Bayesian forecasting with the Holt–Winters model

Abstract

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.

Keywords:

• forecasting
• time series
• prediction intervals
• simulation
• M3-competition

Acknowledgements

We thank anonymous referees for their valuable comments. This research was partially supported by the Ministerio de Educación y Ciencia of Spain, Grant MTM2008-03993.