Some Nonlinear Exponential Smoothing Models are Unstable

Rob Hyndman () and Muhammad Akram ()

No 3/06, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: This paper discusses the instability of eleven nonlinear state space models that underly exponential smoothing. Hyndman et al. (2002) proposed a framework of 24 state space models for exponential smoothing, including the well-known simple exponential smoothing, Holt's linear and Holt-Winters' additive and multiplicative methods. This was extended to 30 models with Taylor's (2003) damped multiplicative methods. We show that eleven of these 30 models are unstable, having infinite forecast variances. The eleven models are those with additive errors and either multiplicative trend or multiplicative seasonality, as well as the models with multiplicative errors, multiplicative trend and additive seasonality. The multiplicative Holt-Winters' model with additive errors is among the eleven unstable models. We conclude that: (1) a model with a multiplicative trend or a multiplicative seasonal component should also have a multiplicative error; and (2) a multiplicative trend should not be mixed with additive seasonality.

Keywords: Exponential smoothing; forecast variance; nonlinear models; prediction intervals; stability; state space models. (search for similar items in EconPapers)
JEL-codes: C53 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
Date: 2006-01
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