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<h1>Source code for pyFTS.benchmarks.Measures</h1><div class="highlight"><pre>
<span></span><span class="c1"># -*- coding: utf8 -*-</span>
<span class="sd">"""</span>
<span class="sd">pyFTS module for common benchmark metrics</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">time</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">from</span> <span class="nn">pyFTS.common</span> <span class="k">import</span> <span class="n">FuzzySet</span><span class="p">,</span> <span class="n">SortedCollection</span>
<span class="kn">from</span> <span class="nn">pyFTS.probabilistic</span> <span class="k">import</span> <span class="n">ProbabilityDistribution</span>
<div class="viewcode-block" id="acf"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.acf">[docs]</a><span class="k">def</span> <span class="nf">acf</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Autocorrelation function estimative</span>
<span class="sd"> :param data: </span>
<span class="sd"> :param k: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</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">data</span><span class="p">)</span>
<span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">):</span>
<span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span>
<span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">((</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="n">s</span></div>
<div class="viewcode-block" id="rmse"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.rmse">[docs]</a><span class="k">def</span> <span class="nf">rmse</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="sd">"""</span>
<span class="sd"> Root Mean Squared Error</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">targets</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">targets</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">forecasts</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="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">((</span><span class="n">targets</span> <span class="o">-</span> <span class="n">forecasts</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span></div>
<div class="viewcode-block" id="rmse_interval"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.rmse_interval">[docs]</a><span class="k">def</span> <span class="nf">rmse_interval</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="sd">"""</span>
<span class="sd"> Root Mean Squared Error</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="n">fmean</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">((</span><span class="n">fmean</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span></div>
<div class="viewcode-block" id="mape"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.mape">[docs]</a><span class="k">def</span> <span class="nf">mape</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="sd">"""</span>
<span class="sd"> Mean Average Percentual Error</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">targets</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">targets</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">forecasts</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="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="n">targets</span> <span class="o">-</span> <span class="n">forecasts</span><span class="p">)</span> <span class="o">/</span> <span class="n">targets</span><span class="p">))</span> <span class="o">*</span> <span class="mi">100</span></div>
<div class="viewcode-block" id="smape"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.smape">[docs]</a><span class="k">def</span> <span class="nf">smape</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="nb">type</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Symmetric Mean Average Percentual Error</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :param type: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">targets</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">targets</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">forecasts</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="k">if</span> <span class="nb">type</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">((</span><span class="n">forecasts</span> <span class="o">+</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span>
<span class="k">elif</span> <span class="nb">type</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">targets</span><span class="p">)))</span> <span class="o">*</span> <span class="mi">100</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">))</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">+</span> <span class="n">targets</span><span class="p">)</span></div>
<div class="viewcode-block" id="mape_interval"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.mape_interval">[docs]</a><span class="k">def</span> <span class="nf">mape_interval</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">fmean</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">fmean</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="n">fmean</span><span class="p">)</span> <span class="o">*</span> <span class="mi">100</span></div>
<div class="viewcode-block" id="UStatistic"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.UStatistic">[docs]</a><span class="k">def</span> <span class="nf">UStatistic</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="sd">"""</span>
<span class="sd"> Theil's U Statistic</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">targets</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">targets</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">targets</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="n">forecasts</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="n">naive</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">l</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">forecasts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">targets</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">naive</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">targets</span><span class="p">[</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">targets</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">naive</span><span class="p">))</span></div>
<div class="viewcode-block" id="TheilsInequality"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.TheilsInequality">[docs]</a><span class="k">def</span> <span class="nf">TheilsInequality</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="sd">"""</span>
<span class="sd"> Theil’s Inequality Coefficient</span>
<span class="sd"> :param targets: </span>
<span class="sd"> :param forecasts: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">targets</span> <span class="o">-</span> <span class="n">forecasts</span>
<span class="n">t</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="n">us</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">u</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">res</span><span class="p">]))</span>
<span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">y</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">targets</span><span class="p">]))</span>
<span class="n">fs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">f</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]))</span>
<span class="k">return</span> <span class="n">us</span> <span class="o">/</span> <span class="p">(</span><span class="n">ys</span> <span class="o">+</span> <span class="n">fs</span><span class="p">)</span></div>
<div class="viewcode-block" id="BoxPierceStatistic"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.BoxPierceStatistic">[docs]</a><span class="k">def</span> <span class="nf">BoxPierceStatistic</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Q Statistic for Box-Pierce test</span>
<span class="sd"> :param data: </span>
<span class="sd"> :param h: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">h</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">acf</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
<span class="n">s</span> <span class="o">+=</span> <span class="n">r</span> <span class="o">**</span> <span class="mi">2</span>
<span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="n">s</span></div>
<div class="viewcode-block" id="BoxLjungStatistic"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.BoxLjungStatistic">[docs]</a><span class="k">def</span> <span class="nf">BoxLjungStatistic</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Q Statistic for Ljung–Box test</span>
<span class="sd"> :param data: </span>
<span class="sd"> :param h: </span>
<span class="sd"> :return: </span>
<span class="sd"> """</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">h</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">r</span> <span class="o">=</span> <span class="n">acf</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
<span class="n">s</span> <span class="o">+=</span> <span class="n">r</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span>
<span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">s</span></div>
<div class="viewcode-block" id="sharpness"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.sharpness">[docs]</a><span class="k">def</span> <span class="nf">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">):</span>
<span class="sd">"""Sharpness - Mean size of the intervals"""</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">i</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span></div>
<div class="viewcode-block" id="resolution"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.resolution">[docs]</a><span class="k">def</span> <span class="nf">resolution</span><span class="p">(</span><span class="n">forecasts</span><span class="p">):</span>
<span class="sd">"""Resolution - Standard deviation of the intervals"""</span>
<span class="n">shp</span> <span class="o">=</span> <span class="n">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="nb">abs</span><span class="p">((</span><span class="n">i</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">i</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">shp</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span></div>
<div class="viewcode-block" id="coverage"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.coverage">[docs]</a><span class="k">def</span> <span class="nf">coverage</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="sd">"""Percent of target values that fall inside forecasted interval"""</span>
<span class="n">preds</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">>=</span> <span class="n">forecasts</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span> <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">forecasts</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">preds</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">preds</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">preds</span><span class="p">)</span></div>
<div class="viewcode-block" id="pinball"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.pinball">[docs]</a><span class="k">def</span> <span class="nf">pinball</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">forecast</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Pinball loss function. Measure the distance of forecast to the tau-quantile of the target</span>
<span class="sd"> :param tau: quantile value in the range (0,1)</span>
<span class="sd"> :param target: </span>
<span class="sd"> :param forecast: </span>
<span class="sd"> :return: float, distance of forecast to the tau-quantile of the target</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">target</span> <span class="o">>=</span> <span class="n">forecast</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">target</span> <span class="o">-</span> <span class="n">forecast</span><span class="p">)</span> <span class="o">*</span> <span class="n">tau</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">forecast</span> <span class="o">-</span> <span class="n">target</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">tau</span><span class="p">)</span></div>
<div class="viewcode-block" id="pinball_mean"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.pinball_mean">[docs]</a><span class="k">def</span> <span class="nf">pinball_mean</span><span class="p">(</span><span class="n">tau</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="sd">"""</span>
<span class="sd"> Mean pinball loss value of the forecast for a given tau-quantile of the targets</span>
<span class="sd"> :param tau: quantile value in the range (0,1)</span>
<span class="sd"> :param targets: list of target values</span>
<span class="sd"> :param forecasts: list of prediction intervals</span>
<span class="sd"> :return: float, the pinball loss mean for tau quantile</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">tau</span> <span class="o"><=</span> <span class="mf">0.5</span><span class="p">:</span>
<span class="n">preds</span> <span class="o">=</span> <span class="p">[</span><span class="n">pinball</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">forecasts</span><span class="p">))]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">preds</span> <span class="o">=</span> <span class="p">[</span><span class="n">pinball</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">forecasts</span><span class="p">))]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">(</span><span class="n">preds</span><span class="p">)</span></div>
<div class="viewcode-block" id="winkler_score"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.winkler_score">[docs]</a><span class="k">def</span> <span class="nf">winkler_score</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">forecast</span><span class="p">):</span>
<span class="sd">'''R. L. Winkler, A Decision-Theoretic Approach to Interval Estimation, J. Am. Stat. Assoc. 67 (337) (1972) 187–191. doi:10.2307/2284720. '''</span>
<span class="n">delta</span> <span class="o">=</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="n">target</span> <span class="ow">and</span> <span class="n">target</span> <span class="o"><</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
<span class="k">return</span> <span class="n">delta</span>
<span class="k">elif</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">></span> <span class="n">target</span><span class="p">:</span>
<span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">target</span><span class="p">)</span> <span class="o">/</span> <span class="n">tau</span>
<span class="k">elif</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o"><</span> <span class="n">target</span><span class="p">:</span>
<span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">target</span> <span class="o">-</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="n">tau</span></div>
<div class="viewcode-block" id="winkler_mean"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.winkler_mean">[docs]</a><span class="k">def</span> <span class="nf">winkler_mean</span><span class="p">(</span><span class="n">tau</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="sd">"""</span>
<span class="sd"> Mean Winkler score value of the forecast for a given tau-quantile of the targets</span>
<span class="sd"> :param tau: quantile value in the range (0,1)</span>
<span class="sd"> :param targets: list of target values</span>
<span class="sd"> :param forecasts: list of prediction intervals</span>
<span class="sd"> :return: float, the Winkler score mean for tau quantile</span>
<span class="sd"> """</span>
<span class="n">preds</span> <span class="o">=</span> <span class="p">[</span><span class="n">winkler_score</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">forecasts</span><span class="p">))]</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">(</span><span class="n">preds</span><span class="p">)</span></div>
<div class="viewcode-block" id="brier_score"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.brier_score">[docs]</a><span class="k">def</span> <span class="nf">brier_score</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">densities</span><span class="p">):</span>
<span class="sd">'''Brier (1950). "Verification of Forecasts Expressed in Terms of Probability". Monthly Weather Review. 78: 1–3. '''</span>
<span class="n">ret</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">d</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">densities</span><span class="p">):</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">bin_index</span><span class="o">.</span><span class="n">find_ge</span><span class="p">(</span><span class="n">targets</span><span class="p">[</span><span class="n">ct</span><span class="p">])</span>
<span class="n">score</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">d</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">bins</span> <span class="k">if</span> <span class="n">k</span> <span class="o">!=</span> <span class="n">v</span><span class="p">])</span>
<span class="n">score</span> <span class="o">+=</span> <span class="p">(</span><span class="n">d</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">score</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">ValueError</span> <span class="k">as</span> <span class="n">ex</span><span class="p">:</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">d</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">bins</span><span class="p">]))</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span></div>
<div class="viewcode-block" id="pmf_to_cdf"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.pmf_to_cdf">[docs]</a><span class="k">def</span> <span class="nf">pmf_to_cdf</span><span class="p">(</span><span class="n">density</span><span class="p">):</span>
<span class="n">ret</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">density</span><span class="o">.</span><span class="n">index</span><span class="p">:</span>
<span class="n">tmp</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">prev</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">density</span><span class="o">.</span><span class="n">columns</span><span class="p">:</span>
<span class="n">prev</span> <span class="o">+=</span> <span class="n">density</span><span class="p">[</span><span class="n">col</span><span class="p">][</span><span class="n">row</span><span class="p">]</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">density</span><span class="p">[</span><span class="n">col</span><span class="p">][</span><span class="n">row</span><span class="p">])</span> <span class="k">else</span> <span class="mi">0</span>
<span class="n">tmp</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">prev</span><span class="p">)</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
<span class="n">df</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">ret</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">density</span><span class="o">.</span><span class="n">columns</span><span class="p">)</span>
<span class="k">return</span> <span class="n">df</span></div>
<div class="viewcode-block" id="heavyside"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.heavyside">[docs]</a><span class="k">def</span> <span class="nf">heavyside</span><span class="p">(</span><span class="nb">bin</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
<span class="k">return</span> <span class="mi">1</span> <span class="k">if</span> <span class="nb">bin</span> <span class="o">>=</span> <span class="n">target</span> <span class="k">else</span> <span class="mi">0</span></div>
<div class="viewcode-block" id="heavyside_cdf"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.heavyside_cdf">[docs]</a><span class="k">def</span> <span class="nf">heavyside_cdf</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">targets</span><span class="p">):</span>
<span class="n">ret</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">targets</span><span class="p">:</span>
<span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span> <span class="k">if</span> <span class="n">b</span> <span class="o">>=</span> <span class="n">t</span> <span class="k">else</span> <span class="mi">0</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bins</span><span class="p">]</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="n">df</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">ret</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">bins</span><span class="p">)</span>
<span class="k">return</span> <span class="n">df</span></div>
<div class="viewcode-block" id="crps"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.crps">[docs]</a><span class="k">def</span> <span class="nf">crps</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">densities</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Continuous Ranked Probability Score</span>
<span class="sd"> :param targets: a list with the target values</span>
<span class="sd"> :param densities: a list with pyFTS.probabil objectsistic.ProbabilityDistribution</span>
<span class="sd"> :return: float</span>
<span class="sd"> '''</span>
<span class="n">_crps</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="mf">0.0</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">densities</span><span class="p">,</span> <span class="n">ProbabilityDistribution</span><span class="o">.</span><span class="n">ProbabilityDistribution</span><span class="p">):</span>
<span class="n">densities</span> <span class="o">=</span> <span class="p">[</span><span class="n">densities</span><span class="p">]</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">densities</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">bins</span><span class="p">)</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">densities</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ct</span><span class="p">,</span> <span class="n">df</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">densities</span><span class="p">):</span>
<span class="n">_crps</span> <span class="o">+=</span> <span class="nb">sum</span><span class="p">([(</span><span class="n">df</span><span class="o">.</span><span class="n">cumulative</span><span class="p">(</span><span class="nb">bin</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="mi">1</span> <span class="k">if</span> <span class="nb">bin</span> <span class="o">>=</span> <span class="n">targets</span><span class="p">[</span><span class="n">ct</span><span class="p">]</span> <span class="k">else</span> <span class="mi">0</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="nb">bin</span> <span class="ow">in</span> <span class="n">df</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
<span class="k">return</span> <span class="n">_crps</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">l</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span></div>
<div class="viewcode-block" id="get_point_statistics"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.get_point_statistics">[docs]</a><span class="k">def</span> <span class="nf">get_point_statistics</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">'''</span>
<span class="sd"> Condensate all measures for point forecasters</span>
<span class="sd"> :param data: test data</span>
<span class="sd"> :param model: FTS model with point forecasting capability</span>
<span class="sd"> :param kwargs:</span>
<span class="sd"> :return: a list with the RMSE, SMAPE and U Statistic</span>
<span class="sd"> '''</span>
<span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'steps_ahead'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'type'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'point'</span>
<span class="n">indexer</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'indexer'</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
<span class="k">if</span> <span class="n">indexer</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ndata</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">indexer</span><span class="o">.</span><span class="n">get_data</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="k">elif</span> <span class="n">model</span><span class="o">.</span><span class="n">is_multivariate</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">):</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"Multivariate data must be a Pandas DataFrame!"</span><span class="p">)</span>
<span class="n">ndata</span> <span class="o">=</span> <span class="n">data</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">ndata</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">data</span><span class="p">)</span>
<span class="n">ret</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">if</span> <span class="n">steps_ahead</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">forecasts</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">ndata</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">if</span> <span class="n">model</span><span class="o">.</span><span class="n">is_multivariate</span> <span class="ow">and</span> <span class="n">model</span><span class="o">.</span><span class="n">has_seasonality</span><span class="p">:</span>
<span class="n">ndata</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">indexer</span><span class="o">.</span><span class="n">get_data</span><span class="p">(</span><span class="n">ndata</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">model</span><span class="o">.</span><span class="n">is_multivariate</span><span class="p">:</span>
<span class="n">ndata</span> <span class="o">=</span> <span class="n">ndata</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">target_variable</span><span class="o">.</span><span class="n">data_label</span><span class="p">]</span><span class="o">.</span><span class="n">values</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)):</span>
<span class="n">forecasts</span> <span class="o">=</span> <span class="p">[</span><span class="n">forecasts</span><span class="p">]</span>
<span class="n">forecasts</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>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">rmse</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">mape</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">UStatistic</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">steps_ahead_sampler</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'steps_ahead_sampler'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">nforecasts</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ndata</span><span class="p">)</span> <span class="o">-</span> <span class="n">steps_ahead</span><span class="p">,</span> <span class="n">steps_ahead_sampler</span><span class="p">):</span>
<span class="n">sample</span> <span class="o">=</span> <span class="n">ndata</span><span class="p">[</span><span class="n">k</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">:</span> <span class="n">k</span><span class="p">]</span>
<span class="n">tmp</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">sample</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">nforecasts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">rmse</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">mape</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">UStatistic</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="k">return</span> <span class="n">ret</span></div>
<div class="viewcode-block" id="get_interval_statistics"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.get_interval_statistics">[docs]</a><span class="k">def</span> <span class="nf">get_interval_statistics</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Condensate all measures for point interval forecasters</span>
<span class="sd"> :param data: test data</span>
<span class="sd"> :param model: FTS model with interval forecasting capability</span>
<span class="sd"> :param kwargs:</span>
<span class="sd"> :return: a list with the sharpness, resolution, coverage, .05 pinball mean,</span>
<span class="sd"> .25 pinball mean, .75 pinball mean and .95 pinball mean.</span>
<span class="sd"> """</span>
<span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'steps_ahead'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'type'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'interval'</span>
<span class="n">ret</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">if</span> <span class="n">steps_ahead</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">forecasts</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">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">resolution</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">coverage</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">order</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">winkler_mean</span><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">winkler_mean</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">2</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">forecasts</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span> <span class="o">-</span> <span class="n">steps_ahead</span><span class="p">):</span>
<span class="n">sample</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">k</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">:</span> <span class="n">k</span><span class="p">]</span>
<span class="n">tmp</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">sample</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">forecasts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span> <span class="mi">1</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">resolution</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">coverage</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">pinball_mean</span><span class="p">(</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">winkler_mean</span><span class="p">(</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">winkler_mean</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
<span class="k">return</span> <span class="n">ret</span></div>
<div class="viewcode-block" id="get_distribution_statistics"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.get_distribution_statistics">[docs]</a><span class="k">def</span> <span class="nf">get_distribution_statistics</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="sd">"""</span>
<span class="sd"> Get CRPS statistic and time for a forecasting model</span>
<span class="sd"> :param data: test data</span>
<span class="sd"> :param model: FTS model with probabilistic forecasting capability</span>
<span class="sd"> :param kwargs:</span>
<span class="sd"> :return: a list with the CRPS and execution time</span>
<span class="sd"> """</span>
<span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'steps_ahead'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'type'</span><span class="p">]</span> <span class="o">=</span> <span class="s1">'distribution'</span>
<span class="n">ret</span> <span class="o">=</span> <span class="nb">list</span><span class="p">()</span>
<span class="k">if</span> <span class="n">steps_ahead</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">_s1</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">forecasts</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">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">_e1</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">crps</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">3</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">_e1</span> <span class="o">-</span> <span class="n">_s1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">brier_score</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</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> <span class="mi">3</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">skip</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'steps_ahead_sampler'</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">forecasts</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">_s1</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span> <span class="o">-</span> <span class="n">steps_ahead</span><span class="p">,</span> <span class="n">skip</span><span class="p">):</span>
<span class="n">sample</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">k</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:</span> <span class="n">k</span><span class="p">]</span>
<span class="n">tmp</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">sample</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">forecasts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">_e1</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">crps</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">skip</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">_e1</span> <span class="o">-</span> <span class="n">_s1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">brier_score</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">skip</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
<span class="k">return</span> <span class="n">ret</span></div>
</pre></div>
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