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发表于 2010-11-4 21:15:18
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MAPE
From dwdus's blog on Baidu
<p><strong>Mean absolute percentage error (MAPE)</strong> is measure of accuracy in a fitted time series value in <a title="Statistics" href="http://en.wikipedia.org/wiki/Statistics"><font color="#0645ad">statistics</font></a>, specifically <a title="Trend estimation" href="http://en.wikipedia.org/wiki/Trend_estimation"><font color="#0645ad">trending</font></a>. It usually expresses accuracy as a percentage, and is defined by the formula:</p>
<dl><dd><img class="tex" alt="\mbox{M} = \frac{1}{n}\sum_{t=1}^n \left| \frac{A_t-F_t}{A_t}\right|" src="http://hiphotos.baidu.com/dwdus/pic/item/18f13b58ce882fc5800a188b.jpg"> </dd></dl>
<p>where <em>A</em><sub><em>t</em></sub> is the actual value and <em>F</em><sub><em>t</em></sub> is the forecast value.</p>
<p>The difference between <em>A</em><sub><em>t</em></sub> and <em>F</em><sub><em>t</em></sub> is divided by the actual value <em>A</em><sub><em>t</em></sub> again. The absolute value of this calculation is summed for every fitted or forecast point in time and divided again by the number of fitted points <em>n</em>. This makes it a percentage error so one can compare the error of fitted time series that differ in level.</p>
<p>Although the concept of MAPE sounds very simple and convincing, it has two major drawbacks in practical application:</p>
<ul>
<li>If there are zero values (which sometimes happens for example in demand series) there will be a division by zero</li>
<li>When having a perfect fit, MAPE is zero. But in regard to its upper level the MAPE has no restriction. When calculating the average MAPE for a number of time series there might be a problem: a few number of series that have a very high MAPE might distort a comparison between the average MAPE of time series fitted with one method compared to the average MAPE when using another method. In order to avoid this problem other measures have been defined, for example the <a class="mw-redirect" title="SMAPE" href="http://en.wikipedia.org/wiki/SMAPE"><font color="#0645ad">sMAPE</font></a> (symmetrical MAPE) or a <a class="new" title="Relative measure of accuracy (page does not exist)" href="http://en.wikipedia.org/w/index.php?title=Relative_measure_of_accuracy&action=edit&redlink=1"><font color="#ba0000">relative measure of accuracy</font></a>.</li>
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