Smooth Transition Exponential SmoothingJames W TaylorSad

Smooth Transition Exponential Smoothing

James W. Taylor
Saïd Business School
University of Oxford

Journal of Forecasting, 2004, Vol. 23, pp. 385-394.

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James W. Taylor
Saïd Business School
University of Oxford
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Smooth Transition Exponential Smoothing

SMOOTH TRANSITION EXPONENTIAL SMOOTHING
Abstract
Adaptive exponential smoothing methods allow a smoothing parameter to change over time, in order to adapt to changes in the characteristics of the time series. However, these methods have tended to produce unstable forecasts and have performed poorly in empirical studies.
This paper presents a new adaptive method, which enables a smoothing parameter to be modelled as a logistic function of a user-specified variable. The approach is analogous to that used to model the time-varying parameter in smooth transition models. Using simulated data, we show that the new approach has the potential to outperform existing adaptive methods and constant parameter methods when the estimation and evaluation samples both contain a level shift or both contain an outlier. An empirical study, using the monthly time series from the M3Competition, gave encouraging results for the new approach.

Keywords: Adaptive exponential smoothing; Smooth transition; Level shifts; Outliers

INTRODUCTION
Exponential smoothing is a simple and pragmatic approach to forecasting, whereby the forecast is constructed from an exponentially weighted average of past observations. The literature generally recommends that the smoothing parameters should be estimated from the data, usually by minimising the sum of ex post 1-step-ahead forecast errors (Gardner, 1985).
Some researchers have argued that the parameters should be allowed to change over time, in order to adapt to the latest characteristics of the time series. For example, if there has been a level shift in the

References: Adya M, Collopy F, Armstrong JS, Kennedy M. 2001. Automatic identification of time series features for rule-based forecasting Balke NS. 1993. Detecting level shifts in time series. Journal of Business and Economic Statistics 11: 81-92. Bunn DW. 1981. Adaptive forecasting using the Kalman filter. Omega 9: 323-324. Dennis JD. 1978. A performance test of a run-based adaptive exponential smoothing. Ekern S. 1981. Adaptive exponential smoothing revisited. Journal of the Operational Research Society 32: 775-782. Ekern S. 1982. On simulation studies of adaptive forecasts. Omega 10: 91-93. Enns PG, Machak JA, Spivey WA, Wroblesk WJ. 1982. Forecasting applications of an adaptive multiple exponential smoothing model Fildes R. 1979. Quantitative forecasting – the state of the art: extrapolative models. Journal of the Operational Research Society 30: 691-710. Gardner ES Jr. 1985. Exponential smoothing: the state of the art. Journal of Forecasting 4: 128. Gardner ES Jr, Dannenbring DG. 1980. Forecasting with exponential smoothing: Some guidelines for model selection Granger CWJ, Teräsvirta T. 1993. Modelling Nonlinear Economic Relationships, Advanced Texts in Econometrics, Oxford University Press: New York. Harvey AC. 1990. Forecasting, structural time series models and the Kalman filter. Cambridge University Press: New York. Hyndman RJ, Koehler AB, Ord JK, Snyder RD. 2001. Prediction intervals for exponential smoothing state space models Hyndman RJ, Koehler AB, Snyder RD, Grose S. 2002. A state space framework for automatic forecasting using exponential smoothing methods Makridakis S, Hibon M. 2000. The M3-Competition: results, conclusions and implications. Mentzer JT. 1988. Forecasting with adaptive extended exponential smoothing. Journal of the Academy of Marketing Science 16: 62-70. Mentzer JT, Gomes, R. 1994. Further extensions of adaptive extended exponential smoothing and comparison with the M-Competition Pantazopoulos SN, Pappis CP. 1996. A new adaptive method for extrapolative forecasting algorithms Snyder RD. 1988. Progressive Tuning of Simple Exponential Smoothing Forecasts. Journal of the Operational Research Society 39: 393-399. Taylor JW, Bunn DW. 1999. A quantile regression approach to generating prediction intervals. Taylor JW. 2003a. Damped multiplicative trend exponential smoothing. Forthcoming International Journal of Forecasting. Taylor JW. 2003b. Volatility forecasting with smooth transition exponential smoothing. Trigg DW, Leach AG. 1967. Exponential smoothing with an adaptive response rate. Tsay RS. 1988. Outliers, level shifts, and variance changes in time series. Journal of Forecasting 7: 1-20. van Dobben de Bruyn CS. 1964. Prediction by progressive correction. Journal of the Royal Statistical Society Series B 26: 113-122. Whybark DC. 1973. Comparison of adaptive forecasting techniques. Logistics Transportation Review 8: 13-26. Williams TM. 1987. Adaptive Holt-Winters forecasting. Journal of the Operational Research Society 38: 553-560. Willaims DW, Miller D. 1999. Level-adjusted exponential smoothing for modelling planned discontinuities Young PC. 1999. Nonstationary time series analysis and forecasting. Progress in Environmental Science 1: 3-48. Young PC, Pedregal DJ, Tych W. 1999. Dynamic harmonic regression. Journal of Forecasting 18: 369-394. Young PC. 2003. Identification of time varying systems. Forthcoming in Encyclopaedia of Life Support Systems, UNESCO.