Random switching exponential smoothing: A new estimation approach

The random switching exponential smoothing as introduced by Sbrana and Silvestrini (International Journal of Production Economics, 156, 2014: 283–294) is a flexible forecasting model that can be used for time series with a (changing) trending behaviour. The estimation method originally proposed by these authors works only when some restrictive conditions on the parameters are met, therefore preventing its use in several practical applications. This paper presents a new, fast and efficient approach for estimating the random switching exponential smoothing model. The new method relies on the algebraic link between the model's structural parameters and the steady-state Kalman gain vector. This link simplifies the likelihood evaluation and thus reduces the computational burden. The finite-sample properties of the new estimation method are assessed in a Monte Carlo experiment and its out-of-sample forecasting performance is explored in an empirical evaluation exercise employing time series for wholesalers' inventories and sales in the United States. These series represent important business cycle indicators. Results show that both estimation methods perform broadly the same in simulations and in forecasting, over both short-term and longer-term horizons. However, despite the equal accuracy and forecasting performance, contrary to the originally proposed method, the new estimation approach can always be used, with no exceptions. In addition, its simplicity is a strong point in its favour for practitioners and forecasters working in business and industry.