The admissible parameter space for exponential smoothing models
We discuss the admissible parameter space for some state space models, including the models that underly exponential smoothing methods. We find that the usual parameter restrictions (requiring all smoothing parameters to lie between 0 and 1) do not always lead to stable models. We also find that all seasonal exponential smoothing methods are unstable as the underlying state space models are neither reachable nor observable. This instability does not affect the forecasts, but does corrupt the state estimates. The problem can be overcome with a simple normalizing procedure. Finally we show that the admissible parameter space of a seasonal exponential smoothing model is much larger than that for a basic structural model, leading to better forecasts from the exponential smoothing model when there is a rapidly changing seasonal pattern.
KeywordsExponential smoothing Invertibility Observability Parameter space Reachability Stability State space models Structural models
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- Archibald B.C. (1984). Invertible region of Holt–Winters’ model, Working paper 31/1984, School of Business Administration. Halifax, Dalhousie UniversityGoogle Scholar
- Archibald B.C. (1991). Invertible region of damped trend, seasonal, exponential smoothing model, Working paper 10/1991, School of Business Administration. Halifax, Dalhousie UniversityGoogle Scholar
- Harvey A.C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge, Cambridge University PressGoogle Scholar
- Makridakis S., Wheelwright S.C., Hyndman R.J. (1998). Forecasting: methods and applications (3rd ed.) New York, WileyGoogle Scholar
- Snyder R.D., Forbes C.S. (2003). Reconstructing the Kalman filter for stationary and non-stationary time series. Studies in nonlinear dynamics and econometrics 7(2): 1–18Google Scholar