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<title>pyFTS.benchmarks.ResidualAnalysis — pyFTS 1.6 documentation</title>
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<h1>Source code for pyFTS.benchmarks.ResidualAnalysis</h1><div class="highlight"><pre>
<span></span><span class="ch">#!/usr/bin/python</span>
<span class="c1"># -*- coding: utf8 -*-</span>
<span class="sd">"""Residual Analysis methods"""</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">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">pyFTS.common</span> <span class="kn">import</span> <span class="n">Transformations</span><span class="p">,</span><span class="n">Util</span>
<span class="kn">from</span> <span class="nn">pyFTS.benchmarks</span> <span class="kn">import</span> <span class="n">Measures</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span>
<div class="viewcode-block" id="residuals"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.ResidualAnalysis.residuals">[docs]</a><span class="k">def</span> <span class="nf">residuals</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">forecasts</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="sd">"""First order residuals"""</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">targets</span><span class="p">[</span><span class="n">order</span><span class="p">:])</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">forecasts</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span></div>
<div class="viewcode-block" id="ljung_box_test"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.ResidualAnalysis.ljung_box_test">[docs]</a><span class="k">def</span> <span class="nf">ljung_box_test</span><span class="p">(</span><span class="n">residuals</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">):</span>
<span class="kn">from</span> <span class="nn">statsmodels.stats.diagnostic</span> <span class="kn">import</span> <span class="n">acorr_ljungbox</span>
<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">chi2</span>
<span class="n">stat</span><span class="p">,</span> <span class="n">pval</span> <span class="o">=</span> <span class="n">acorr_ljungbox</span><span class="p">(</span><span class="n">residuals</span><span class="p">,</span> <span class="n">lags</span><span class="o">=</span><span class="n">lags</span><span class="p">)</span>
<span class="n">rows</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">ct</span><span class="p">,</span> <span class="n">Q</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">stat</span><span class="p">):</span>
<span class="n">lag</span> <span class="o">=</span> <span class="n">ct</span><span class="o">+</span><span class="mi">1</span>
<span class="n">p_value</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">chi2</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">df</span><span class="o">=</span><span class="n">lag</span><span class="p">)</span>
<span class="n">critical_value</span> <span class="o">=</span> <span class="n">chi2</span><span class="o">.</span><span class="n">ppf</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">df</span><span class="o">=</span><span class="n">lag</span><span class="p">)</span>
<span class="n">rows</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">lag</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">p_value</span><span class="p">,</span> <span class="n">critical_value</span><span class="p">,</span> <span class="s1">'H0 accepted'</span> <span class="k">if</span> <span class="n">Q</span> <span class="o">></span> <span class="n">critical_value</span> <span class="k">else</span> <span class="s1">'H0 rejected'</span><span class="p">])</span>
<span class="k">return</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">'Lag'</span><span class="p">,</span><span class="s1">'Statistic'</span><span class="p">,</span><span class="s1">'p-Value'</span><span class="p">,</span><span class="s1">'Critical Value'</span><span class="p">,</span> <span class="s1">'Result'</span><span class="p">])</span></div>
<div class="viewcode-block" id="compare_residuals"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.ResidualAnalysis.compare_residuals">[docs]</a><span class="k">def</span> <span class="nf">compare_residuals</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">models</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=.</span><span class="mi">05</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Compare residual's statistics of several models</span>
<span class="sd"> :param data: test data</span>
<span class="sd"> :param models: </span>
<span class="sd"> :return: a Pandas dataframe with the Box-Ljung statistic for each model</span>
<span class="sd"> """</span>
<span class="kn">from</span> <span class="nn">statsmodels.stats.diagnostic</span> <span class="kn">import</span> <span class="n">acorr_ljungbox</span>
<span class="n">rows</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">columns</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"Model"</span><span class="p">,</span><span class="s2">"Order"</span><span class="p">,</span><span class="s2">"AVG"</span><span class="p">,</span><span class="s2">"STD"</span><span class="p">,</span><span class="s2">"Box-Ljung"</span><span class="p">,</span><span class="s2">"p-value"</span><span class="p">,</span><span class="s2">"Result"</span><span class="p">]</span>
<span class="k">for</span> <span class="n">mfts</span> <span class="ow">in</span> <span class="n">models</span><span class="p">:</span>
<span class="n">forecasts</span> <span class="o">=</span> <span class="n">mfts</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">residuals</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">forecasts</span><span class="p">,</span> <span class="n">mfts</span><span class="o">.</span><span class="n">order</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">mu</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">res</span><span class="p">)</span>
<span class="n">sig</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">row</span> <span class="o">=</span> <span class="p">[</span><span class="n">mfts</span><span class="o">.</span><span class="n">shortname</span><span class="p">,</span> <span class="n">mfts</span><span class="o">.</span><span class="n">order</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">sig</span><span class="p">]</span>
<span class="n">stat</span><span class="p">,</span> <span class="n">pval</span> <span class="o">=</span> <span class="n">acorr_ljungbox</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">test</span> <span class="o">=</span> <span class="s1">'H0 Accepted'</span> <span class="k">if</span> <span class="n">pval</span> <span class="o">></span> <span class="n">alpha</span> <span class="k">else</span> <span class="s1">'H0 Rejected'</span>
<span class="n">row</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="n">stat</span><span class="p">,</span> <span class="n">pval</span><span class="p">,</span> <span class="n">test</span><span class="p">])</span>
<span class="n">rows</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
<span class="k">return</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">rows</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">columns</span><span class="p">)</span></div>
<div class="viewcode-block" id="plot_residuals_by_model"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.ResidualAnalysis.plot_residuals_by_model">[docs]</a><span class="k">def</span> <span class="nf">plot_residuals_by_model</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">models</span><span class="p">,</span> <span class="n">tam</span><span class="o">=</span><span class="p">[</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">],</span> <span class="n">save</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="kn">import</span> <span class="nn">scipy</span> <span class="k">as</span> <span class="nn">sp</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">models</span><span class="p">),</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="n">tam</span><span class="p">)</span>
<span class="k">for</span> <span class="n">c</span><span class="p">,</span> <span class="n">mfts</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">models</span><span class="p">,</span> <span class="n">start</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">models</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span>
<span class="n">forecasts</span> <span class="o">=</span> <span class="n">mfts</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">targets</span><span class="p">)</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">residuals</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">forecasts</span><span class="p">,</span> <span class="n">mfts</span><span class="o">.</span><span class="n">order</span><span class="p">)</span>
<span class="n">mu</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">res</span><span class="p">)</span>
<span class="n">sig</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">if</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Residuals"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">mfts</span><span class="o">.</span><span class="n">shortname</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">' '</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">if</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Autocorrelation"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'ACS'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'Lag'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">acorr</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">if</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Histogram"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'Freq'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'Bins'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">if</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"QQ Plot"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">__</span><span class="p">,</span> <span class="n">___</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">plot</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">fit</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">Util</span><span class="o">.</span><span class="n">show_and_save_image</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">file</span><span class="p">,</span> <span class="n">save</span><span class="p">)</span></div>
<div class="viewcode-block" id="single_plot_residuals"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.ResidualAnalysis.single_plot_residuals">[docs]</a><span class="k">def</span> <span class="nf">single_plot_residuals</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">order</span><span class="p">,</span> <span class="n">tam</span><span class="o">=</span><span class="p">[</span><span class="mi">10</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span> <span class="n">save</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="kn">import</span> <span class="nn">scipy</span> <span class="k">as</span> <span class="nn">sp</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="n">tam</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Residuals"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Autocorrelation"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'ACF'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'Lag'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">acorr</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Histogram"</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s1">'large'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'Freq'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'Bins'</span><span class="p">)</span>
<span class="n">ax</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="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">__</span><span class="p">,</span> <span class="n">___</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">plot</span><span class="o">=</span><span class="n">ax</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">fit</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">Util</span><span class="o">.</span><span class="n">show_and_save_image</span><span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">file</span><span class="p">,</span> <span class="n">save</span><span class="p">)</span></div>
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