Random switching exponential smoothing and inventory forecasting

Exponential smoothing models represent an important prediction tool both in business and in macroeconomics. This paper provides 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 local linear trend. Therefore it enables controlling, in a flexible manner, the random changing dynamic behavior 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 the parametric mapping allows overcoming the difficulties that are likely to emerge in estimating directly the random coefficient state-space model. Finally, it presents an empirical application comparing the forecast accuracy of the suggested model vis-à-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.