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Predictive Modelling Task - 2.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>Predictive Modelling Task - 2</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
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<h1 id="Predictive-Modelling-Task---2">Predictive Modelling Task - 2<a class="anchor-link" href="#Predictive-Modelling-Task---2">¶</a></h1><p>In this workbook, I will process all stocks provided in the dataset using the process-pipeline I developed in task-1.</p>
<p>First, I will wrap the forecasting routine into a function:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">warnings</span>
<span class="c1"># Dickey-Fuller Test</span>
<span class="kn">from</span> <span class="nn">statsmodels.tsa.stattools</span> <span class="k">import</span> <span class="n">adfuller</span>
<span class="c1"># auto corelation</span>
<span class="kn">from</span> <span class="nn">statsmodels.tsa.stattools</span> <span class="k">import</span> <span class="n">acf</span>
<span class="kn">from</span> <span class="nn">statsmodels.tsa.stattools</span> <span class="k">import</span> <span class="n">pacf</span>
<span class="c1"># seasonal decompose</span>
<span class="kn">from</span> <span class="nn">statsmodels.tsa.seasonal</span> <span class="k">import</span> <span class="n">seasonal_decompose</span>
<span class="c1"># ARIMA</span>
<span class="kn">import</span> <span class="nn">statsmodels.tsa</span> <span class="k">as</span> <span class="nn">tsa</span>
<span class="c1"># display</span>
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="k">import</span> <span class="n">display</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">filterwarnings</span><span class="p">(</span><span class="s1">'ignore'</span><span class="p">)</span>
<span class="c1"># plot utilities</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">mpld3</span>
<span class="n">mpld3</span><span class="o">.</span><span class="n">enable_notebook</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">testStationarity</span><span class="p">(</span><span class="n">ts</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">displaySummary</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">displayPlot</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">''' Test whether the input series is stationary or not</span>
<span class="sd"> '''</span>
<span class="c1"># remove NAN's</span>
<span class="n">ts</span> <span class="o">=</span> <span class="n">ts</span><span class="o">.</span><span class="n">dropna</span><span class="p">()</span>
<span class="c1"># create a data frame for X1</span>
<span class="n">dframe</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">ts</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'P(t)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">ts</span><span class="o">.</span><span class="n">values</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">dframe</span><span class="p">[</span><span class="s1">'P(t)'</span><span class="p">][</span><span class="o">~</span><span class="n">dframe</span><span class="p">[</span><span class="s1">'P(t)'</span><span class="p">]</span><span class="o">.</span><span class="n">isnull</span><span class="p">()]</span>
<span class="c1"># dickyey-fuller test</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">adfuller</span><span class="p">(</span><span class="n">ts</span><span class="p">)</span>
<span class="k">if</span> <span class="n">df</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="n">df</span><span class="p">[</span><span class="mi">4</span><span class="p">][</span><span class="s1">'1%'</span><span class="p">]:</span>
<span class="n">confi</span> <span class="o">=</span> <span class="mf">0.99</span>
<span class="n">isStationary</span> <span class="o">=</span> <span class="kc">True</span><span class="p">;</span>
<span class="n">strStationary</span> <span class="o">=</span> <span class="s1">' DFTest: Stationary'</span><span class="o">+</span> <span class="s1">' (confidence= </span><span class="si">%.2f</span><span class="s1">)'</span> <span class="o">%</span> <span class="n">confi</span>
<span class="k">elif</span> <span class="n">df</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="n">df</span><span class="p">[</span><span class="mi">4</span><span class="p">][</span><span class="s1">'5%'</span><span class="p">]:</span>
<span class="n">confi</span> <span class="o">=</span> <span class="mf">0.95</span>
<span class="n">isStationary</span> <span class="o">=</span> <span class="kc">True</span><span class="p">;</span>
<span class="n">strStationary</span> <span class="o">=</span> <span class="s1">' DFTest: Stationary'</span><span class="o">+</span> <span class="s1">' (confidence= </span><span class="si">%.2f</span><span class="s1">)'</span> <span class="o">%</span> <span class="n">confi</span>
<span class="k">elif</span> <span class="n">df</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="n">df</span><span class="p">[</span><span class="mi">4</span><span class="p">][</span><span class="s1">'10%'</span><span class="p">]:</span>
<span class="n">confi</span> <span class="o">=</span> <span class="mf">0.90</span>
<span class="n">isStationary</span> <span class="o">=</span> <span class="kc">True</span><span class="p">;</span>
<span class="n">strStationary</span> <span class="o">=</span> <span class="s1">' DFTest: Stationary'</span> <span class="o">+</span> <span class="s1">' (confidence= </span><span class="si">%.2f</span><span class="s1">)'</span> <span class="o">%</span> <span class="n">confi</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">confi</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">isStationary</span> <span class="o">=</span> <span class="kc">False</span><span class="p">;</span>
<span class="n">strStationary</span> <span class="o">=</span> <span class="s1">' DFTest: Non Stationary'</span>
<span class="c1"># moving averages</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'MA_30'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> <span class="c1"># 30 -day MA</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'MA_60'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">60</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> <span class="c1"># 60 -day MA</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'MA_120'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">120</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> <span class="c1"># 120 -day MA</span>
<span class="c1"># standard devs</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'SD_30'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span><span class="o">.</span><span class="n">std</span><span class="p">()</span> <span class="c1"># 30 -day SD</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'SD_60'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">60</span><span class="p">)</span><span class="o">.</span><span class="n">std</span><span class="p">()</span> <span class="c1"># 60 -day SD</span>
<span class="n">dframe</span><span class="p">[</span><span class="s1">'SD_120'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">120</span><span class="p">)</span><span class="o">.</span><span class="n">std</span><span class="p">()</span> <span class="c1"># 120 -day SD</span>
<span class="k">if</span> <span class="n">displayPlot</span><span class="p">:</span>
<span class="c1"># plot</span>
<span class="n">dframe</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span> <span class="p">[</span><span class="s1">'MA_30'</span><span class="p">,</span> <span class="s1">'MA_60'</span><span class="p">,</span> <span class="s1">'MA_120'</span><span class="p">]]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">title</span><span class="o">=</span><span class="s1">'Moving Averages - '</span> <span class="o">+</span> <span class="n">ts</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="n">strStationary</span><span class="p">)</span>
<span class="n">dframe</span><span class="o">.</span><span class="n">loc</span><span class="p">[:,</span> <span class="p">[</span><span class="s1">'SD_30'</span><span class="p">,</span> <span class="s1">'SD_60'</span><span class="p">,</span> <span class="s1">'SD_120'</span><span class="p">]]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span> <span class="n">title</span><span class="o">=</span><span class="s1">'Variance - '</span> <span class="o">+</span> <span class="n">ts</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="n">strStationary</span><span class="p">)</span>
<span class="k">if</span> <span class="n">displaySummary</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">df</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'Time series - '</span><span class="o">+</span><span class="n">ts</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">','</span> <span class="o">+</span> <span class="n">strStationary</span><span class="p">)</span>
<span class="k">return</span> <span class="n">isStationary</span>
<span class="k">def</span> <span class="nf">convert2Stationary</span><span class="p">(</span><span class="n">ts</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">disp</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="sd">''' Convert a non-stationary time-series to stationary using simple differencing of</span>
<span class="sd"> log-transformed timeseries</span>
<span class="sd"> The input time-series is first checked for stationarity then the conversion is done</span>
<span class="sd"> </span>
<span class="sd"> input: ts -> time-series in normal price</span>
<span class="sd"> output: stationary timeseries</span>
<span class="sd"> '''</span>
<span class="c1"># log</span>
<span class="n">ts_log</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">ts</span><span class="o">.</span><span class="n">dropna</span><span class="p">())</span>
<span class="n">out</span> <span class="o">=</span> <span class="n">ts_log</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">testStationarity</span><span class="p">(</span><span class="n">ts</span><span class="p">,</span> <span class="n">displayPlot</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">displaySummary</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="c1"># differencing</span>
<span class="n">out</span> <span class="o">=</span> <span class="n">ts_log</span> <span class="o">-</span> <span class="n">ts_log</span><span class="o">.</span><span class="n">shift</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># perform test</span>
<span class="k">if</span> <span class="n">disp</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"=== after conversion test for Stationarity==="</span><span class="p">)</span>
<span class="n">testStationarity</span><span class="p">(</span><span class="n">out</span><span class="p">,</span> <span class="n">displayPlot</span><span class="o">=</span><span class="n">disp</span><span class="p">,</span> <span class="n">displaySummary</span><span class="o">=</span><span class="n">disp</span><span class="p">)</span>
<span class="k">return</span> <span class="n">out</span>
<span class="k">def</span> <span class="nf">forecast_3day_returns</span><span class="p">(</span><span class="n">ts</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">ARIMAorder</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">''' Forecast 3-day returns using ARIMA modelling</span>
<span class="sd"> '''</span>
<span class="c1"># original timeseries</span>
<span class="n">orig_tseries</span> <span class="o">=</span> <span class="n">ts</span>
<span class="c1"># create a new time series by pushing it 3-days ahead and fill it with 0</span>
<span class="n">pushed_tseries</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">orig_tseries</span><span class="o">.</span><span class="n">index</span> <span class="o">+</span> <span class="n">pd</span><span class="o">.</span><span class="n">Timedelta</span><span class="p">(</span><span class="s1">'3 day'</span><span class="p">))</span>
<span class="c1"># extract the last 3-days from pushed_tseries and append it to original timeseries</span>
<span class="n">tseries</span> <span class="o">=</span> <span class="n">orig_tseries</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pushed_tseries</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span> <span class="p">:</span> <span class="n">pushed_tseries</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> <span class="n">verify_integrity</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># convert original timeseries X3 to stationary</span>
<span class="n">day_returns</span> <span class="o">=</span> <span class="n">convert2Stationary</span><span class="p">(</span><span class="n">ts</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
<span class="c1"># index-0 of day_returns will be NAN due to differencing.</span>
<span class="c1"># usually day_returns[original_length+1] will have -INF due to 0 insertion.</span>
<span class="k">if</span> <span class="n">ARIMAorder</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ARIMAorder</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="c1"># modelling (use all data starting from index-1 day of day_returns to the lastday of the orignal timeseries)</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">tsa</span><span class="o">.</span><span class="n">arima_model</span><span class="o">.</span><span class="n">ARIMA</span><span class="p">(</span><span class="n">day_returns</span><span class="o">.</span><span class="n">ix</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">ARIMAorder</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">disp</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span>
<span class="c1"># index of day_returns runs from 0:day_returns.shape[0]-1, there are total of day_returns.shape[0] elements</span>
<span class="c1"># we are ignoring inedx-0 while training (it might contain NAN due to differencing), hence we are only training</span>
<span class="c1"># with day_returns.shape[0]-1 elements (with indexing running from 1:day_returns.shape[0]-1). </span>
<span class="c1"># Therefore the the trained-model will have a length of ((day_returns.shape[0]-1)-1)</span>
<span class="c1"># For prediction, the starting index should atleast be the last fittedvalue.</span>
<span class="c1"># predict</span>
<span class="n">preds</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="mi">2</span> <span class="p">)</span>
<span class="c1">### calculate error metrics and accuracy of fittedvalues</span>
<span class="c1"># Original-returns: calculate rolling_sum of log-returns over a window of 4 days, including current day</span>
<span class="n">orig_returns</span> <span class="o">=</span> <span class="n">day_returns</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="n">rollsum</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">orig_returns</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">orig_3day_returns</span> <span class="o">=</span> <span class="n">orig_returns</span> <span class="o">-</span> <span class="n">rollsum</span><span class="o">.</span><span class="n">shift</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">)</span>
<span class="c1"># fitted-returns: </span>
<span class="n">rollsum</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">fitted_3day_returns</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span> <span class="o">-</span> <span class="n">rollsum</span><span class="o">.</span><span class="n">shift</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">)</span>
<span class="c1"># display dataframe</span>
<span class="n">statsFrame</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">orig_returns</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'Orig Log Returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">orig_returns</span><span class="o">.</span><span class="n">values</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'Pred Log Returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">values</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'AbsError'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">orig_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'AbsPercentError(%)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="n">orig_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">values</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">orig_returns</span><span class="o">.</span><span class="n">values</span><span class="o">+</span><span class="mf">0.00000001</span><span class="p">))</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'DirectionAccuracy'</span><span class="p">]</span> <span class="o">=</span> <span class="o">~</span><span class="p">((</span><span class="n">orig_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">!=</span> <span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="o">.</span><span class="n">values</span> <span class="o">></span> <span class="mi">0</span><span class="p">))</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'Orig 3-day Log returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">orig_3day_returns</span><span class="o">.</span><span class="n">values</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'Pred 3-day Log returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">fitted_3day_returns</span><span class="o">.</span><span class="n">values</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day AbsError'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">orig_3day_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">-</span> <span class="n">fitted_3day_returns</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day AbsPercentError(%)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="n">orig_3day_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">-</span> <span class="n">fitted_3day_returns</span><span class="o">.</span><span class="n">values</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">orig_3day_returns</span><span class="o">.</span><span class="n">values</span><span class="o">+</span><span class="mf">0.00000001</span><span class="p">))</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day DirectionAccuracy'</span><span class="p">]</span> <span class="o">=</span> <span class="o">~</span><span class="p">((</span><span class="n">orig_3day_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">></span> <span class="mi">0</span><span class="p">)</span> <span class="o">!=</span> <span class="p">(</span><span class="n">fitted_3day_returns</span><span class="o">.</span><span class="n">values</span> <span class="o">></span> <span class="mi">0</span><span class="p">))</span>
<span class="c1"># calculate</span>
<span class="c1"># create a fitted_day_returns series using index from new timeseries (created used pushed_timeseries) and fittedvalues</span>
<span class="n">fitted_day_returns</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">fittedvalues</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="n">tseries</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
<span class="c1"># copy the forecast values to correct dates</span>
<span class="n">fitted_day_returns</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span> <span class="p">:</span> <span class="n">fitted_day_returns</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> <span class="o">=</span> <span class="n">preds</span>
<span class="n">forecast_day_returns</span> <span class="o">=</span> <span class="n">fitted_day_returns</span><span class="p">[</span><span class="o">-</span><span class="mi">4</span> <span class="p">:</span> <span class="n">fitted_day_returns</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<span class="c1"># Predicted-returns: </span>
<span class="n">rollsum</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="o">.</span><span class="n">rolling</span><span class="p">(</span><span class="n">forecast_day_returns</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="n">forecast_3day_returns</span> <span class="o">=</span> <span class="n">forecast_day_returns</span> <span class="o">-</span> <span class="n">rollsum</span><span class="o">.</span><span class="n">shift</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">)</span>
<span class="c1"># Display</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"===== 3-day Returns forecast for closing price of last-day in timeseries ======"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" Note: The first row in the table corresponds to the last day </span><span class="se">\n</span><span class="s2"> closing price of the stock"</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">" Stock: "</span><span class="o">+</span> <span class="n">ts</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
<span class="n">futureFrame</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">forecast_day_returns</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Forecast Log Returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">forecast_day_returns</span><span class="o">.</span><span class="n">values</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Forecast 3-day Log Returns'</span><span class="p">]</span> <span class="o">=</span> <span class="n">forecast_3day_returns</span><span class="o">.</span><span class="n">values</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term MAE (log returns)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'AbsError'</span><span class="p">])</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term MAPE (log returns) %'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'AbsPercentError(%)'</span><span class="p">]</span><span class="o">/</span><span class="mi">100</span><span class="p">)</span><span class="o">*</span><span class="mi">100</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term DirectionAccuracy (log returns) %'</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'DirectionAccuracy'</span><span class="p">])</span><span class="o">/</span><span class="n">statsFrame</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term MAE (3-day log returns)'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day AbsError'</span><span class="p">])</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term MAPE (3-day log returns) %'</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day AbsPercentError(%)'</span><span class="p">]</span><span class="o">/</span><span class="mi">100</span><span class="p">)</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">futureFrame</span><span class="p">[</span><span class="s1">'Long term DirectionAccuracy (3-day log returns) %'</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">statsFrame</span><span class="p">[</span><span class="s1">'3-day DirectionAccuracy'</span><span class="p">])</span><span class="o">/</span><span class="n">statsFrame</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="mi">100</span>
<span class="n">display</span><span class="p">(</span><span class="n">futureFrame</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">futureFrame</span>
<span class="c1"># test- forecast</span>
<span class="c1"># convert data to time-series data while reading from csv itself</span>
<span class="n">dailyPrices</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">'dailyPrices_AtClose.csv'</span><span class="p">,</span> <span class="n">parse_dates</span><span class="o">=</span><span class="s1">'t()'</span><span class="p">,</span> <span class="n">index_col</span><span class="o">=</span><span class="s1">'t()'</span><span class="p">)</span>
<span class="c1">#dailyPrices.index # check if the index is datetime</span>
<span class="c1"># re-index and set frequency='D'</span>
<span class="n">dates</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">date_range</span><span class="p">(</span><span class="n">dailyPrices</span><span class="o">.</span><span class="n">index</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">dailyPrices</span><span class="o">.</span><span class="n">index</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">freq</span><span class="o">=</span><span class="s1">'D'</span><span class="p">)</span>
<span class="n">dailyPrices</span> <span class="o">=</span> <span class="n">dailyPrices</span><span class="o">.</span><span class="n">reindex</span><span class="p">(</span><span class="n">dates</span><span class="p">)</span>
<span class="c1">#dailyPrices.index</span>
<span class="n">forecast_3day_returns</span><span class="p">(</span><span class="n">dailyPrices</span><span class="o">.</span><span class="n">X3</span><span class="p">)</span>
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<pre> ARMA Model Results
==============================================================================
Dep. Variable: X3 No. Observations: 2768
Model: ARMA(1, 1) Log Likelihood 6734.171
Method: css-mle S.D. of innovations 0.021
Date: Tue, 07 Jun 2016 AIC -13460.342
Time: 21:45:35 BIC -13436.639
Sample: 01-04-2005 HQIC -13451.781
- 12-31-2015
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 0.0003 0.000 0.772 0.440 -0.000 0.001
ar.L1.X3 0.5033 0.112 4.487 0.000 0.283 0.723
ma.L1.X3 -0.5830 0.105 -5.553 0.000 -0.789 -0.377
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 1.9869 +0.0000j 1.9869 0.0000
MA.1 1.7152 +0.0000j 1.7152 0.0000
-----------------------------------------------------------------------------
===== 3-day Returns forecast for closing price of last-day in timeseries ======
Note: The first row in the table corresponds to the last day
closing price of the stock
Stock: X3
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>-0.000133</td>
<td>-0.001179</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>1</th>
<td>2016-01-01</td>
<td>0.000486</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>2</th>
<td>2016-01-02</td>
<td>0.000374</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>3</th>
<td>2016-01-03</td>
<td>0.000318</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
</tbody>
</table>
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<pre>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
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<div>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>-0.000133</td>
<td>-0.001179</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>1</th>
<td>2016-01-01</td>
<td>0.000486</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>2</th>
<td>2016-01-02</td>
<td>0.000374</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
<tr>
<th>3</th>
<td>2016-01-03</td>
<td>0.000318</td>
<td>NaN</td>
<td>0.014031</td>
<td>146605.880408</td>
<td>52.998555</td>
<td>0.025966</td>
<td>204584.211969</td>
<td>35.07948</td>
</tr>
</tbody>
</table>
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<h3 id="Process-All-Stocks">Process All Stocks<a class="anchor-link" href="#Process-All-Stocks">¶</a></h3><p>I will now loop through all stocks and present the results.</p>
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<div class="prompt input_prompt">In [3]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># process</span>
<span class="k">for</span> <span class="n">stock</span> <span class="ow">in</span> <span class="n">dailyPrices</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'******************************* Stock : '</span> <span class="o">+</span> <span class="n">dailyPrices</span><span class="p">[</span><span class="n">stock</span><span class="p">]</span><span class="o">.</span><span class="n">name</span> <span class="o">+</span> <span class="s1">' ****************************'</span><span class="p">)</span>
<span class="n">forecast_3day_returns</span><span class="p">(</span><span class="n">dailyPrices</span><span class="p">[</span><span class="n">stock</span><span class="p">],</span> <span class="n">ARIMAorder</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">))</span>
</pre></div>
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<pre>******************************* Stock : X1 ****************************
ARMA Model Results
==============================================================================
Dep. Variable: X1 No. Observations: 977
Model: ARMA(1, 0) Log Likelihood 2927.165
Method: css-mle S.D. of innovations 0.012
Date: Tue, 07 Jun 2016 AIC -5848.330
Time: 21:45:45 BIC -5833.676
Sample: 01-04-2005 HQIC -5842.754
- 11-18-2008
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 0.0004 0.000 1.201 0.230 -0.000 0.001
ar.L1.X1 -0.1273 0.032 -4.013 0.000 -0.189 -0.065
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -7.8562 +0.0000j 7.8562 0.5000
-----------------------------------------------------------------------------
===== 3-day Returns forecast for closing price of last-day in timeseries ======
Note: The first row in the table corresponds to the last day
closing price of the stock
Stock: X1
</pre>
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>0.000316</td>
<td>-0.001284</td>
<td>0.008147</td>
<td>90475.878952</td>
<td>53.224156</td>
<td>0.014308</td>
<td>33165.12993</td>
<td>36.745138</td>
</tr>
<tr>
<th>1</th>
<td>2016-01-01</td>
<td>0.000465</td>
<td>NaN</td>
<td>0.008147</td>
<td>90475.878952</td>
<td>53.224156</td>
<td>0.014308</td>
<td>33165.12993</td>
<td>36.745138</td>
</tr>
<tr>
<th>2</th>
<td>2016-01-02</td>
<td>0.000406</td>
<td>NaN</td>
<td>0.008147</td>
<td>90475.878952</td>
<td>53.224156</td>
<td>0.014308</td>
<td>33165.12993</td>
<td>36.745138</td>
</tr>
<tr>
<th>3</th>
<td>2016-01-03</td>
<td>0.000413</td>
<td>NaN</td>
<td>0.008147</td>
<td>90475.878952</td>
<td>53.224156</td>
<td>0.014308</td>
<td>33165.12993</td>
<td>36.745138</td>
</tr>
</tbody>
</table>
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<pre>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
******************************* Stock : X2 ****************************
ARMA Model Results
==============================================================================
Dep. Variable: X2 No. Observations: 1008
Model: ARMA(1, 0) Log Likelihood 2749.797
Method: css-mle S.D. of innovations 0.016
Date: Tue, 07 Jun 2016 AIC -5493.594
Time: 21:45:45 BIC -5478.847
Sample: 01-04-2005 HQIC -5487.992
- 01-05-2009
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 0.0006 0.000 1.150 0.250 -0.000 0.001
ar.L1.X2 -0.0413 0.031 -1.313 0.190 -0.103 0.020
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -24.2207 +0.0000j 24.2207 0.5000
-----------------------------------------------------------------------------
===== 3-day Returns forecast for closing price of last-day in timeseries ======
Note: The first row in the table corresponds to the last day
closing price of the stock
Stock: X2
</pre>
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>0.000525</td>
<td>-0.001672</td>
<td>0.009607</td>
<td>72649.480731</td>
<td>50.892857</td>
<td>0.017149</td>
<td>172515.825677</td>
<td>51.190476</td>
</tr>
<tr>
<th>1</th>
<td>2016-01-01</td>
<td>0.000573</td>
<td>NaN</td>
<td>0.009607</td>
<td>72649.480731</td>
<td>50.892857</td>
<td>0.017149</td>
<td>172515.825677</td>
<td>51.190476</td>
</tr>
<tr>
<th>2</th>
<td>2016-01-02</td>
<td>0.000549</td>
<td>NaN</td>
<td>0.009607</td>
<td>72649.480731</td>
<td>50.892857</td>
<td>0.017149</td>
<td>172515.825677</td>
<td>51.190476</td>
</tr>
<tr>
<th>3</th>
<td>2016-01-03</td>
<td>0.000550</td>
<td>NaN</td>
<td>0.009607</td>
<td>72649.480731</td>
<td>50.892857</td>
<td>0.017149</td>
<td>172515.825677</td>
<td>51.190476</td>
</tr>
</tbody>
</table>
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<pre>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
******************************* Stock : X3 ****************************
ARMA Model Results
==============================================================================
Dep. Variable: X3 No. Observations: 2768
Model: ARMA(1, 0) Log Likelihood 6727.408
Method: css-mle S.D. of innovations 0.021
Date: Tue, 07 Jun 2016 AIC -13448.817
Time: 21:45:45 BIC -13431.039
Sample: 01-04-2005 HQIC -13442.396
- 12-31-2015
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 0.0003 0.000 0.684 0.494 -0.000 0.001
ar.L1.X3 -0.0598 0.019 -3.154 0.002 -0.097 -0.023
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -16.7111 +0.0000j 16.7111 0.5000
-----------------------------------------------------------------------------
===== 3-day Returns forecast for closing price of last-day in timeseries ======
Note: The first row in the table corresponds to the last day
closing price of the stock
Stock: X3
</pre>
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<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>0.000616</td>
<td>-0.001105</td>
<td>0.014021</td>
<td>99861.344553</td>
<td>51.66185</td>
<td>0.025225</td>
<td>75643.114964</td>
<td>32.189306</td>
</tr>
<tr>
<th>1</th>
<td>2016-01-01</td>
<td>0.000602</td>
<td>NaN</td>
<td>0.014021</td>
<td>99861.344553</td>
<td>51.66185</td>
<td>0.025225</td>
<td>75643.114964</td>
<td>32.189306</td>
</tr>
<tr>
<th>2</th>
<td>2016-01-02</td>
<td>0.000241</td>
<td>NaN</td>
<td>0.014021</td>
<td>99861.344553</td>
<td>51.66185</td>
<td>0.025225</td>
<td>75643.114964</td>
<td>32.189306</td>
</tr>
<tr>
<th>3</th>
<td>2016-01-03</td>
<td>0.000262</td>
<td>NaN</td>
<td>0.014021</td>
<td>99861.344553</td>
<td>51.66185</td>
<td>0.025225</td>
<td>75643.114964</td>
<td>32.189306</td>
</tr>
</tbody>
</table>
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<pre>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
******************************* Stock : X4 ****************************
ARMA Model Results
==============================================================================
Dep. Variable: X4 No. Observations: 2346
Model: ARMA(1, 0) Log Likelihood 6042.728
Method: css-mle S.D. of innovations 0.018
Date: Tue, 07 Jun 2016 AIC -12079.456
Time: 21:45:46 BIC -12062.175
Sample: 01-04-2005 HQIC -12073.162
- 04-30-2014
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 0.0002 0.000 0.634 0.526 -0.001 0.001
ar.L1.X4 0.0275 0.021 1.333 0.183 -0.013 0.068
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 36.3580 +0.0000j 36.3580 0.0000
-----------------------------------------------------------------------------
===== 3-day Returns forecast for closing price of last-day in timeseries ======
Note: The first row in the table corresponds to the last day
closing price of the stock
Stock: X4
</pre>
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<thead>
<tr style="text-align: right;">
<th></th>
<th>0</th>
<th>Forecast Log Returns</th>
<th>Forecast 3-day Log Returns</th>
<th>Long term MAE (log returns)</th>
<th>Long term MAPE (log returns) %</th>
<th>Long term DirectionAccuracy (log returns) %</th>
<th>Long term MAE (3-day log returns)</th>
<th>Long term MAPE (3-day log returns) %</th>
<th>Long term DirectionAccuracy (3-day log returns) %</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>2015-12-31</td>
<td>0.000238</td>
<td>-0.000743</td>
<td>0.011833</td>
<td>20460.270749</td>