Analysis of AHW and EAHW Time-Series Forecasting Methods: A Mathematical and Computational Perspective
Article Sidebar
Main Article Content
Abstract
Recently, an Extended Additive Holts-Winter method (EAHW) as a modified version of the well-known Additive Holt-Winters method (AHW) has been introduced. Many works in the research literature applied such a method to forecast time-series data, and results indicated that the EAHW provided optimal forecasting accuracy. However, we have found that there is no work in the literature analyzing the AHW and the EAHW in terms of the mathematical operations, which refer to the computation time and complexity of the methods. Since the AHW and EAHW can be implemented on hardware platform for using in many related systems and applications, in this paper, analysis of both methods from a mathematical and computational perspective is presented, where the mathematical operations of the EAHW compared with the AHW is provided. We show that the major difference between the EAHW and the AHW is the calculation of the level of time-series data, while the calculation of the trend and the seasonal factors are the same. With such a difference, the EAHW provided different possible solutions for forecasting. Also, in the worst case scenario, the EAHW has more multiplication operations (i.e., operation ×) than the case of the AHW method (but it is not too high); 2N for the AHW and 3N for the EAHW, where N is the number of data samples. By our finding, the EAHW is one of the appropriate forecasting methods for implementation (i.e., both on computers and embedded hardware platforms), since it provided good accuracy and computational complexity.
Article Details
References
Booranawong, T., & Booranawong, A. (2017). Simple and double exponential smoothing methods with designed input data for forecasting a seasonal time series: in an application for lime prices in Thailand. Suranaree Journal of Science & Technology, 24(3), 301-310.
Booranawong, T., & Booranawong, A. (2018). Double exponential smoothing and Holt-Winters methods with optimal initial values and weighting factors for forecasting lime, Thai chili and lemongrass prices in Thailand. Engineering and Applied Science Research, 45(1), 32-38.
Brown, R. G. (1956). Exponential smoothing for predicting demand. https://www.industrydocuments.ucsf.edu/tobacco/docs/#id=jzlc0130
Gardner, E. S. (1985). Exponential smoothing: the state of the art. Journal of Forecasting, 4(1), 1-28.https://doi.org/10.1002/for.3980040103
Gelper, S., Fried, R., & Croux, C. (2010). Robust forecasting with exponential and Holt-Winters smoothing. Journal of Forecasting, 29(3), 285-300. https://doi.org/10.1002/for.1125
Holt, C. C., (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 20(1), 5-10.
Hunter, J. H. (1986). The exponentially weighted moving average. Journal of Quality Technology, 18(4), 203-210.
Kalekar, P. S. (2004). Time Series Forecasting Using Holt- Winters Exponential Smoothing. Kanwal Rekhi School of Information Technology.
Montgomery, D. C., Jennings, C. L., & Kulahci, M. (2008). Exponential Smoothing Methods. In D. J. Balding, N. A. C. Cressie, G. M. Fitzmaurice, I. M. Johnstone, G. Molenberghs, D.W. Scott, A. F. M. Smith, R. S. Tsay & S. Weisberg (Eds.), Introduction to Time Series Analysis and Forecasting (pp. 171-220). John Wiley and Sons.
Siregar, B., Butar-Butar, I. A., Rahmat, R. F., Andayani, U. & Fahmi, F. (2017). Comparison of exponential smoothing methods in forecasting palm oil real production. Journal of Physics Conference Series, 801(1), 1-9.
Suppalakpanya, K., Nikhom, R., Booranawong, A., & Booranawong, T. (2019). An evaluation of Holt-winters methods with different initial trend values for forecasting crude palm oil production and prices in Thailand. Suranaree Journal of Science & Technology, 26(1), 13-22.
Suppalakpanya, K., Nikhom, R., Booranawong, T., & Booranawong, A. (2019). Forecasting oil palm and crude palm oil data in Thailand using exponential time-series methods. Engineering and Applied Science Research, 46(1), 44-55.
Suppalakpanya, K., Nikhom, R., Booranawong, T., & Booranawong, A. (2019). Study of Several Exponential Smoothing Methods for Forecasting Crude Palm Oil Productions in Thailand. Current Applied Science and Technology, 19(2), 123-139
Tratar, L. F., Mojškerc, B., & Toman, A. (2016). Demand forecasting with four-parameter exponential smoothing. International Journal of Production Economics, 181, 162-173. https://doi.org/10.1016/j.ijpe.2016.08.004
Tratar, L. F. & Srmcnik, E. (2016). The comparison of Holt-Winters method and multiple regression methods: a case study. Energy, 109, 266-276. https://doi.org/10.1016/j.energy.2016.04.115
Tratar, L. F., & Strmčnik, E. (2019, October). Forecasting methods in engineering. IOP Conference Series: Materials Science and Engineering, 657(1), 1-8.
Ventura, L. M. B., de Oliveira Pinto, F., Soares, L. M., Luna, A. S., & Gioda, A. (2019). Forecast of daily PM 2.5 concentrations applying artificial neural networks and Holt–Winters models. Air Quality, Atmosphere & Health, 12(3), 317-325.
Winters, P. (1960). Forecasting sales by exponentially weighted moving averages. Management Science, 6(3), 324-342.
Yakovyna, V., & Bachkai, O. (2018). The Comparison of Holt-Winters and Box-Jenkins Methods for Software Failures Prediction.https://www.semanticscholar.org/paper/The-Comparison-of-Holt-Winters-and-Box-Jenkins-for-YakovynaBachkai/286a0d67bfd8f2b448b964689a84a0822fbbb92e