Working_With_Market_Data_Example_Julia.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>.container { width:100% !important; }</style>"
      ],
      "text/plain": [
       "HTML{String}(\"<style>.container { width:100% !important; }</style>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(HTML(\"<style>.container { width:100% !important; }</style>\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### MIT License (c) 2019 by Andrew Lyasoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jupyter notebook written in the Julia 1.1.0. It illustrates some basic operations with large chunks of market data (extracted from public sources), creating histograms from the returns, and other similar operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First load the database library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Dates\n",
    "using JuliaDB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The historical quotes are downloaded in .csv format from nasdaq.com and are placed\n",
    "in the directory \"HistoricalQuotes.\" Before those files can be used here they\n",
    "must be modified (slightly) in Excel, LibreOffice Calc, or a text editor (e.g., Emacs):\n",
    "there should be no empty line, or a line that contains a time-stamp (all lines except\n",
    "the first one must be identically formatted -- this may involve removing the second\n",
    "line in the spreadhseet). The data for all stocks can be stored in a single variable\n",
    "(note that HistoricalQuotes is the name of the sub-directory that contains all .csv files)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-d NDSparse with 10076 values (5 field named tuples):\n",
       "ticker  date       │ close    volume     open     high     low\n",
       "───────────────────┼──────────────────────────────────────────────\n",
       "\"AAPL\"  2008-08-11 │ 24.7943  222653337  24.2957  25.2143  24.2386\n",
       "\"AAPL\"  2008-08-12 │ 25.2471  208987793  24.7886  25.6128  24.7871\n",
       "\"AAPL\"  2008-08-13 │ 25.6143  210556213  25.4257  25.7143  25.1286\n",
       "\"AAPL\"  2008-08-14 │ 25.6171  177684343  25.4757  25.7786  25.4057\n",
       "\"AAPL\"  2008-08-15 │ 25.1057  176996663  25.5771  25.6786  25.0071\n",
       "\"AAPL\"  2008-08-18 │ 25.0557  137832351  25.0814  25.4014  24.8314\n",
       "\"AAPL\"  2008-08-19 │ 24.79    153915766  24.9343  25.2957  24.5443\n",
       "\"AAPL\"  2008-08-20 │ 25.12    126718798  24.9676  25.2771  24.8014\n",
       "\"AAPL\"  2008-08-21 │ 24.8986  134917270  24.9243  25.0643  24.5557\n",
       "\"AAPL\"  2008-08-22 │ 25.2557  109873363  25.1171  25.3571  25.0814\n",
       "\"AAPL\"  2008-08-25 │ 24.65    121049286  25.1643  25.1757  24.5228\n",
       "\"AAPL\"  2008-08-26 │ 24.8057  111348823  24.68    24.9828  24.6586\n",
       "                   ⋮\n",
       "\"MSFT\"  2018-07-27 │ 107.68   36916780   110.18   110.18   106.14\n",
       "\"MSFT\"  2018-07-30 │ 105.37   34495720   107.19   107.53   104.76\n",
       "\"MSFT\"  2018-07-31 │ 106.08   27181070   106.49   106.72   105.38\n",
       "\"MSFT\"  2018-08-01 │ 106.28   23617980   106.03   106.446  105.42\n",
       "\"MSFT\"  2018-08-02 │ 107.57   26080740   105.4    108.09   104.84\n",
       "\"MSFT\"  2018-08-03 │ 108.04   18629310   107.8    108.05   106.82\n",
       "\"MSFT\"  2018-08-06 │ 108.13   20234680   108.12   108.42   107.559\n",
       "\"MSFT\"  2018-08-07 │ 108.88   16070070   108.56   109.1    108.17\n",
       "\"MSFT\"  2018-08-08 │ 109.49   15461420   109.33   109.75   108.76\n",
       "\"MSFT\"  2018-08-09 │ 109.67   13634510   109.71   110.16   109.6\n",
       "\"MSFT\"  2018-08-10 │ 109.0    18171350   109.42   109.69   108.38"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata = loadndsparse(\"HistoricalQuotes\"; filenamecol = :ticker, indexcols = [:ticker, :date])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same database can now be saved in a special binary format that makes reloading at a later time very fast.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-d NDSparse with 10076 values (5 field named tuples):\n",
       "ticker  date       │ close    volume     open     high     low\n",
       "───────────────────┼──────────────────────────────────────────────\n",
       "\"AAPL\"  2008-08-11 │ 24.7943  222653337  24.2957  25.2143  24.2386\n",
       "\"AAPL\"  2008-08-12 │ 25.2471  208987793  24.7886  25.6128  24.7871\n",
       "\"AAPL\"  2008-08-13 │ 25.6143  210556213  25.4257  25.7143  25.1286\n",
       "\"AAPL\"  2008-08-14 │ 25.6171  177684343  25.4757  25.7786  25.4057\n",
       "\"AAPL\"  2008-08-15 │ 25.1057  176996663  25.5771  25.6786  25.0071\n",
       "\"AAPL\"  2008-08-18 │ 25.0557  137832351  25.0814  25.4014  24.8314\n",
       "\"AAPL\"  2008-08-19 │ 24.79    153915766  24.9343  25.2957  24.5443\n",
       "\"AAPL\"  2008-08-20 │ 25.12    126718798  24.9676  25.2771  24.8014\n",
       "\"AAPL\"  2008-08-21 │ 24.8986  134917270  24.9243  25.0643  24.5557\n",
       "\"AAPL\"  2008-08-22 │ 25.2557  109873363  25.1171  25.3571  25.0814\n",
       "\"AAPL\"  2008-08-25 │ 24.65    121049286  25.1643  25.1757  24.5228\n",
       "\"AAPL\"  2008-08-26 │ 24.8057  111348823  24.68    24.9828  24.6586\n",
       "                   ⋮\n",
       "\"MSFT\"  2018-07-27 │ 107.68   36916780   110.18   110.18   106.14\n",
       "\"MSFT\"  2018-07-30 │ 105.37   34495720   107.19   107.53   104.76\n",
       "\"MSFT\"  2018-07-31 │ 106.08   27181070   106.49   106.72   105.38\n",
       "\"MSFT\"  2018-08-01 │ 106.28   23617980   106.03   106.446  105.42\n",
       "\"MSFT\"  2018-08-02 │ 107.57   26080740   105.4    108.09   104.84\n",
       "\"MSFT\"  2018-08-03 │ 108.04   18629310   107.8    108.05   106.82\n",
       "\"MSFT\"  2018-08-06 │ 108.13   20234680   108.12   108.42   107.559\n",
       "\"MSFT\"  2018-08-07 │ 108.88   16070070   108.56   109.1    108.17\n",
       "\"MSFT\"  2018-08-08 │ 109.49   15461420   109.33   109.75   108.76\n",
       "\"MSFT\"  2018-08-09 │ 109.67   13634510   109.71   110.16   109.6\n",
       "\"MSFT\"  2018-08-10 │ 109.0    18171350   109.42   109.69   108.38"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save(stocksdata, \"stocksdata.jdb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.006708 seconds (30.30 k allocations: 725.484 KiB)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2-d NDSparse with 10076 values (5 field named tuples):\n",
       "ticker  date       │ close    volume     open     high     low\n",
       "───────────────────┼──────────────────────────────────────────────\n",
       "\"AAPL\"  2008-08-11 │ 24.7943  222653337  24.2957  25.2143  24.2386\n",
       "\"AAPL\"  2008-08-12 │ 25.2471  208987793  24.7886  25.6128  24.7871\n",
       "\"AAPL\"  2008-08-13 │ 25.6143  210556213  25.4257  25.7143  25.1286\n",
       "\"AAPL\"  2008-08-14 │ 25.6171  177684343  25.4757  25.7786  25.4057\n",
       "\"AAPL\"  2008-08-15 │ 25.1057  176996663  25.5771  25.6786  25.0071\n",
       "\"AAPL\"  2008-08-18 │ 25.0557  137832351  25.0814  25.4014  24.8314\n",
       "\"AAPL\"  2008-08-19 │ 24.79    153915766  24.9343  25.2957  24.5443\n",
       "\"AAPL\"  2008-08-20 │ 25.12    126718798  24.9676  25.2771  24.8014\n",
       "\"AAPL\"  2008-08-21 │ 24.8986  134917270  24.9243  25.0643  24.5557\n",
       "\"AAPL\"  2008-08-22 │ 25.2557  109873363  25.1171  25.3571  25.0814\n",
       "\"AAPL\"  2008-08-25 │ 24.65    121049286  25.1643  25.1757  24.5228\n",
       "\"AAPL\"  2008-08-26 │ 24.8057  111348823  24.68    24.9828  24.6586\n",
       "                   ⋮\n",
       "\"MSFT\"  2018-07-27 │ 107.68   36916780   110.18   110.18   106.14\n",
       "\"MSFT\"  2018-07-30 │ 105.37   34495720   107.19   107.53   104.76\n",
       "\"MSFT\"  2018-07-31 │ 106.08   27181070   106.49   106.72   105.38\n",
       "\"MSFT\"  2018-08-01 │ 106.28   23617980   106.03   106.446  105.42\n",
       "\"MSFT\"  2018-08-02 │ 107.57   26080740   105.4    108.09   104.84\n",
       "\"MSFT\"  2018-08-03 │ 108.04   18629310   107.8    108.05   106.82\n",
       "\"MSFT\"  2018-08-06 │ 108.13   20234680   108.12   108.42   107.559\n",
       "\"MSFT\"  2018-08-07 │ 108.88   16070070   108.56   109.1    108.17\n",
       "\"MSFT\"  2018-08-08 │ 109.49   15461420   109.33   109.75   108.76\n",
       "\"MSFT\"  2018-08-09 │ 109.67   13634510   109.71   110.16   109.6\n",
       "\"MSFT\"  2018-08-10 │ 109.0    18171350   109.42   109.69   108.38"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@time reloaded_stocksdata = load(\"stocksdata.jdb\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the saved database for consistency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata == reloaded_stocksdata"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look up the data associated only with Apple (symbol AAPL):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-d NDSparse with 2519 values (5 field named tuples):\n",
       "date       │ close    volume     open     high     low\n",
       "───────────┼──────────────────────────────────────────────\n",
       "2008-08-11 │ 24.7943  222653337  24.2957  25.2143  24.2386\n",
       "2008-08-12 │ 25.2471  208987793  24.7886  25.6128  24.7871\n",
       "2008-08-13 │ 25.6143  210556213  25.4257  25.7143  25.1286\n",
       "2008-08-14 │ 25.6171  177684343  25.4757  25.7786  25.4057\n",
       "2008-08-15 │ 25.1057  176996663  25.5771  25.6786  25.0071\n",
       "2008-08-18 │ 25.0557  137832351  25.0814  25.4014  24.8314\n",
       "2008-08-19 │ 24.79    153915766  24.9343  25.2957  24.5443\n",
       "2008-08-20 │ 25.12    126718798  24.9676  25.2771  24.8014\n",
       "2008-08-21 │ 24.8986  134917270  24.9243  25.0643  24.5557\n",
       "2008-08-22 │ 25.2557  109873363  25.1171  25.3571  25.0814\n",
       "2008-08-25 │ 24.65    121049286  25.1643  25.1757  24.5228\n",
       "2008-08-26 │ 24.8057  111348823  24.68    24.9828  24.6586\n",
       "           ⋮\n",
       "2018-07-27 │ 190.98   23975350   194.99   195.19   190.1\n",
       "2018-07-30 │ 189.91   20912890   191.9    192.2    189.07\n",
       "2018-07-31 │ 190.29   37847260   190.3    192.14   189.34\n",
       "2018-08-01 │ 201.5    67812280   199.13   201.76   197.31\n",
       "2018-08-02 │ 207.39   62317430   200.58   208.38   200.35\n",
       "2018-08-03 │ 207.99   33408050   207.03   208.74   205.48\n",
       "2018-08-06 │ 209.07   25396100   208.0    209.25   207.07\n",
       "2018-08-07 │ 207.11   25525650   209.32   209.5    206.76\n",
       "2018-08-08 │ 207.25   22493750   206.05   207.81   204.52\n",
       "2018-08-09 │ 208.88   23389530   207.28   209.78   207.2\n",
       "2018-08-10 │ 207.53   24592460   207.36   209.1    206.67"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata[\"AAPL\",:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2519"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(stocksdata[\"AAPL\",:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, look up the data linked to Microsoft. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-d NDSparse with 2519 values (5 field named tuples):\n",
       "date       │ close   volume    open    high     low\n",
       "───────────┼───────────────────────────────────────────\n",
       "2008-08-11 │ 27.9    68729270  27.86   28.4     27.66\n",
       "2008-08-12 │ 28.12   62796400  27.78   28.36    27.58\n",
       "2008-08-13 │ 27.91   51162290  28.07   28.5     27.76\n",
       "2008-08-14 │ 27.91   49642110  27.82   28.28    27.56\n",
       "2008-08-15 │ 27.81   47266670  27.98   28.15    27.58\n",
       "2008-08-18 │ 27.69   38041010  27.78   28.05    27.55\n",
       "2008-08-19 │ 27.32   40307900  27.54   27.75    27.27\n",
       "2008-08-20 │ 27.29   41483210  27.535  27.58    27.17\n",
       "2008-08-21 │ 27.18   43614130  27.1    27.23    26.86\n",
       "2008-08-22 │ 27.84   47892790  27.23   27.88    27.22\n",
       "2008-08-25 │ 27.66   51372940  27.61   27.84    27.46\n",
       "2008-08-26 │ 27.27   44773030  27.58   27.72    27.17\n",
       "           ⋮\n",
       "2018-07-27 │ 107.68  36916780  110.18  110.18   106.14\n",
       "2018-07-30 │ 105.37  34495720  107.19  107.53   104.76\n",
       "2018-07-31 │ 106.08  27181070  106.49  106.72   105.38\n",
       "2018-08-01 │ 106.28  23617980  106.03  106.446  105.42\n",
       "2018-08-02 │ 107.57  26080740  105.4   108.09   104.84\n",
       "2018-08-03 │ 108.04  18629310  107.8   108.05   106.82\n",
       "2018-08-06 │ 108.13  20234680  108.12  108.42   107.559\n",
       "2018-08-07 │ 108.88  16070070  108.56  109.1    108.17\n",
       "2018-08-08 │ 109.49  15461420  109.33  109.75   108.76\n",
       "2018-08-09 │ 109.67  13634510  109.71  110.16   109.6\n",
       "2018-08-10 │ 109.0   18171350  109.42  109.69   108.38"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata[\"MSFT\",:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2519"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(stocksdata[\"MSFT\",:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look up the price of Google on a particular date in the past:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(close = 234.3721, volume = 2191940, open = 231.8918, high = 235.5339, low = 231.7605)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata[\"GOOGL\", Date(2009,9,9)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "234.3721"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata[\"GOOGL\", Date(2009,9,9)].close"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how one can look up only the closing prices of Amazon. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-d NDSparse with 2519 values (Float64):\n",
       "date       │\n",
       "───────────┼────────\n",
       "2008-08-11 │ 88.09\n",
       "2008-08-12 │ 87.25\n",
       "2008-08-13 │ 86.69\n",
       "2008-08-14 │ 88.03\n",
       "2008-08-15 │ 86.4\n",
       "2008-08-18 │ 83.11\n",
       "2008-08-19 │ 81.29\n",
       "2008-08-20 │ 82.13\n",
       "2008-08-21 │ 83.26\n",
       "2008-08-22 │ 85.26\n",
       "2008-08-25 │ 82.85\n",
       "2008-08-26 │ 81.76\n",
       "           ⋮\n",
       "2018-07-27 │ 1817.27\n",
       "2018-07-30 │ 1779.22\n",
       "2018-07-31 │ 1777.44\n",
       "2018-08-01 │ 1797.17\n",
       "2018-08-02 │ 1834.33\n",
       "2018-08-03 │ 1823.29\n",
       "2018-08-06 │ 1847.75\n",
       "2018-08-07 │ 1862.48\n",
       "2018-08-08 │ 1886.52\n",
       "2018-08-09 │ 1898.52\n",
       "2018-08-10 │ 1886.3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selectvalues(stocksdata,:close)[\"AMZN\",:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Tuple{String,Date}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keytype(stocksdata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look up the dates for which the closing prices for Apple are available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2519-element Array{Date,1}:\n",
       " 2008-08-11\n",
       " 2008-08-12\n",
       " 2008-08-13\n",
       " 2008-08-14\n",
       " 2008-08-15\n",
       " 2008-08-18\n",
       " 2008-08-19\n",
       " 2008-08-20\n",
       " 2008-08-21\n",
       " 2008-08-22\n",
       " 2008-08-25\n",
       " 2008-08-26\n",
       " 2008-08-27\n",
       " ⋮         \n",
       " 2018-07-26\n",
       " 2018-07-27\n",
       " 2018-07-30\n",
       " 2018-07-31\n",
       " 2018-08-01\n",
       " 2018-08-02\n",
       " 2018-08-03\n",
       " 2018-08-06\n",
       " 2018-08-07\n",
       " 2018-08-08\n",
       " 2018-08-09\n",
       " 2018-08-10"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAPLdate=columns(stocksdata[\"AAPL\",:])[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look up the closing prices of Apple on those days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2519-element Array{Float64,1}:\n",
       "  24.7943\n",
       "  25.2471\n",
       "  25.6143\n",
       "  25.6171\n",
       "  25.1057\n",
       "  25.0557\n",
       "  24.79  \n",
       "  25.12  \n",
       "  24.8986\n",
       "  25.2557\n",
       "  24.65  \n",
       "  24.8057\n",
       "  24.9528\n",
       "   ⋮     \n",
       " 194.21  \n",
       " 190.98  \n",
       " 189.91  \n",
       " 190.29  \n",
       " 201.5   \n",
       " 207.39  \n",
       " 207.99  \n",
       " 209.07  \n",
       " 207.11  \n",
       " 207.25  \n",
       " 208.88  \n",
       " 207.53  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AAPLclose=columns(stocksdata[\"AAPL\",:])[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.7943"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stocksdata[\"AAPL\", Date(2008,8,11)].close"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we produce some plots. First load the library that contains the plotting functions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.PyPlotBackend()"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "pyplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(AAPLdate, AAPLclose,label=\"AAPL closing price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the daily returns of AAPL."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "llc=length(AAPLclose);\n",
    "AAPLreturns=(AAPLclose[2:llc]-AAPLclose[1:llc-1])./AAPLclose[1:llc-1];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(AAPLdate[2:llc],AAPLreturns,label=\"AAPL daily returns\",markersize=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now build the histogram from the returns using a custom made 'histogram' function\n",
    "(called 'hstgram' to avoid the confucion with the standard 'histogram').\n",
    "It takes as an input a single 1-dimensional array of data. The number of bins in\n",
    "the histogram is determined automatically by using the Diaconis-Friedman rule.\n",
    "The function returns two arrays: the mid-points of the bins and the (unnormalized)\n",
    "heights of the bars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "using StatsBase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "hstgram (generic function with 1 method)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function hstgram(data_sample::Array{Float64,1})\n",
    "    data_sorted=sort(data_sample)\n",
    "    first=data_sorted[1]\n",
    "    last=data_sorted[end]\n",
    "    nmb=length(data_sorted)\n",
    "    IQR=percentile(data_sorted,75)-percentile(data_sorted,25)\n",
    "    bin_size_loc = 2*IQR*(nmb^(-1.0/3))\n",
    "    num_bins=Int(floor((last-first)/bin_size_loc))\n",
    "    bin_size=(last-first)/(num_bins)\n",
    "    bin_end_points=[first+(i-1)*bin_size for i=1:(num_bins+1)]\n",
    "    ahist_val=[length(data_sorted[data_sorted .< u]) for u in bin_end_points]\n",
    "    hist_val=[ahist_val[i+1]-ahist_val[i] for i=1:num_bins]\n",
    "    mid_bins=[first-bin_size/2+i*bin_size for i=1:num_bins]\n",
    "    return mid_bins, hist_val\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the bars so that the area of the histogram equals 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "U,V=hstgram(AAPLreturns);\n",
    "VV=V/(sum(V)*(U[2]-U[1]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(U,VV,line=(:sticks,0.75),label=\"\")\n",
    "xlabel!(\"returns\")\n",
    "ylabel!(\"normalized frequency\")\n",
    "title!(\"Histogram from the 10y daily returns from AAPL.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area of the histogram is indeed 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(VV)*(U[2]-U[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is another way to plot the same histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(U.+(U[2]-U[1])/2,VV,label=\"\",line=(:steppre,1),linewidth=0.05)\n",
    "xlabel!(\"samples\")\n",
    "ylabel!(\"normalized frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bars in the histogram can be normalized to give the probabilities for hitting the bins:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VVV=V/sum(V);\n",
    "plot(U.+(U[2]-U[1])/2,VVV,label=\"\",line=(:steppre,1),linewidth=0.05)\n",
    "xlabel!(\"samples\")\n",
    "ylabel!(\"probability\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probabilities do sum to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(VVV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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