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<a name="forecastetspiadd"></a>
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<h1 id="hd_id0603201617134175" dir="auto">FORECAST.ETS.PI.ADD function</h1>
<p id="par_id0603201617141750" class="paragraph" dir="auto"><span class="avis">Calculates the prediction interval(s) for additive forecast based on the historical data using ETS or EDS algorithms.</span> EDS is used when argument <span class="emph">period_length</span> is 0, otherwise ETS is used.</p>
<div class="embedded">
<a name="intro"></a>
<p id="par_id0403201618694534" class="paragraph" dir="auto">Exponential Smoothing is a method to smooth real values in time series in order to forecast probable future values.</p>
<p id="par_id0403201618694535" class="paragraph" dir="auto">Exponential Triple Smoothing (ETS) is a set of algorithms in which both trend and periodical (seasonal) influences are processed. Exponential Double Smoothing (EDS) is an algorithm like ETS, but without the periodical influences. EDS produces linear forecasts.</p>
<div class="tip">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/tip.svg" alt="Tip Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">See the <a target="_blank" href="https://en.wikipedia.org/wiki/Exponential_smoothing">Wikipedia on Exponential smoothing algorithms</a> for more information.</p></div>
</div>
<br>
</div>
<p id="par_id0603201610005998" class="paragraph" dir="auto">FORECAST.ETS.PI.ADD calculates with the model</p>
<div class="embedded">
<a name="etsadd"></a>
<p id="par_id0603201608440579" class="code" dir="auto">forecast = basevalue + trend * ∆x + periodical_aberration.</p>
</div>
<div class="embedded">
<a name="func_head_syntax"></a>
<h3 id="hd_id126511265112651" dir="auto">Syntax</h3>
</div>
<p id="par_id0603201610010044" class="code" dir="auto">FORECAST.ETS.PI.ADD(target, values, timeline, [confidence_level], [period_length], [data_completion], [aggregation])</p>
<div class="embedded">
<a name="target"></a>
<p id="par_id0403201618594534" class="paragraph" dir="auto"><span class="emph">target (mandatory):</span> A date, time or numeric single value or range. The data point/range for which to calculate a forecast.</p>
</div>
<div class="embedded">
<a name="values"></a>
<p id="par_id040320161859459" class="paragraph" dir="auto"><span class="emph">values (mandatory):</span> A numeric array or range. <span class="emph">values</span> are the historical values, for which you want to forecast the next points.</p>
</div>
<div class="embedded">
<a name="timeline"></a>
<p id="par_id0403201618594553" class="paragraph" dir="auto"><span class="emph">timeline (mandatory):</span> A numeric array or range. The timeline (x-value) range for the historical values. </p>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="Note Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">The timeline does not have to be sorted, the functions will sort it for calculations.<br>The timeline values must have a consistent step between them.<br>If a constant step cannot be identified in the sorted timeline, the functions will return the #NUM! error.<br>If the ranges of both the timeline and the historical values are not the same size, the functions will return the #N/A error.<br>If the timeline contains fewer than 2 data periods, the functions will return the #VALUE! error.</p></div>
</div>
<br>
</div>
<div class="embedded">
<a name="confidence"></a>
<p id="par_id0503201619582665" class="paragraph" dir="auto"><span class="emph">confidence_level (mandatory)</span>: A numeric value between 0 and 1 (exclusive), default is 0.95. A value indicating a confidence level for the calculated prediction interval.</p>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="Note Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">With values <= 0 or >= 1, the functions will return the #NUM! Error.</p></div>
</div>
<br>
</div>
<div class="embedded">
<a name="numsampperiod"></a>
<p id="par_id0603201609412381" class="paragraph" dir="auto"><span class="emph">period_length (optional)</span>: A numeric value >= 0, the default is 1. A positive integer indicating the number of samples in a period. </p>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="Note Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">A value of 1 indicates that Calc is to determine the number of samples in a period automatically. <br>A value of 0 indicates no periodic effects, a forecast is calculated with EDS algorithms. <br>For all other positive values, forecasts are calculated with ETS algorithms.<br>For values that not being a positive whole number, the functions will return the #NUM! Error.</p></div>
</div>
<br>
</div>
<div class="embedded">
<a name="datacompletion"></a>
<p id="par_id0403201618594513" class="paragraph" dir="auto"><span class="emph">data_completion (optional):</span> a logical value TRUE or FALSE, a numeric 1 or 0, default is 1 (TRUE). A value of 0 (FALSE) will add missing data points with zero as historical value. A value of 1 (TRUE) will add missing data points by interpolating between the neighboring data points.</p>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="Note Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">Although the time line requires a constant step between data points, the function support up to 30% missing data points, and will add these data points. </p></div>
</div>
<br>
</div>
<div class="embedded">
<a name="aggregation"></a>
<p id="par_id0403201618594650" class="paragraph" dir="auto"><span class="emph">aggregation (optional):</span> A numeric value from 1 to 7, with default 1. The aggregation parameter indicates which method will be used to aggregate identical time values:</p>
<table border="1" class="" cellpadding="0" cellspacing="0">
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0403201618594696" class="tableheadintable" dir="auto">Aggregation</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id040320161859464" class="tableheadintable" dir="auto">Function</p>
</th>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618564423" class="tablecontentintable" dir="auto">1</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594636" class="tablecontentintable" dir="auto">AVERAGE</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618565433" class="tablecontentintable" dir="auto">2</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594692" class="tablecontentintable" dir="auto">COUNT</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618565982" class="tablecontentintable" dir="auto">3</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594633" class="tablecontentintable" dir="auto">COUNTA</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618570026" class="tablecontentintable" dir="auto">4</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id040320161859460" class="tablecontentintable" dir="auto">MAX</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618570154" class="tablecontentintable" dir="auto">5</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594658" class="tablecontentintable" dir="auto">MEDIAN</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618570236" class="tablecontentintable" dir="auto">6</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594671" class="tablecontentintable" dir="auto">MIN</p>
</td>
</tr>
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618570394" class="tablecontentintable" dir="auto">7</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0403201618594639" class="tablecontentintable" dir="auto">SUM</p>
</td>
</tr>
</table>
<br>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="Note Icon
" style="width:40px;height:40px;"></div>
<div class="notetext"><p dir="auto">Although the time line requires a constant step between data points, the functions will aggregate multiple points which have the same time stamp. </p></div>
</div>
<br>
</div>
<p id="par_id0403201618595126" class="paragraph" dir="auto">For example, with a 90% Confidence level, a 90% prediction interval will be computed (90% of future points are to fall within this radius from forecast). </p>
<div class="note">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/note.svg" alt="note" style="width:40px;height:40px;"></div>
<div class="notetext"><p id="par_id0403201618595143" dir="auto">Note on prediction intervals: there is no exact mathematical way to calculate this for forecasts, there are various approximations. Prediction intervals tend to be increasingly 'over-optimistic' when increasing distance of the forecast-X from the observation data set.</p></div>
</div>
<br>
<p id="par_id0403201618595150" class="paragraph" dir="auto">For ETS, Calc uses an approximation based on 1000 calculations with random variations within the standard deviation of the observation data set (the historical values).</p>
<div class="embedded">
<a name="exampledata"></a>
<div class="embedded">
<a name="sectionexample"></a>
<h4 id="hd_id281171" dir="auto">Example</h4>
</div>
<p id="hd_id0603201610005723" class="paragraph" dir="auto">The table below contains a timeline and its associated values:</p>
<table border="1" class="" cellpadding="0" cellspacing="0">
<tr>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610293753" class="tablecontentintable" dir="auto"></p>
</td>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610300936" class="tableheadintable" dir="auto">A</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610303544" class="tableheadintable" dir="auto">B</p>
</th>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610294112" class="tableheadintable" dir="auto">1</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610312235" class="tableheadintable" dir="auto">Timeline</p>
</th>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610312228" class="tableheadintable" dir="auto">Values</p>
</th>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id090320161029434" class="tableheadintable" dir="auto">2</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610301211" class="tablecontentintable" dir="auto">01/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610303777" class="tablecontentintable" dir="auto">112</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610294532" class="tableheadintable" dir="auto">3</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610301377" class="tablecontentintable" dir="auto">02/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610303972" class="tablecontentintable" dir="auto">118</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610294658" class="tableheadintable" dir="auto">4</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610301586" class="tablecontentintable" dir="auto">03/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610304214" class="tablecontentintable" dir="auto">132</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610294721" class="tableheadintable" dir="auto">5</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610301829" class="tablecontentintable" dir="auto">04/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610304365" class="tablecontentintable" dir="auto">100</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610294810" class="tableheadintable" dir="auto">6</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610301986" class="tablecontentintable" dir="auto">05/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610304419" class="tablecontentintable" dir="auto">121</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295069" class="tableheadintable" dir="auto">7</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302140" class="tablecontentintable" dir="auto">06/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id090320161030452" class="tablecontentintable" dir="auto">135</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295133" class="tableheadintable" dir="auto">8</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302288" class="tablecontentintable" dir="auto">07/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610304756" class="tablecontentintable" dir="auto">148</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295347" class="tableheadintable" dir="auto">9</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302389" class="tablecontentintable" dir="auto">08/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id090320161030480" class="tablecontentintable" dir="auto">148</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295495" class="tableheadintable" dir="auto">10</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302420" class="tablecontentintable" dir="auto">09/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610304994" class="tablecontentintable" dir="auto">136</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295668" class="tableheadintable" dir="auto">11</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302687" class="tablecontentintable" dir="auto">10/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610305156" class="tablecontentintable" dir="auto">119</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610295729" class="tableheadintable" dir="auto">12</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302713" class="tablecontentintable" dir="auto">11/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610305294" class="tablecontentintable" dir="auto">104</p>
</td>
</tr>
<tr>
<th rowspan="" colspan="" class="tableheadcell" dir="auto">
<p id="par_id0903201610300473" class="tableheadintable" dir="auto">13</p>
</th>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610302922" class="tablecontentintable" dir="auto">12/2013</p>
</td>
<td rowspan="" colspan="" dir="auto">
<p id="par_id0903201610305330" class="tablecontentintable" dir="auto">118</p>
</td>
</tr>
</table>
<br>
</div>
<p id="hd_id04032016185123" class="code" dir="auto">=FORECAST.ETS.PI.ADD(DATE(2014;1;1);Values;Timeline;0.9;1;TRUE();1)</p>
<p id="hd_id04032016112394554" class="paragraph" dir="auto">Returns 18.8061295551355, the prediction interval for additive forecast for January 2014 based on <span class="emph">Values</span> and <span class="emph">Timeline</span> named ranges above, 90% (=0.9) confidence level, with one sample per period, no missing data, and AVERAGE as aggregation.</p>
<p id="hd_id04032123185123" class="code" dir="auto">=FORECAST.ETS.PI.ADD(DATE(2014;1;1);Values;Timeline;0.8;4;TRUE();7)</p>
<p id="hd_id040312316112394554" class="paragraph" dir="auto">Returns 23.4416821953741, the prediction interval for additive forecast for January 2014 based on <span class="emph">Values</span> and <span class="emph">Timeline</span> named ranges above, with confidence level of 0.8, period length of 4, no missing data, and SUM as aggregation.</p>
<div class="embedded">
<a name="sectiontechinfo"></a>
<h4 id="hd_id301640873452726" dir="auto">Technical information</h4>
</div>
<div class="embedded">
<a name="5.2"></a>
<div class="tip">
<div class="noteicon" dir="auto"><img src="media/icon-themes/res/helpimg/tip.svg" alt="tip" style="width:40px;height:40px;"></div>
<div class="notetext"><p id="par_id651551401041652" dir="auto">This function is available since LibreOffice 5.2.</p></div>
</div>
<br>
</div>
<div class="embedded">
<a name="notODFF"></a>
<p id="par_id251640873774457" class="paragraph" dir="auto">This function is not part of the <span class="emph">Open Document Format for Office Applications (OpenDocument) Version 1.3. Part 4: Recalculated Formula (OpenFormula) Format</span> standard. The name space is</p>
</div>
<p id="par_id341640873986703" class="paragraph" dir="auto"><span class="literal">COM.MICROSOFT.FORECAST.ETS.COFINT</span></p>
<a name="relatedtopics"></a><div class="relatedtopics">
<p class="related" itemprop="mentions" dir="auto"><a name="related"></a><span class="emph">Related Topics</span>
</p>
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<div class="notetext"><p id="par_id221677015965308" dir="auto"><a target="_blank" href="https://wiki.documentfoundation.org/Documentation/Calc_Functions/FORECAST.ETS.PI.ADD">FORECAST.ETS.PI.ADD wiki page</a>.</p></div>
</div>
<br>
<p id="par_id0603201619261276" class="paragraph" dir="auto">See also:
<a target="_top" href="en-US/text/scalc/01/func_forecastetsadd.html">FORECAST.ETS.ADD</a>,
<a target="_top" href="en-US/text/scalc/01/func_forecastetsmult.html">FORECAST.ETS.MULT</a>,
<a target="_top" href="en-US/text/scalc/01/func_forecastetsstatadd.html">FORECAST.ETS.STAT.ADD</a>,
<a target="_top" href="en-US/text/scalc/01/func_forecastetsstatmult.html">FORECAST.ETS.STAT.MULT</a>,
<a target="_top" href="en-US/text/scalc/01/func_forecastetspimult.html">FORECAST.ETS.PI.MULT</a>
<a target="_top" href="en-US/text/scalc/01/func_forecastetsseason.html">FORECAST.ETS.SEASONALITY</a>,
<a target="_top" href="en-US/text/scalc/01/04060185.html#forecast">FORECAST</a>,
<a target="_top" href="en-US/text/scalc/01/04060185.html#forecastlinear">FORECAST.LINEAR</a>
</p>
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