Smape vs mape

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Many accuracy measures have been proposed in the past for time series forecasting comparisons.

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However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error.

Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error UMBRAEwhich combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria.

Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred.

Forecasting has always been an attractive research area since it plays an important role in daily life. As one of the most popular research domains, time series forecasting has received particular concern from researchers [ 1 — 5 ].

Many comparative studies have been conducted with the aim of identifying the most accurate methods for time series forecasting [ 6 ]. However, research findings indicate that the performance of forecasting methods varies according to the accuracy measure being used [ 7 ].

Errors on percentage errors

Various accuracy measures have been proposed as the best to use in the past decades. However, many of these measures are not generally applicable due to issues such as being infinite or undefined under certain circumstances, which may produce misleading results. The criteria required for accuracy measures have been explicitly addressed by Armstrong and Collopy [ 6 ] and further discussed by Fildes [ 8 ] and Clements and Hendry [ 9 ].

As discussed, a good accuracy measure should provide an informative and clear summary of the error distribution. The criteria should also include reliability, construct validity, computational complexity, outlier protection, scale-independency, sensitivity to changes and interpretability.

It has been suggested by many researchers that no single measure can be superior to all others in these criteria [ 61011 ]. The evolution of accuracy measures can be seen through the measures used in the major comparative studies of forecasting methods. They were the primary measures used in the original M-Competition [ 12 ]. Despite well-known issues such as their high sensitivity to outliers, they are still being widely used [ 13 — 15 ].

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When using these accuracy measures, errors which are small and appear to be good, such as 0. Wei et al. The average error obtained was 84 and it was claimed to be superior to some other previous models. However, without comparison, the error 84 as a number is not easy to interpret. In fact, the average fluctuation of stock indices used was 83 which is smaller than the error of their proposed model. A similar case can be found regarding MAPE.

Forecasting Methods made simple - Exponential Smoothing

Esfahanipour and Aghamiri [ 17 ] proposed a model with an error of 1. Yet, this error was larger than the average daily fluctuation of the stock price, which was approximately 1. The poor interpretation here is mainly due to the lack of comparable benchmark used by the accuracy measure. Armstrong and Collopy [ 6 ] recommended the use of relative absolute errors as a potential solution to the above issue. Accuracy measures based on relative errors, such as Mean Relative Absolute Error MRAEcan provide a better interpretation of how good the evaluated forecasting method perform compared to the benchmark method.

However, when the benchmark error is small or equal to zero, the relative error could become extremely large or infinite. This may lead to an undefined mean or at least a distortion of the result. However, this process will also add some complexity to the calculation and an appropriate trimming level has to be specified [ 18 ]. Similarly, MAPE also has the issue of being infinite or undefined due to zeros in the denominator [ 19 ].Nicolas Vandeput.

Data Science for Supply Chain Forecast. Note that the error is the forecast minus the demand. So a negative bias means that you undershoot the demand. Obviously, just with the bias as an indicator of your forecast quality you will never be able to asses its precision. But a highly biased forecast is already an indication that something is wrong in the forecast model. It is quite well known among business managers but actually is a really poor indicator as it is really skewed.

As you see in the formula, the MAPE divides each separate error by the demand one by one. So big errors during low demand periods will have a major impact on the MAPE. Due to this, optimizing the MAPE will result in a strange forecast that will most likely undershoot the demand. The only good point about MAPE is that it is easy to interpret.

As is, the MAE has one issue: it is not scaled. Is a MAE of 10 good or bad? But if you know that the average demand isthen a MAE of 10 seems good. I find this much more useful as you can compare different items. Median : the value for which half of the demand is higher and half of the demand is lower. Well, even though it might sound like a reasonable thing to do, this is actually not straightforward as you will always get a biased forecast if the demand mean differs from the median.

If you divide the RMSE by the average demand, you get a percentage indicator which is scaled to the average demand. In most situation this is optimal. There is also another issue: the sensitivity to outliers. We discussed above the fact that optimizing MAE results in a forecast of the demand median whereas an optimization of the RMSE will result in a forecast of the mean. If you forecast the median you will most likely suffer from bias as the median is not the demand mean.

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But if you forecast the demand mean you might be too sensitive to outliers. The median is 8. We already observe that if we forecast the median 8.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

smape vs mape

Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. Both are functions of errors between predicted and true value. I am just wondering if there are certain cases where one should be preferred above another?

And this actually makes a lot of sense. This is often what we want. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 2 years, 5 months ago. Active 2 years, 1 month ago. Viewed 9k times. Stephan Kolassa PagMax PagMax 1 1 silver badge 6 6 bronze badges. Active Oldest Votes. Stephan Kolassa Stephan Kolassa Sign up or log in Sign up using Google. Sign up using Facebook.

smape vs mape

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The new moderator agreement is now live for moderators to accept across the…. Linked Hot Network Questions. Question feed. Cross Validated works best with JavaScript enabled.Forecast accuracy measurement is important for a number of reasons including the investigation of existing or potential problems in the supply chain and ensuring that the forecasting system is under control. It is also an important component in safety stock calculation. Measuring accuracy starts with some measure of forecast error.

In the past it was often Mean Absolute Percentage Error MAPE that was regarded as the best practice measurement, but it does come with certain limitations - a number of better options are now available. Forecast Solutions can carry out a forecast accuracy health check. It comprises a review of methods and procedures together with an analysis of the levels of forecasting accuracy that are being achieved in the current sales forecasting system.

Forecasts can be checked for bias. In a full forecast accuracy analysis, a forecast simulation can be set up using powerful sales forecasting software in order to compare the forecast accuracy thus achieved with that from the existing process.

The health check can be an important component in the early stages of a sales forecasting improvement program with the objective to improve forecast accuracy. The first step in an improvement program may well be to carry out the accuracy health check as mentioned above. A full understanding of the current state will be gained, then documented and shared with all parties. Improvements should then be identified, fully discussed and agreed.

If there is a need for new software there will need to be the major stage of evaluating alternatives and making the best possible selection. Where possible any improvements should be tested prior to implementation.

Mean absolute percentage error

The revised process should be subject to regular monitoring with modification if necessary. MAE mean absolute error or MAD mean absolute deviation - the average of the absolute errors across products or time periods. So should we report forecast error or forecast accuracy? Some companies feel it is better to dwell on a positive note and report accuracy rather than error. Mean Absolute Percent Error is widely used as a method of summarising forecast error across a number of time periods or products.

Firstly each individual percent error is calculated as a percentage of Actual Sales or as a percentage of Forecast Sales.

So the 'base' the denominator in the calculation is either Actual Sales or Forecast Sales. MAPE is the average of the absolute percent errors. Then, if a measure of accuracy is preferred over a measure of error, this is calculated as - MAPE. A major difficulty that arises with MAPE is that if there is any instance where the base in any individual percent error calculation is zero, the result cannot be calculated. This is often referred to as the divide by zero problem. Various work-arounds have been used to deal with this issue, but none of them are mathematically correct.

Perhaps the biggest problem arises when MAPE is used to assess the historical errors associated with different forecasting models with a view to selecting the best model. Thus MAPE is totally unsuitable for assessing in this way any item with an intermittent demand pattern. If MAPE is being used to summarise accuracy across a number of products there is the additional disadvantage that it does not give any greater weighting to fast-moving as compared to slow-moving products. Because slow-moving products tend to exhibit high percentage errors, MAPE may tend to overstate the average error across a product family or total business.

Weighted Mean Absolute Percentage Error, as the name suggests, is a measure that gives greater importance to faster selling products.

Thus it overcomes one of the potential drawbacks of MAPE. This involves adding together the absolute errors at the detailed level, then calculating the total of the errors as a percentage of total sales. This method of calculation leads to the additional benefit that it is robust to individual instances when the base is zero, thus overcoming the divide by zero problem that often occurs with MAPE.

smape vs mape

Instead of using a base in the percentage error calculation which is either Actual Sales or Forecast Sales, it uses the average of Actual Sales and Forecast Sales. It is a rather strange measure to explain to colleagues, therefore does not often appear in company forecast accuracy reports, but it sometimes plays a part within certain software packages in the selection of a recommended forecasting model. The scaled error is calculated as the ratio of the error to the Mean Absolute Error from a 'simple forecasting technique'.Businesses often use forecast to project what they are going to sell.

This allows them to prepare themselves for the future sales in terms of raw material, labor, and other requirements they might have. When done right, this allows a business to keep the customer happy while keeping the costs in check. One of the key questions in the forecasting process has to do with the measuring of the forecast accuracy.

There is a very long list of metrics that different businesses use to measure this forecast accuracy. The formula for APE is:. The M stands for mean or average and is simply the average of the calculated APE numbers across different periods. It is derived by dividing the APE by the number of periods considered. Since MAPE is a measure of error, high numbers are bad and low numbers are good. For reporting purposes, some companies will translate this to accuracy numbers by subtracting the MAPE from You can think of that as the mean absolute percent accuracy MAPA; however this is not an industry recognized acronym.

I hope this is useful info on the MAPE as a forecast accuracy metric. I am interested in your thoughts and comments. Like this blog? Follow us on LinkedIn or Twitterand we will send you notifications on all future blogs. Because of its limitations, one should use it in conjunction with other metrics.

While a point value of the metric is good, the focus should be on the trend line to ensure that the metric is improving over time.

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Its popularity probably feeds back into this. It does not depend on scale and can apply easily to both high and low volume products. However, there are reasons why this error measure has its detractors: If MAPE is calculated at a high level think product family, or business level or across different periods the pluses and minuses cancel each other out to often paint a very rosy picture.

This example is obvious in the first table. MAPE does not provide a good way to differentiate the important from not so important. MAPE is asymmetric and reports higher errors if the forecast is more than the actual and lower errors when the forecast is less than the actual.What does MAPE tell you?

Furthermore, when the Actual value is not zero, but quite small, the MAPE will often take on extreme values.

Symmetric mean absolute percentage error

See Full Answer. What does MAPE stand for? Error analysis is a method used to document the errors that appear in learner language, determine whether those errors are systematic, and if possible explain what caused them.

The Interlingual errors are those that result from language transfer and are caused by the learner's native language, say LI whereas the Intralingual errors are those which result from faulty or partial learning of L2, rather than from language transfer RichardsGass and Selinker,Brown, Overregularization is a part of the language-learning process in which children extend regular grammatical patterns to irregular words, such as the use of "goed " for "went", or "tooths" for "teeth".

This is also known as regularization. What is a forecast bias? A forecast bias occurs when there are consistent differences between actual outcomes and previously generated forecasts of those quantities; that is: forecasts may have a general tendency to be too high or too low. A normal property of a good forecast is that it is not biased. In statistics, the bias or bias function of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

An estimator or decision rule with zero bias is called unbiased. Related Terms. A planning tool that helps management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends. Forecasting starts with certain assumptions based on the management's experience, knowledge, and judgment. Forecasting can be classified into four basic types: qualitative, time series analysis, causal relationships, and simulation.

Qualitative techniques in forecasting can include grass roots forecasting, market research, panel consensus, historical analogy, and the Delphi method. What is positive bias in forecasting? A quick word on improving the forecast accuracy in the presence of bias.

If the forecast is greater than actual demand than the bias is positive indicates over- forecast. The inverse, of course, results in a negative bias indicates under- forecast. Type - Safe is code that accesses only the memory locations it is authorized to access, and only in well-defined, allowable ways. Type - safe code cannot perform an operation on an object that is invalid for that object.

Python is a dynamically- typed language. Java is a statically- typed language. In a weakly typed language, variables can be implicitly coerced to unrelated types, whereas in a strongly typed language they cannot, and an explicit conversion is required.

Both Java and Python are strongly typed languages. Weakly typed is the opposite: Perl can use a string like "" in a numeric context, by automatically converting it into the int A strongly typed language like python will not do this.The mean absolute percentage error MAPEalso known as mean absolute percentage deviation MAPDis a measure of prediction accuracy of a forecasting method in statisticsfor example in trend estimationalso used as a loss function for regression problems in machine learning.

It usually expresses the accuracy as a ratio defined by the formula:. The MAPE is also sometimes reported as a percentage, which is the above equation multiplied by The difference between A t and F t is divided by the actual value A t again.

Mean absolute percentage error is commonly used as a loss function for regression problems and in model evaluation, because of its very intuitive interpretation in terms of relative error. From a practical point of view, the use of the MAPE as a quality function for regression model is equivalent to doing weighted mean absolute error MAE regression, also known as quantile regression.

This property is trivial since. As a consequence, the use of the MAPE is very easy in practice, for example using existing libraries for quantile regression allowing weights.

The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical one, since the existence of an optimal model and the consistency of the empirical risk minimization can be proved. Problems can occur when calculating the MAPE value with a series of small denominators.

This alternative is still being used for measuring the performance of models that forecast spot electricity prices.

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Note that this is equivalent to dividing the sum of absolute differences by the sum of actual values, and is sometimes referred to as WAPE weighted absolute percentage error. Although the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application, [3] and there are many studies on shortcomings and misleading results from MAPE. From Wikipedia, the free encyclopedia. Measure of prediction accuracy of a forecast. This article needs additional citations for verification.

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