Box-Cox Transformation for Exponential Smoothing With Application

Authors

  • Alla Ahmed Ali Department of Statistics, University of Duhok, Kurdistan Region, Iraq
  • Haithem Taha Mohammed Ali Department of Economic Sciences, University of Zakho, Kurdistan Region, Iraq, and Department of Economics, Nawroz University, Kurdistan Region, Iraq

DOI:

https://doi.org/10.25007/ajnu.v12n4a1717

Abstract

This article introduces a novel algorithm for incorporating power transformation into the estimation process of a Holt-Winters Seasonal model. The algorithm outlines a series of steps aimed at selecting the most appropriate power parameter estimate. This selection is achieved using the conventional Maximum Likelihood Estimation method in combination with various criteria for enhancing statistical modeling efficiency. Supplementary decision rules include assessing Mean Square Error, Mean Absolute Error, and conducting a p-value test for the normality of errors. The algorithm's effectiveness is demonstrated through its application to real-world data. Ultimately, the article affirms the feasibility of obtaining viable solutions for selecting the optimal power parameter.

Downloads

Download data is not yet available.

References

Lima, Susana, A. Manuela Gonçalves, and Marco Costa. "Time series forecasting using Holt-Winters exponential smoothing: An application to economic data." AIP Conference Proceedings. Vol. 2186. No. 1. AIP Publishing LLC, 2019.‏

P. Goodwin, “The holt-winters approach to exponential smoothing: 50 years old and going strong,” Foresight 19.19, pp. 30–33, 2010.

M. S. Bartlett, “The use of transformations,” Biometrics, vol. 3.1, pp. 39–52, 1947, doi: 10.1177/002224376600300304.

J. W. Tukey, “On the comparative anatomy of transformations,” Ann. Math. Stat., vol. 28, no. 3, pp. 602–632, 1957.

Box, George EP, and Paul W. Tidwell. "Transformation of the independent variables." Technometrics 4.4 (1962): 531-550.‏

Box, George EP, and David R. Cox. "An analysis of transformations." Journal of the Royal Statistical Society: Series B (Methodological) 26.2 (1964): 211-243.‏

Draper, Norman R., and David R. Cox. "On distributions and their transformation to normality." Journal of the Royal Statistical Society: Series B (Methodological) 31.3 (1969): 472-476.‏

D. J. Poirier, “The use of the Box-Cox transformation in limited dependent variable models.,” J. Am. Stat. Assoc., vol. 73, no. 362, pp. 284–287, 1978, doi: 10.1080/01621459.1978.10481570.

R. J. Carroll, “A robust method for testing transformations to achieve approximate normality,” J. R. Stat. Soc. Ser. B, vol. 42, no. 1, pp. 71–78, 1980, doi: 10.1111/j.2517-6161.1980.tb01102.x.

Yeo, In‐Kwon, and Richard A. Johnson. "A new family of power transformations to improve normality or symmetry." Biometrika 87.4 (2000): 954-959.‏

A. N. Beaumont, “Data transforms with exponential smoothing methods of forecasting.,” Int. J. Forecast., vol. 30, no. 4, pp. 918–927, 2014, doi: 10.1016/j.ijforecast.2014.03.013.

Bergmeir, Christoph, Rob J. Hyndman, and José M. Benítez. "Bagging exponential smoothing methods using STL decomposition and Box–Cox transformation." International journal of forecasting 32.2 (2016): 303-312.‏ [13] M. K. Voulgaraki, “Box Cox transformation in forecasting sales . Evidence of the Greek Market .,” no. June, pp. 1–20, 2019.

E. Aytaç, “Forecasting Turkey’s Hazelnut Export Quantities with Facebook’s Prophet Algorithm and Box-Cox Transformation,” ADCAIJ Adv. Distrib. Comput. Artif. Intell. J. 10.1, pp. 33–47, 2021.

T. B. Fomby, “Exponential smoothing models,” Econ. 1, pp. 1-23., 2008.

Washington, Simon, et al. Statistical and econometric methods for transportation data analysis. Chapman and Hall/CRC, 2020.‏

Hyndman, Rob, et al. forecasting with exponential smoothing: the state space approach. Springer Science & Business Media, 2008.‏

Yaffee, Robert A., and Monnie McGee. An introduction to time series analysis and forecasting: with applications of SAS® and SPSS®. Elsevier, 2000.‏

Shastri, Sourabh, et al. "A study on exponential smoothing method for forecasting." International Journal of Computer Sciences and Engineering 6.4 (2018): 482-485.‏

C. C. Pegels, “Exponential forecasting: Some new variations,” Manage. Sci., vol. 15, no. 5, pp. 311–315, 1969.

R. J. Hyndman, A. B. Koehler, R. D. Snyder, and S. Grose, “A state space framework for automatic forecasting using exponential smoothing methods,” 2002. [Online]. Available: www.elsevier.com/locate/ijforecast

E. S. Gardner, “Exponential Smoothing: The State of the Art,” 1985.

Taylor, James W., and Ralph D. Snyder. "Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing." Omega 40.6 (2012): 748-757.‏

Setiawan, Wawan, Enjun Juniati, and Ida Farida. "The use of Triple Exponential Smoothing Method (Winter) in forecasting passenger of PT Kereta Api Indonesia with optimization alpha, beta, and gamma parameters." 2016 2nd International Conference on Science in Information Technology (ICSITech). IEEE, 2016.‏

Nurhamidah, Nurhamidah, Nusyirwan Nusyirwan, and Ahmad Faisol. "Forecasting seasonal time series data using the holt-winters exponential smoothing method of additive models." Jurnal Matematika Integratif 16.2 (2020): 151-157.‏.

J. Mi, L. Fan, X. Duan, and Y. Qiu, “Short-Term Power Load Forecasting Method Based on Improved Exponential Smoothing Grey Model,” Math. Probl. Eng., vol. 2018, 2018, doi: 10.1155/2018/3894723.

R. M. Sakia, “The Box‐Cox transformation technique: a review,” 1992.

Downloads

Published

2023-10-14

How to Cite

Ahmed Ali, A., & Taha Mohammed Ali, H. (2023). Box-Cox Transformation for Exponential Smoothing With Application. Academic Journal of Nawroz University, 12(4), 311–316. https://doi.org/10.25007/ajnu.v12n4a1717

Issue

Vol. 12 No. 4 (2023)

Section

Articles

License

Copyright (c) 2023 Academic Journal of Nawroz University

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright

The use of a Creative Commons License enables authors/editors to retain copyright to their work. Publications can be reused and redistributed as long as the original author is correctly attributed.

 

  1. Copyright

 

  1. The researcher(s), whether a single or joint research paper, must sell and transfer to the publisher (the Academic Journal of Nawroz University) through all the duration of the publication which starts from the date of entering this Agreement into force, the exclusive rights of the research paper/article. These rights include the translation, reuse of papers/articles, transmit or distribute, or use the material or parts(s) contained therein to be published in scientific, academic, technical, professional journals or any other periodicals including any other works derived from them, all over the world, in English and Arabic, whether in print or in electronic edition of such journals and periodicals in all types of media or formats now or that may exist in the future. Rights also include giving license (or granting permission) to a third party to use the materials and any other works derived from them and publish them in such journals and periodicals all over the world. Transfer right under this Agreement includes the right to modify such materials to be used with computer systems and software, or to reproduce or publish it in e-formats and also to incorporate them into retrieval systems.

 

  1. Reproduction, reference, transmission, distribution or any other use of the content, or any parts of the subjects included in that content in any manner permitted by this Agreement, must be accompanied by mentioning the source which is (the Academic Journal of Nawroz University) and the publisher in addition to the title of the article, the name of the author (or co-authors), journal’s name, volume or issue, publisher's copyright, and publication year.

 

  1. The Academic Journal of Nawroz University reserves all rights to publish research papers/articles issued under a “Creative Commons License (CC BY-NC-ND 4.0) which permits unrestricted use, distribution, and reproduction of the paper/article by any means, provided that the original work is correctly cited.

 

  1. Reservation of Rights

The researcher(s) preserves all intellectual property rights (except for the one transferred to the publisher under this Agreement).

  1. Researcher’s guarantee

The researcher(s) hereby guarantees that the content of the paper/article is original. It has been submitted only to the Academic Journal of Nawroz University and has not been previously published by any other party.

In the event that the paper/article is written jointly with other researchers, the researcher guarantees that he/she has informed the other co-authors about the terms of this agreement, as well as obtaining their signature or written permission to sign on their behalf.

The author further guarantees:

  • The research paper/article does not contain any defamatory statements or illegal comments.
  • The research paper/article does not violate other's rights (including but not limited to copyright, patent, and trademark rights).

This research paper/article does not contain any facts or instructions that could cause damages or harm to others, and publishing it does not lead to disclosure of any confidential information.