# Error Measures in Forecasting

In forecasting, error measures play important roles because of their potential in helping to identify the forecasting method that would be the most appropriate in a given context. Each error measure can have certain limitations and thus lead to the inaccurate evaluation of forecasting results, which contributes to the increased complexity of choosing appropriate error measurements. Moving averages represent the tools used by active traders for measuring momentum, with the critical difference between the exponential moving average (EMA), the weighted moving average (WMA), and the simple moving average (SMA) lying in the formula used for their creation (Anderson et al., 2016). SMA was popular before the invention of computers because of the ease of its calculation.

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A moving average was calculated using the average of indicators (e.g., closing prices) for a specific time period. WMA is more complex than SMA because it assigns a heavier weighting to the more recent data points because they are more relevant. The sum of the weighting is expected to add up to 100%. EMA also focuses on more recent data points; however, the rate of decrease between one point and its preceding point is inconsistent.

The low value of error measures can be useful for showing that the corresponding forecasting method is considered reliable. The lower is the measure of error, the better is the forecasting method. Measurement error refers to the difference between the true value and a measured quantity, and includes both random and systematic errors. According to the findings of Mukhlashin and Nugraha (2018), in comparing the measures of forecast errors between average models, it is imperative to choose good values that yield low errors, which would make sense in intense decision-making environments.

This means that the method that has the least measurement of errors is seen as the most suitable for the purpose of forecasting and subsequent decision-making. For example, mean squared error (MSE) or mean squared deviation (MSD) is useful for evaluating a forecasting method. The error is “squared from the summed and divided with the number of observations” (Mukhlashin and Nugraha 2018, p. 1746). This method yields significant forecasting errors because they are squared. It is useful for optimizing the averages because it is a risk function that corresponds to the expected value of the squared error loss.

The fact that mean squared error is in most cases, strictly positive is due to randomness of because the estimator does not always considers the information that could facilitate a more accurate estimate. The mean absolute percentage error (MAPE) indicates the average absolute error of forecasting data as compared and contrasted with the actual data.

## Summary

Articles that would help to gain a better understanding of error measures and their influence on moving averages are greatly limited. The significant gap in research calls for more considerable attention to the topic among scholars exploring issues related to forecasting and quantitative methods. The research article by Mukhlashin and Nugraha (2018) focused on exploring the forecasting rate of return as applicable to Brown’s weighted exponential moving average. While the subject matter of the study was concerned with the Turkish context, the findings can be applied to multiple industries globally. However, it is imperative to note that even in this research, there is a lack of attention given to studying the usefulness of error measures, which supports the need for further studies on the topic.

## References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. L., Fry, M. J., & Ohlmann, J. W. (2016). Quantitative methods for business with CengageNOW (13th ed.). Boston, MA: Cengage Learning.

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Mukhlashin, P., & Nugraha, J. (2018). Brown’s weighted exponential moving average (BWEMA) with Levenberg-Marquardt optimization to forecasting rate of return. The Turkish Online Journal of Design, Art and Communication, 2018, 1744-1749.

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