Automatic forecasting with a modified exponential smoothing state space framework

Abstract

A new automatic forecasting procedure is proposed based on a recent exponential smoothing framework which incorporates a Box-Cox transformation and ARMA residual corrections. The procedure is complete with well-defined methods for initialization, estimation, likelihood evaluation, and analytical derivation of point and interval predictions under a Gaussian error assumption. The algorithm is examined extensively by applying it to single seasonal and non-seasonal time series from the M and the M3 competitions, and is shown to provide competitive out-of-sample forecast accuracy compared to the best methods in these competitions and to the traditional exponential smoothing framework. The proposed algorithm can be used as an alternative to existing automatic forecasting procedures in modeling single seasonal and non-seasonal time series. In addition, it provides the new option of automatic modeling of multiple seasonal time series which cannot be handled using any of the existing automatic forecasting procedures. The proposed automatic procedure is further illustrated by applying it to two multiple seasonal time series involving call center data and electricity demand data.Exponential smoothing, state space models, automatic forecasting, Box-Cox transformation, residual adjustment, multiple seasonality, time series