The admissible parameter space for exponential smoothing models |
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Authors: | Rob J Hyndman Muhammad Akram Blyth C Archibald |
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Institution: | (1) Department of Econometrics and Business Statistics, Monash University, Clayton, VIC, 3800, Australia;(2) School of Business Administration, Dalhousie University, Halifax, Canada, B3H 1Z5 |
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Abstract: | 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. |
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Keywords: | Exponential smoothing Invertibility Observability Parameter space Reachability Stability State space models Structural models |
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