Developing two 4-parameter and 5-parameter exponential smoothing methods with multiplicative trend for demand forecasting

Journal of Industrial Engineering International

دوره 17، شماره 3، آبان 2021، صفحه 79-90   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/jiei.2021.1922678.1096

نویسندگان

Sobhan Davarpanah¹؛ Reza Yousefi Zenouz^{* 1}؛ Amir-Reza Abtahi²

¹Operations Management and Information Technology, Kharazmi University

²Department of Operations Management and Information Technology, Kharazmi University, Tehran, Iran

چکیده

Exponential smoothing methods, especially Holt-Winters family, have been extensively utilized to demand time series forecasting. Previous studies show that Extended Holt Winters methods, by adding a smoothing constant to the level equation of Holt Winters methods, can improve the forecasting performance significantly. The improvements gained by the Extended Holt Winters method with additive trend motivated this research to extend this idea to the Holt Winters method with multiplicative trends too.
In this paper, adding a smoothing constant to the Holt-Winters with multiplicative trend and also Holt-Winters with damped multiplicative trend was investigated, and the performance of these methods was compared with the classical methods. Quarterly and monthly time series of M3-Competition with the minimum length of ten years were used to measure the performance of proposed methods.
The results showed that EHW and XHW proposed in this paper, significantly outperformed the classical Holt Winters multiplicative trend methods and can be considered by forecasters due to their better smoothing and forecasting performances.

کلیدواژه‌ها

Holt-Winters methods؛ Damped trend methods؛ Multiplicative Trend؛ M3-Competition؛ Symmetric relative efficiency measure

مراجع

- Brown, R. G. (1959). Statistical forecasting for inventory control. McGraw/Hill.

- Fildes, R. A. (2001). Beyond forecasting competitions. International Journal of Forecasting,
17(4), 556-560.

- Fildes, R., Nikolopoulos, K., Crone, S. F., & Syntetos, A. A. (2008). Forecasting and operational
research: a review. Journal of the Operational Research Society, 59(9), 1150-1172.

- Gardner Jr, E. S., & McKenzie, E. D. (1985). Forecasting trends in time series. Management
Science, 31(10), 1237-1246.

- Holt, C. C. (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International journal of forecasting, 20(1), 5-10.- Makridakis, S., Wheelwright, S., & Hyndman, R. J. (1997).. (3rd, Ed.) John Wiley & Sons.

-  Monfared, M. A. S., Ghandali, R., & Esmaeili, M. (2014). A new adaptive exponential smoothing
method for non-stationary time series with level shifts. Journal of industrial engineering
international, 10(4), 209-216.

- Omidi, M. R., Jafari Eskandari, M., Raissi, S., & Shojaei, A. A. (2019). Application of a statistical
model to forecast drowning deaths in Iran. Health in Emergencies and Disasters, 4(4), 201-208.
- Pegels, C. C. (1969). Exponential forecasting: some new variations. Management Science, 311-315.
- Petropoulos, F., Makridakis, S., Assimakopoulos, V., & Nikolopoulos, K. (2014). Horses for Courses’ in demand forecasting. European Journal of Operational Research, 237(1), 152-163.
- Rasmussen, R. (2004). On time series data and optimal parameters. Omega, 32(2), 111-120.
- Ravinder, H. V. (2016). Determining The Optimal Values Of Exponential Smoothing Constants–Does Solver Really Work? . American Journal of Business Education (AJBE), 9(1), 1-14.
- Roehrich, J. (2008). Supply chain management: Strategy, planning & operations, by Chopra, S. and Meindl, P. Journal of Purchasing & Supply Management, 14(4), 273-274.
- Taylor, J. W. (2003). Exponential smoothing with a damped multiplicative trend. International journal of Forecasting, 19(4), 715-725.
- Tratar, L. F., Mojškerc, B., & Toman, A. (2016). Demand forecasting with four-parameter exponential smoothing. International Journal of Production Economics, 181, 162-173.
- Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages. Management science, 6(3), 324-342.