant mean\n",
    "* A fixed, constant variance\n",
    "* No correlation over time\n",
    "\n",
    "The ARIMA sim function can be used top simulate white noise data. \n",
    "\n",
    "***ARIMA*** stands for: Autoregressive Integrated Moving Average. It is a very broad class of time series models that includes white noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.449729397969777</li>\n",
       "\t<li>0.507988960922872</li>\n",
       "\t<li>0.4624639829815</li>\n",
       "\t<li>0.099998758888142</li>\n",
       "\t<li>-0.187680268397845</li>\n",
       "\t<li>-0.763083410511716</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.449729397969777\n",
       "\\item 0.507988960922872\n",
       "\\item 0.4624639829815\n",
       "\\item 0.099998758888142\n",
       "\\item -0.187680268397845\n",
       "\\item -0.763083410511716\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.449729397969777\n",
       "2. 0.507988960922872\n",
       "3. 0.4624639829815\n",
       "4. 0.099998758888142\n",
       "5. -0.187680268397845\n",
       "6. -0.763083410511716\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  0.44972940  0.50798896  0.46246398  0.09999876 -0.18768027 -0.76308341"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate n = 50 observations from the WN model\n",
    "# order = c(0, 0, 0) specifies the WN\n",
    "# default mean and stdev are 0 and 1, respectively.\n",
    "\n",
    "WN_1 <- arima.sim(model = list(order = c(0, 0, 0)), n = 50)\n",
    "head(WN_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nmAKH+wAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot(WN_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3.91265916220113</li>\n",
       "\t<li>1.39718601291289</li>\n",
       "\t<li>6.67996388378042</li>\n",
       "\t<li>5.26984577641988</li>\n",
       "\t<li>1.1232687542897</li>\n",
       "\t<li>6.36895336325393</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3.91265916220113\n",
       "\\item 1.39718601291289\n",
       "\\item 6.67996388378042\n",
       "\\item 5.26984577641988\n",
       "\\item 1.1232687542897\n",
       "\\item 6.36895336325393\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3.91265916220113\n",
       "2. 1.39718601291289\n",
       "3. 6.67996388378042\n",
       "4. 5.26984577641988\n",
       "5. 1.1232687542897\n",
       "6. 6.36895336325393\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3.912659 1.397186 6.679964 5.269846 1.123269 6.368953"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate from WN model with mean = 4 and stdev = 2\n",
    "\n",
    "WN_2 <- arima.sim(model = list(order = c(0, 0, 0)),\n",
    "                     n = 50,\n",
    "                     mean = 4, \n",
    "                     sd = 2)\n",
    "\n",
    "head(WN_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAMFBMVEUAAABNTU1oaGh8fHyM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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot(WN_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a given time series, we can estimate the WN model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "arima(x = WN_2, order = c(0, 0, 0))\n",
       "\n",
       "Coefficients:\n",
       "      intercept\n",
       "         3.5472\n",
       "s.e.     0.2648\n",
       "\n",
       "sigma^2 estimated as 3.506:  log likelihood = -102.31,  aic = 208.61"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit the WN model with arima()\n",
    "\n",
    "arima(WN_2, order = c(0, 0, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, you can just use the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.54715454980484"
      ],
      "text/latex": [
       "3.54715454980484"
      ],
      "text/markdown": [
       "3.54715454980484"
      ],
      "text/plain": [
       "[1] 3.547155"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(WN_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.57721696894215"
      ],
      "text/latex": [
       "3.57721696894215"
      ],
      "text/markdown": [
       "3.57721696894215"
      ],
      "text/plain": [
       "[1] 3.577217"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var(WN_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}