Random Switching Exponential Smoothing and Inventory Forecasting

Abstract

Exponential smoothing models are an important prediction tool in macroeconomics, finance and business. This paper presents the analytical forecasting properties of the random coefficient exponential smoothing model in the multiple source of error framework. The random coefficient state-space representation allows for switching between simple exponential smoothing and the local linear trend. Therefore it is possible to control, in a flexible manner, the random changing dynamic behaviour of the time series. The paper establishes the algebraic mapping between the state-space parameters and the implied reduced form ARIMA parameters. In addition, it shows that parametric mapping surmounts the difficulties that are likely to emerge in a direct estimatation of the random coefficient state-space model. Finally, it presents an empirical application comparing the forecast accuracy of the suggested model vis-a-vis other benchmark models, both in the ARIMA and in the Exponential Smoothing class. Using time series relative to wholesalers’ inventories in the USA, the out-of-sample results show that the reduced form of the random coefficient exponential smoothing model tends to be superior to its competitors.