Percentage Error Formula Wikipedia
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may be challenged and removed. (December 2009) (Learn how and when to remove this template message) The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics, for example in trend estimation. percent difference formula It usually expresses accuracy as a percentage, and is defined by the formula: M = 100 relative change formula n ∑ t = 1 n | A t − F t A t | , {\displaystyle {\mbox{M}}={\frac {100}{n}}\sum _{t=1}^{n}\left|{\frac {A_{t}-F_{t}}{A_{t}}}\right|,} where At is
Relative Difference Formula
the actual value and Ft is the forecast value. The difference between At and Ft is divided by the Actual value At again. The absolute value in this calculation is summed for every forecasted point in time and divided
Percent Difference Vs Percent Error
by the number of fitted pointsn. Multiplying by 100 makes it a percentage error. Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application [1] It cannot be used if there are zero values (which sometimes happens for example in demand data) because there would be a division by zero. For forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper absolute change formula limit to the percentage error. When MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the ratio of the predicted to actual value (called the Accuracy Ratio), this approach leads to superior statistical properties and leads to predictions which can be interpreted in terms of the geometric mean.[1] Contents 1 Alternative MAPE definitions 2 Issues 3 See also 4 External links 5 References Alternative MAPE definitions[edit] Problems can occur when calculating the MAPE value with a series of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error, caused by a small deviation in error, can occur. As an alternative, each actual value (At) of the series in the original formula can be replaced by the average of all actual values (Āt) of that series. This alternative is still being used for measuring the performance of models that forecast spot electricity prices.[2] Note that this is the same as dividing the sum of absolute differences by the sum of actual values, and is sometimes referred to as WAPE. Issues[edit] While MAPE is one of the most popular measures for forecasting error, there are many studies on shortcomings and misleading
may be challenged and removed. (December 2009) (Learn how and when to remove this template message) The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction
Percent Error Example
accuracy of a forecasting method in statistics, for example in trend estimation. It usually mean percentage error expresses accuracy as a percentage, and is defined by the formula: M = 100 n ∑ t = 1 n percent difference vs percent change | A t − F t A t | , {\displaystyle {\mbox{M}}={\frac {100}{n}}\sum _{t=1}^{n}\left|{\frac {A_{t}-F_{t}}{A_{t}}}\right|,} where At is the actual value and Ft is the forecast value. The difference between At and Ft is https://en.wikipedia.org/wiki/Mean_absolute_percentage_error divided by the Actual value At again. The absolute value in this calculation is summed for every forecasted point in time and divided by the number of fitted pointsn. Multiplying by 100 makes it a percentage error. Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application [1] It cannot be used if there are zero values (which sometimes happens https://en.wikipedia.org/wiki/Mean_absolute_percentage_error for example in demand data) because there would be a division by zero. For forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper limit to the percentage error. When MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the ratio of the predicted to actual value (called the Accuracy Ratio), this approach leads to superior statistical properties and leads to predictions which can be interpreted in terms of the geometric mean.[1] Contents 1 Alternative MAPE definitions 2 Issues 3 See also 4 External links 5 References Alternative MAPE definitions[edit] Problems can occur when calculating the MAPE value with a series of small denominators. A singularity problem of the form 'one divided by zero' and/or the creation of very large changes in the Absolute Percentage Error, caused by a small deviation in error, can occur. As an alternative, each actual value (At) of the series in the original formula can be replaced by the average of all
1 ( x ) = 1 + x {\displaystyle P_{1}(x)=1+x} (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0. https://en.wikipedia.org/wiki/Approximation_error The approximation error in some data is the discrepancy between an exact value and https://en.wikipedia.org/wiki/Calculating_demand_forecast_accuracy some approximation to it. An approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5cm but since the ruler does not use decimals, you round it to 5cm.) or approximations are used instead of the real data percent difference (e.g., 3.14 instead of π). In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm. Contents 1 Formal Definition 1.1 Generalizations 2 Examples 3 Uses of relative error 4 Instruments 5 See also 6 References 7 External links Formal Definition[edit] One commonly distinguishes between the relative error and the absolute error. Given some value v percent difference vs and its approximation vapprox, the absolute error is ϵ = | v − v approx | , {\displaystyle \epsilon =|v-v_{\text{approx}}|\ ,} where the vertical bars denote the absolute value. If v ≠ 0 , {\displaystyle v\neq 0,} the relative error is η = ϵ | v | = | v − v approx v | = | 1 − v approx v | , {\displaystyle \eta ={\frac {\epsilon }{|v|}}=\left|{\frac {v-v_{\text{approx}}}{v}}\right|=\left|1-{\frac {v_{\text{approx}}}{v}}\right|,} and the percent error is δ = 100 % × η = 100 % × ϵ | v | = 100 % × | v − v approx v | . {\displaystyle \delta =100\%\times \eta =100\%\times {\frac {\epsilon }{|v|}}=100\%\times \left|{\frac {v-v_{\text{approx}}}{v}}\right|.} In words, the absolute error is the magnitude of the difference between the exact value and the approximation. The relative error is the absolute error divided by the magnitude of the exact value. The percent error is the relative error expressed in terms of per 100. Generalizations[edit] These definitions can be extended to the case when v {\displaystyle v} and v approx {\displaystyle v_{\text{approx}}} are n-dimensional vectors, by replacing the absolute value with an n-norm.[1] Examples[edit] As an example, if the exact value is 50 and the approximation is 49.9, then the absolute error is
accuracy is the process of determining the accuracy of forecasts made regarding customer demand for a product. Contents 1 Importance of forecasts 2 Calculating the accuracy of supply chain forecasts 3 Calculating forecast error 4 See also 5 References Importance of forecasts[edit] Understanding and predicting customer demand is vital to manufacturers and distributors to avoid stock-outs and maintain adequate inventory levels. While forecasts are never perfect, they are necessary to prepare for actual demand. In order to maintain an optimized inventory and effective supply chain, accurate demand forecasts are imperative. Calculating the accuracy of supply chain forecasts[edit] Forecast accuracy in the supply chain is typically measured using the Mean Absolute Percent Error or MAPE. Statistically MAPE is defined as the average of percentage errors. Most practitioners, however, define and use the MAPE as the Mean Absolute Deviation divided by Average Sales, which is just a volume weighted MAPE, also referred to as the MAD/Mean ratio. This is the same as dividing the sum of the absolute deviations by the total sales of all products. This calculation ∑ ( | A − F | ) ∑ A {\displaystyle \sum {(|A-F|)} \over \sum {A}} , where A {\displaystyle A} is the actual value and F {\displaystyle F} the forecast, is also known as WAPE, Weighted Absolute Percent Error. Another interesting option is the weighted M A P E = ∑ ( w ⋅ | A − F | ) ∑ ( w ⋅ A ) {\displaystyle MAPE={\frac {\sum (w\cdot |A-F|)}{\sum (w\cdot A)}}} . The advantage of this measure is that could weight errors, so you can define how to weight for your relevant business, ex gross profit or ABC. The only problem is that for seasonal products you will create an undefined result when sales = 0 and that is not symmetrical, that means that you can be much more inaccurate if sales are higher than if they are lower than the forecast. So sMAPE is also used to correct this, it is known as symmetric Mean Absolute Percentage Error. Last but not least, for intermittent demand patterns none of the above are really useful. So you can consider MASE (Mean Absolute Scaled Error) as