Prediction intervals for exponential smoothing using two new classes of state space models
Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non-linear structure in the observation equation as well as heteroscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods. We use these classes to provide exact analytic (matrix) expressions for forecast error variances that can be used to construct prediction intervals one or multiple steps ahead. These formulas are reduced to non-matrix expressions for 15 state space models that underlie the most common exponential smoothing methods. We discuss relationships between our expressions and previous suggestions for finding forecast error variances and prediction intervals for exponential smoothing methods. Simpler approximations are developed for the more complex schemes and their validity examined. The paper concludes with a numerical example using a non-linear model. Copyright © 2005 John Wiley & Sons, Ltd.
Volume (Year): 24 (2005)
Issue (Month): 1 ()
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- Koehler, Anne B. & Snyder, Ralph D. & Ord, J. Keith, 2001.
"Forecasting models and prediction intervals for the multiplicative Holt-Winters method,"
International Journal of Forecasting,
Elsevier, vol. 17(2), pages 269-286.
- Koehler, A.B. & Snyder, R.D. & Ord, J.K., 1999. "Forecasting Models and Prediction Intervals for the Multiplicative Holt-Winters Method," Monash Econometrics and Business Statistics Working Papers 1/99, Monash University, Department of Econometrics and Business Statistics.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Yar, Mohammed & Chatfield, Chris, 1990. "Prediction intervals for the Holt-Winters forecasting procedure," International Journal of Forecasting, Elsevier, vol. 6(1), pages 127-137.
- Chatfield, Chris & Yar, Mohammed, 1991. "Prediction intervals for multiplicative Holt-Winters," International Journal of Forecasting, Elsevier, vol. 7(1), pages 31-37, May. Full references (including those not matched with items on IDEAS)