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<h1 id="hd_id1000110" dir="auto">
<a name="exponentialsmoothingh1"></a>Exponential Smoothing</h1>
<p id="par_id1002120" class="paragraph" dir="auto"><span class="avis">Results in a smoothed data series</span></p>
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<div><p class="howtogetheader" dir="auto"><a name="wie"></a>To access this command...</p></div>
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<p id="par_id1002130" class="paragraph" dir="auto"><a name="sam01"></a>Choose <span class="menuitem">Data - Statistics - Exponential Smoothing</span></p>
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<p id="par_id1002140" class="paragraph" dir="auto">Exponential smoothing is a filtering technique that when applied to a data set, produces smoothed results. It is employed in many domains such as stock market, economics and in sampled measurements.</p>
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<div class="notetext"><p id="par_id1002150" dir="auto">For more information on exponential smoothing, refer to the <a target="_blank" href="https://en.wikipedia.org/wiki/Exponential_smoothing">corresponding Wikipedia article</a>.</p></div>
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<h3 id="hd_id1000010" dir="auto">Data</h3>
<p id="par_id1000010" class="paragraph" dir="auto"><span class="emph">Input Range</span>: The reference of the range of the data to analyze.</p>
<p id="par_id1000020" class="paragraph" dir="auto"><span class="emph">Results to</span>: The reference of the top left cell of the range where the results will be displayed.</p>
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<h4 id="hd_id1000020" dir="auto">Grouped By</h4>
<p id="par_id1000030" class="paragraph" dir="auto">Select whether the input data has <span class="emph">columns</span> or <span class="emph">rows</span> layout.</p>
</div>
<h2 id="hd_id1000120" dir="auto">Parameters</h2>
<p id="par_id1002160" class="paragraph" dir="auto"><span class="emph">Smoothing Factor</span>: A parameter between 0 and 1 that represents the damping factor Alpha in the smoothing equation.</p>
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<h4 id="hd_id281171" dir="auto">Example</h4>
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<p id="par_id1000550" class="paragraph" dir="auto">The following table has two time series, one representing an impulse function at time t=0 and the other an impulse function at time t=2.</p>
<table border="1" class="" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="" colspan="" dir="auto">
</td>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000560" class="tableheadintable" dir="auto">A</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000570" class="tableheadintable" dir="auto">B</p>
</th>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000580" class="tableheadintable" dir="auto">1</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000590" class="tablecontentintable" dir="auto">1</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000600" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000610" class="tableheadintable" dir="auto">2</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000620" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000630" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000640" class="tableheadintable" dir="auto">3</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000650" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000660" class="tablecontentintable" dir="auto">1</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000670" class="tableheadintable" dir="auto">4</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000680" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000690" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000700" class="tableheadintable" dir="auto">5</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000710" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000720" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000730" class="tableheadintable" dir="auto">6</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000740" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000750" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000760" class="tableheadintable" dir="auto">7</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000770" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000780" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000790" class="tableheadintable" dir="auto">8</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000800" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000810" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000820" class="tableheadintable" dir="auto">9</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000830" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000840" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000850" class="tableheadintable" dir="auto">10</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000860" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000870" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000880" class="tableheadintable" dir="auto">11</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000890" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000900" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000910" class="tableheadintable" dir="auto">12</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000920" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000930" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1000940" class="tableheadintable" dir="auto">13</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000950" class="tablecontentintable" dir="auto">0</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1000960" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
</table>
<br>
</div>
<p id="par_id1002170" class="paragraph" dir="auto">The resulting smoothing is below with smoothing factor as 0.5:</p>
<table border="1" class="" cellpadding="0" cellspacing="0">
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1002180" class="tableheadintable" dir="auto">Alpha</p>
</th>
<td rowspan="" colspan="" dir="auto">
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002190" class="tablecontentintable" dir="auto">0.5</p>
</td>
<td rowspan="" colspan="" dir="auto">
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1002200" class="tableheadintable" dir="auto">Column 1</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id1002210" class="tableheadintable" dir="auto">Column 2</p>
</th>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002220" class="tablecontentintable" dir="auto">1</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002230" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002240" class="tablecontentintable" dir="auto">1</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002250" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002260" class="tablecontentintable" dir="auto">0.5</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002270" class="tablecontentintable" dir="auto">0</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002280" class="tablecontentintable" dir="auto">0.25</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002290" class="tablecontentintable" dir="auto">0.5</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002300" class="tablecontentintable" dir="auto">0.125</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002310" class="tablecontentintable" dir="auto">0.25</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002320" class="tablecontentintable" dir="auto">0.0625</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002330" class="tablecontentintable" dir="auto">0.125</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002340" class="tablecontentintable" dir="auto">0.03125</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002350" class="tablecontentintable" dir="auto">0.0625</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002360" class="tablecontentintable" dir="auto">0.015625</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002370" class="tablecontentintable" dir="auto">0.03125</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002380" class="tablecontentintable" dir="auto">0.0078125</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002390" class="tablecontentintable" dir="auto">0.015625</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002400" class="tablecontentintable" dir="auto">0.00390625</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002410" class="tablecontentintable" dir="auto">0.0078125</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002420" class="tablecontentintable" dir="auto">0.001953125</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002430" class="tablecontentintable" dir="auto">0.00390625</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002440" class="tablecontentintable" dir="auto">0.0009765625</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002450" class="tablecontentintable" dir="auto">0.001953125</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002460" class="tablecontentintable" dir="auto">0.0004882813</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002470" class="tablecontentintable" dir="auto">0.0009765625</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002480" class="tablecontentintable" dir="auto">0.0002441406</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id1002490" class="tablecontentintable" dir="auto">0.0004882813</p>
</td>
</tr>
</table>
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