1. MMC
  2. All Volumes and Issues
  3. Volume 9, Number 1, 2022
  4. Exponential smoothing constant determination to minimize the forecast error

Exponential smoothing constant determination to minimize the forecast error

MMC.
2022;
Volume 9, Number 1
: pp. 50–56
https://doi.org/10.23939/mmc2022.01.050
Received: July 07, 2021
Accepted: November 16, 2021

Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 50–56 (2022)

Authors:
  1. N. A. M. Noor
  2. N. H. A. Rahman
1
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia
2
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia

One of the fundamental issues in exponential smoothing is to determine the smoothing constants.  Researchers usually use the determination available in the statistical software.  However, the result may not able to minimize the forecast error.  For this study, the optimal values of smoothing constant are based on minimizing the forecast errors, mean absolute percentage error (MAPE) and root mean squared error (RMSE).  The double exponential smoothing method or Holt's method is chosen where two constant values must identify specifically the level and trend estimate, respectively.  The real data set of tourism emphasize the number of international tourists visit Malacca from year 2003 to 2016 has been studied.  The result shows that the values of level and trend obtained from this analysis is small and close to zero.  This indicates that the level and trend react slowly towards the data.  In addition, simulation also have been computed using the random walk model.  The result suggested, by using optimal result available by statistical software is not recommended since the obtained smoothing constants do not minimize the forecast error.

smoothing constant
forecasting
trend
level
error minimizing
  1. Musii R. S., Nakonechnyy A. Y.  Mathematical model for temperature estimation forecasting of electrically conductive plate elements under action of pulsed electromagnetic radiation of radio-frequency range.  Mathematical Modeling and Computing. 8 (1), 35–42 (2021).
  2. Gardner Jr. E. S.  Exponential smoothing: The state of the art-part II.  International Journal of Forecasting.  22 (4), 637–666 (2006).
  3. Brown R. G.  Statistical forecasting for inventory control.  McGraw/Hill (1959).
  4. Brown R. G.  Smoothing, forecasting and prediction of discrete time series.  Courier Corporation (2004).
  5. Hyndman R., Koehler A. B., Ord J K., Snyder R. D.  Forecasting with exponential smoothing.  Springer Science & Business Media (2008).
  6. Meira E., Oliveira F. L. C., Jeon J.  Treating and Pruning: New approaches to forecasting model selection and combination using prediction intervals.  International Journal of Forecasting. 37 (2), 547–568 (2021).
  7. Krajewski L., Ritzman L., Malhotra M.  Operations management: processes and value chains.  Pearsons Education (2007).
  8. Karmaker C.  Determination of optimum smoothing constant of single exponential smoothing method: A case study.  International Journal of Research in Industrial Engineering.  6 (3), 184–192 (2017).
  9. Paul S. K.  Determination of exponential smoothing constant to minimize mean square error and mean absolute deviation.  Global Journal of Research In Engineering. 11 (3), (2011).
  10. Ravinder H. V.  Forecasting with exponential smoothing whats the right smoothing constant?  Review of Business Information Systems.  17 (3), 117–126 (2013).
  11. Mu'azu H.  New approach for determining the smoothing constant $\alpha$ of a single exponential smoothing method.  International Journal of Science and Technology.  3 (11), 717–727 (2014).
  12. Hyndman R. J., Khandakar Y.  Automatic Time Series Forecasting: The forecast Package for R.  Journal of Statistical Software.  27 (3), 1–22 (2008).
  13. Hyndman R. J., Koehler A. B.  Another look at measures of forecast accuracy.  International Journal of Forecasting.  22 (4), 679–688 (2006).
  14. De Myttenaere A., Golden B., Le Grand B., Rossi F.  Mean absolute percentage error for regression models.  Neurocomputing.  192, 38–48 (2016).