examples/emh_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The emh Rpackage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The emh package allows you to test the effeciency of any univariate zoo time series object in R.\n",
    "\n",
    "The package achieves this using the following methodology,\n",
    "\n",
    "* Downsample the data into a number of subfrequencies\n",
    "* Run a suite of statistical tests of randomness on each subfrequency\n",
    "* Aggregate the results (p values, Z scores, etc.) in a data.frame and return it\n",
    "\n",
    "In addition to randomness tests emh also includes a number of stochastic process models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Installing the package"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step to using the package is to download it and install it using the devtools R package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "library(devtools)\n",
    "suppressMessages(install_github(repo=\"stuartgordonreid/emh\", \n",
    "                                force = TRUE))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now check that you can load the package,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "suppressMessages(library(emh))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The emh package includes a few functions which allow you to download a bunch of global stock market indices from Quandl.com right off the bat. You can, of course, also pass in your own data. I recommend sticking with zoo objects when using emh because of how the downsampling works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"DOWNLOADING DATASETS ...\"\n",
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     ]
    }
   ],
   "source": [
    "# This may take some time. Use the S3, $ operator to see the datasets.\n",
    "global_indices <- emh::data_quandl_downloader(data_quandl_indices())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating a data.frame with the results from each of the randomness tests is as easy as passing a zoo object into the is_random function in emh. This function will downsample the data into multiple lower frequencies and run a battery of tests on each subfrequency. \n",
    "\n",
    "Frequencies are specified by the freqs1 and freqs2 arguments,\n",
    "\n",
    "* freqs1 - this specifies the _lags_ to use when computing returns\n",
    "* freqs2 - this specifies time-aware lags. Options are: c(\"Mon\", \"Tue\", \"Wed\", \"Thu\", \"Fri\", \"Week\", \"Month\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "results <- is_random(S = global_indices$'YAHOO/INDEX_SML',\n",
    "                     a = 0.99, # To get a 99% confident result\n",
    "                     freqs1 = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),\n",
    "                     freqs2 = c(\"Mon\", \"Tue\", \"Wed\", \"Thu\", \"Fri\", \"Week\", \"Month\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Viewing the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now view the results (a data.frame object) or plot some interesting statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Test_Name</th><th scope=col>Frequency</th><th scope=col>Sample_Size</th><th scope=col>Statistic</th><th scope=col>Two_sided_p</th><th scope=col>Z_Score</th><th scope=col>Non_Random</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Independent Runs    </td><td>(t-1 to t)          </td><td>7031                </td><td>3222.000000         </td><td>0.000000            </td><td>-6.401018           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Durbin-Watson       </td><td>(t-1 to t)          </td><td>7031                </td><td>   2.000085         </td><td>0.997102            </td><td> 2.759057           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Ljung-Box           </td><td>(t-1 to t)          </td><td>7031                </td><td>  40.018562         </td><td>0.000451            </td><td>-3.319694           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Breusch-Godfrey     </td><td>(t-1 to t)          </td><td>7031                </td><td>   1.493007         </td><td>0.221750            </td><td>-0.766295           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Bartell Rank        </td><td>(t-1 to t)          </td><td>7031                </td><td>  -4.581588         </td><td>0.000005            </td><td>-4.434487           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Variance-Ratio LoMac</td><td>(t-1 to t)          </td><td>7031                </td><td>   0.524304         </td><td>0.612558            </td><td> 0.285993           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Independent Runs    </td><td>(t-2 to t)          </td><td>3515                </td><td>1615.000000         </td><td>0.000025            </td><td>-4.056609           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Durbin-Watson       </td><td>(t-2 to t)          </td><td>3515                </td><td>   1.999914         </td><td>0.997877            </td><td> 2.859250           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Ljung-Box           </td><td>(t-2 to t)          </td><td>3515                </td><td>  35.686137         </td><td>0.001962            </td><td>-2.884263           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Breusch-Godfrey     </td><td>(t-2 to t)          </td><td>3515                </td><td>   0.002772         </td><td>0.958014            </td><td> 1.728094           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Bartell Rank        </td><td>(t-2 to t)          </td><td>3515                </td><td>  -1.561292         </td><td>0.118455            </td><td>-1.182746           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Variance-Ratio LoMac</td><td>(t-2 to t)          </td><td>3515                </td><td>  -0.298505         </td><td>0.427464            </td><td>-0.182833           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Independent Runs    </td><td>(t-3 to t)          </td><td>2343                </td><td>1107.000000         </td><td>0.034269            </td><td>-1.821457           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Durbin-Watson       </td><td>(t-3 to t)          </td><td>2343                </td><td>   2.000828         </td><td>0.983218            </td><td> 2.125265           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Ljung-Box           </td><td>(t-3 to t)          </td><td>2343                </td><td>  36.372465         </td><td>0.001562            </td><td>-2.955341           </td><td> TRUE               </td></tr>\n",
       "\t<tr><td>Breusch-Godfrey     </td><td>(t-3 to t)          </td><td>2343                </td><td>   1.496615         </td><td>0.221193            </td><td>-0.768171           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Bartell Rank        </td><td>(t-3 to t)          </td><td>2343                </td><td>   0.044739         </td><td>0.964315            </td><td> 1.803117           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Variance-Ratio LoMac</td><td>(t-3 to t)          </td><td>2343                </td><td>   2.593742         </td><td>0.889218            </td><td> 1.222378           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Independent Runs    </td><td>(t-4 to t)          </td><td>1757                </td><td> 861.000000         </td><td>0.467113            </td><td>-0.082529           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Durbin-Watson       </td><td>(t-4 to t)          </td><td>1757                </td><td>   1.993175         </td><td>0.886997            </td><td> 1.210711           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Ljung-Box           </td><td>(t-4 to t)          </td><td>1757                </td><td>  18.857366         </td><td>0.220270            </td><td>-0.771281           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Breusch-Godfrey     </td><td>(t-4 to t)          </td><td>1757                </td><td>   0.064177         </td><td>0.800012            </td><td> 0.841665           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Bartell Rank        </td><td>(t-4 to t)          </td><td>1757                </td><td>   1.664227         </td><td>0.096067            </td><td>-1.304292           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Variance-Ratio LoMac</td><td>(t-4 to t)          </td><td>1757                </td><td>   2.066387         </td><td>0.898717            </td><td> 1.274274           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Independent Runs    </td><td>(t-5 to t)          </td><td>1406                </td><td> 713.000000         </td><td>0.905517            </td><td> 1.313647           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Durbin-Watson       </td><td>(t-5 to t)          </td><td>1406                </td><td>   1.995872         </td><td>0.938608            </td><td> 1.543194           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Ljung-Box           </td><td>(t-5 to t)          </td><td>1406                </td><td>  14.701537         </td><td>0.473122            </td><td>-0.067424           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Breusch-Godfrey     </td><td>(t-5 to t)          </td><td>1406                </td><td>   0.446644         </td><td>0.503933            </td><td> 0.009859           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Bartell Rank        </td><td>(t-5 to t)          </td><td>1406                </td><td>   1.576687         </td><td>0.114868            </td><td>-1.201041           </td><td>FALSE               </td></tr>\n",
       "\t<tr><td>Variance-Ratio LoMac</td><td>(t-5 to t)          </td><td>1406                </td><td>   0.509927         </td><td>0.623519            </td><td> 0.314736           </td><td>FALSE               </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllll}\n",
       " Test\\_Name & Frequency & Sample\\_Size & Statistic & Two\\_sided\\_p & Z\\_Score & Non\\_Random\\\\\n",
       "\\hline\n",
       "\t Independent Runs     & (t-1 to t)           & 7031                 & 3222.000000          & 0.000000             & -6.401018            &  TRUE               \\\\\n",
       "\t Durbin-Watson        & (t-1 to t)           & 7031                 &    2.000085          & 0.997102             &  2.759057            &  TRUE               \\\\\n",
       "\t Ljung-Box            & (t-1 to t)           & 7031                 &   40.018562          & 0.000451             & -3.319694            &  TRUE               \\\\\n",
       "\t Breusch-Godfrey      & (t-1 to t)           & 7031                 &    1.493007          & 0.221750             & -0.766295            & FALSE               \\\\\n",
       "\t Bartell Rank         & (t-1 to t)           & 7031                 &   -4.581588          & 0.000005             & -4.434487            &  TRUE               \\\\\n",
       "\t Variance-Ratio LoMac & (t-1 to t)           & 7031                 &    0.524304          & 0.612558             &  0.285993            & FALSE               \\\\\n",
       "\t Independent Runs     & (t-2 to t)           & 3515                 & 1615.000000          & 0.000025             & -4.056609            &  TRUE               \\\\\n",
       "\t Durbin-Watson        & (t-2 to t)           & 3515                 &    1.999914          & 0.997877             &  2.859250            &  TRUE               \\\\\n",
       "\t Ljung-Box            & (t-2 to t)           & 3515                 &   35.686137          & 0.001962             & -2.884263            &  TRUE               \\\\\n",
       "\t Breusch-Godfrey      & (t-2 to t)           & 3515                 &    0.002772          & 0.958014             &  1.728094            & FALSE               \\\\\n",
       "\t Bartell Rank         & (t-2 to t)           & 3515                 &   -1.561292          & 0.118455             & -1.182746            & FALSE               \\\\\n",
       "\t Variance-Ratio LoMac & (t-2 to t)           & 3515                 &   -0.298505          & 0.427464             & -0.182833            & FALSE               \\\\\n",
       "\t Independent Runs     & (t-3 to t)           & 2343                 & 1107.000000          & 0.034269             & -1.821457            & FALSE               \\\\\n",
       "\t Durbin-Watson        & (t-3 to t)           & 2343                 &    2.000828          & 0.983218             &  2.125265            & FALSE               \\\\\n",
       "\t Ljung-Box            & (t-3 to t)           & 2343                 &   36.372465          & 0.001562             & -2.955341            &  TRUE               \\\\\n",
       "\t Breusch-Godfrey      & (t-3 to t)           & 2343                 &    1.496615          & 0.221193             & -0.768171            & FALSE               \\\\\n",
       "\t Bartell Rank         & (t-3 to t)           & 2343                 &    0.044739          & 0.964315             &  1.803117            & FALSE               \\\\\n",
       "\t Variance-Ratio LoMac & (t-3 to t)           & 2343                 &    2.593742          & 0.889218             &  1.222378            & FALSE               \\\\\n",
       "\t Independent Runs     & (t-4 to t)           & 1757                 &  861.000000          & 0.467113             & -0.082529            & FALSE               \\\\\n",
       "\t Durbin-Watson        & (t-4 to t)           & 1757                 &    1.993175          & 0.886997             &  1.210711            & FALSE               \\\\\n",
       "\t Ljung-Box            & (t-4 to t)           & 1757                 &   18.857366          & 0.220270             & -0.771281            & FALSE               \\\\\n",
       "\t Breusch-Godfrey      & (t-4 to t)           & 1757                 &    0.064177          & 0.800012             &  0.841665            & FALSE               \\\\\n",
       "\t Bartell Rank         & (t-4 to t)           & 1757                 &    1.664227          & 0.096067             & -1.304292            & FALSE               \\\\\n",
       "\t Variance-Ratio LoMac & (t-4 to t)           & 1757                 &    2.066387          & 0.898717             &  1.274274            & FALSE               \\\\\n",
       "\t Independent Runs     & (t-5 to t)           & 1406                 &  713.000000          & 0.905517             &  1.313647            & FALSE               \\\\\n",
       "\t Durbin-Watson        & (t-5 to t)           & 1406                 &    1.995872          & 0.938608             &  1.543194            & FALSE               \\\\\n",
       "\t Ljung-Box            & (t-5 to t)           & 1406                 &   14.701537          & 0.473122             & -0.067424            & FALSE               \\\\\n",
       "\t Breusch-Godfrey      & (t-5 to t)           & 1406                 &    0.446644          & 0.503933             &  0.009859            & FALSE               \\\\\n",
       "\t Bartell Rank         & (t-5 to t)           & 1406                 &    1.576687          & 0.114868             & -1.201041            & FALSE               \\\\\n",
       "\t Variance-Ratio LoMac & (t-5 to t)           & 1406                 &    0.509927          & 0.623519             &  0.314736            & FALSE               \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "   Test_Name            Frequency  Sample_Size Statistic   Two_sided_p\n",
       "1  Independent Runs     (t-1 to t) 7031        3222.000000 0.000000   \n",
       "2  Durbin-Watson        (t-1 to t) 7031           2.000085 0.997102   \n",
       "3  Ljung-Box            (t-1 to t) 7031          40.018562 0.000451   \n",
       "4  Breusch-Godfrey      (t-1 to t) 7031           1.493007 0.221750   \n",
       "5  Bartell Rank         (t-1 to t) 7031          -4.581588 0.000005   \n",
       "6  Variance-Ratio LoMac (t-1 to t) 7031           0.524304 0.612558   \n",
       "7  Independent Runs     (t-2 to t) 3515        1615.000000 0.000025   \n",
       "8  Durbin-Watson        (t-2 to t) 3515           1.999914 0.997877   \n",
       "9  Ljung-Box            (t-2 to t) 3515          35.686137 0.001962   \n",
       "10 Breusch-Godfrey      (t-2 to t) 3515           0.002772 0.958014   \n",
       "11 Bartell Rank         (t-2 to t) 3515          -1.561292 0.118455   \n",
       "12 Variance-Ratio LoMac (t-2 to t) 3515          -0.298505 0.427464   \n",
       "13 Independent Runs     (t-3 to t) 2343        1107.000000 0.034269   \n",
       "14 Durbin-Watson        (t-3 to t) 2343           2.000828 0.983218   \n",
       "15 Ljung-Box            (t-3 to t) 2343          36.372465 0.001562   \n",
       "16 Breusch-Godfrey      (t-3 to t) 2343           1.496615 0.221193   \n",
       "17 Bartell Rank         (t-3 to t) 2343           0.044739 0.964315   \n",
       "18 Variance-Ratio LoMac (t-3 to t) 2343           2.593742 0.889218   \n",
       "19 Independent Runs     (t-4 to t) 1757         861.000000 0.467113   \n",
       "20 Durbin-Watson        (t-4 to t) 1757           1.993175 0.886997   \n",
       "21 Ljung-Box            (t-4 to t) 1757          18.857366 0.220270   \n",
       "22 Breusch-Godfrey      (t-4 to t) 1757           0.064177 0.800012   \n",
       "23 Bartell Rank         (t-4 to t) 1757           1.664227 0.096067   \n",
       "24 Variance-Ratio LoMac (t-4 to t) 1757           2.066387 0.898717   \n",
       "25 Independent Runs     (t-5 to t) 1406         713.000000 0.905517   \n",
       "26 Durbin-Watson        (t-5 to t) 1406           1.995872 0.938608   \n",
       "27 Ljung-Box            (t-5 to t) 1406          14.701537 0.473122   \n",
       "28 Breusch-Godfrey      (t-5 to t) 1406           0.446644 0.503933   \n",
       "29 Bartell Rank         (t-5 to t) 1406           1.576687 0.114868   \n",
       "30 Variance-Ratio LoMac (t-5 to t) 1406           0.509927 0.623519   \n",
       "   Z_Score   Non_Random\n",
       "1  -6.401018  TRUE     \n",
       "2   2.759057  TRUE     \n",
       "3  -3.319694  TRUE     \n",
       "4  -0.766295 FALSE     \n",
       "5  -4.434487  TRUE     \n",
       "6   0.285993 FALSE     \n",
       "7  -4.056609  TRUE     \n",
       "8   2.859250  TRUE     \n",
       "9  -2.884263  TRUE     \n",
       "10  1.728094 FALSE     \n",
       "11 -1.182746 FALSE     \n",
       "12 -0.182833 FALSE     \n",
       "13 -1.821457 FALSE     \n",
       "14  2.125265 FALSE     \n",
       "15 -2.955341  TRUE     \n",
       "16 -0.768171 FALSE     \n",
       "17  1.803117 FALSE     \n",
       "18  1.222378 FALSE     \n",
       "19 -0.082529 FALSE     \n",
       "20  1.210711 FALSE     \n",
       "21 -0.771281 FALSE     \n",
       "22  0.841665 FALSE     \n",
       "23 -1.304292 FALSE     \n",
       "24  1.274274 FALSE     \n",
       "25  1.313647 FALSE     \n",
       "26  1.543194 FALSE     \n",
       "27 -0.067424 FALSE     \n",
       "28  0.009859 FALSE     \n",
       "29 -1.201041 FALSE     \n",
       "30  0.314736 FALSE     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(results, 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zo/2kaHZLanbzlfeHXTrqkRpUrtlNC1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",
      "text/plain": [
       "Plot with title “Percentage of tests with non-random result by frequency”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YlCqrwo3s2+0Wu2i4WUv6k5wYVunD1b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\ntp5mr4vv/X1EYbQSdRHS54bfPO9Tu217yQ2/eUFhtLmjR5uPh99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      "text/plain": [
       "Plot with title “Percentage of tests with non-random result by test name”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_results(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the two graphs above we can see that there are a large number of non-random results at the $t-1$ to $t$, and $t-2$ to $t$ frequencies. \n",
    "\n",
    "This might imply that the selected market, the small cap index of the S&P 500, is non-random at those frequencies. When we look at the second graph we see that most of the results were produced by the Ljung-Box and Durbin-Watson statistical tests which implies that there might exist some serial correlations in the data which are significantly different from zero. These tests do not tell us how _economically_ significant the serial correlations are nor does it tell us _where_ in the data these serial correlations were observed. These questions are best left to the entrepid quant trader to answer."
   ]
  }
 ],
 "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": "3.2.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}