Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization
Abstract
Exponential smoothing methods have been commonly used for time series forecasting. Holt’s linear trend exponential smoothing is a well-known exponential smoothing method and it can give successful forecasting results for time series which have trend component. In this study, a new modified Holt method is introduced. In modified Holt method, update formulas have second order lagged terms apart from classical Holt method. Moreover, initial values for trend and level and smoothing parameters are estimated by using particle swarm optimization. Strong and weak sides of the modified Holt method are investigated by using real-world data sets and simulated data sets.
Keywords
References
- Holt, C.C. (1957). Forecasting seasonal and trends by exponentially weighted moving averages, Office of Naval Research, Research Memorandum, No: 52.
- Brown, R.G. (1959). Statistical forecasting for inventory control, New-York, McGraw-Hill.
- Winters, P.R. (1960). Forecasting sales by exponentially weighted moving averages, Management Science, 6, pp. 324-242.
- Brown, R.G. (1963). Smoothing, forecasting, prediction, Engle-wood Cliffs, N.J.: Prentice-Hall.
- Pegel, C.C. (1969). Exponential forecasting: some new variations, Management Science, 12 (5), pp. 311-315.
- Box, G. E. P., Jenkins, G. M. (1970). Time series analysis: Forecasting and control, San Francisco Holden Day (revised. 1976).
- Roberts, S.A. (1982). A general class of Holt–Winters type forecasting models, Management Science, 28, pp. 808–820.
- Abraham, B., Ledolter, J. (1983). Statistical methods for forecasting, New York, John Wiley and Sons.
Details
Primary Language
English
Subjects
Computational Statistics
Journal Section
Research Article
Publication Date
September 30, 2025
Submission Date
September 27, 2025
Acceptance Date
September 28, 2025
Published in Issue
Year 2025 Volume: 9 Number: 2
APA
Aksakal, S. Ş., & Eğrioğlu, E. (2025). Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization. Turkish Journal of Forecasting, 9(2), 44-50. https://doi.org/10.34110/forecasting.1792276
AMA
1.Aksakal SŞ, Eğrioğlu E. Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization. TJF. 2025;9(2):44-50. doi:10.34110/forecasting.1792276
Chicago
Aksakal, Saime Şule, and Erol Eğrioğlu. 2025. “Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization”. Turkish Journal of Forecasting 9 (2): 44-50. https://doi.org/10.34110/forecasting.1792276.
EndNote
Aksakal SŞ, Eğrioğlu E (September 1, 2025) Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization. Turkish Journal of Forecasting 9 2 44–50.
IEEE
[1]S. Ş. Aksakal and E. Eğrioğlu, “Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization”, TJF, vol. 9, no. 2, pp. 44–50, Sept. 2025, doi: 10.34110/forecasting.1792276.
ISNAD
Aksakal, Saime Şule - Eğrioğlu, Erol. “Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization”. Turkish Journal of Forecasting 9/2 (September 1, 2025): 44-50. https://doi.org/10.34110/forecasting.1792276.
JAMA
1.Aksakal SŞ, Eğrioğlu E. Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization. TJF. 2025;9:44–50.
MLA
Aksakal, Saime Şule, and Erol Eğrioğlu. “Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization”. Turkish Journal of Forecasting, vol. 9, no. 2, Sept. 2025, pp. 44-50, doi:10.34110/forecasting.1792276.
Vancouver
1.Saime Şule Aksakal, Erol Eğrioğlu. Modified Holt’s Linear Trend Method Based on Particle Swarm Optimization. TJF. 2025 Sep. 1;9(2):44-50. doi:10.34110/forecasting.1792276