Holt–Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data
- 15 November 2007
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Applied Statistics
- Vol. 34 (9), 1075-1090
- https://doi.org/10.1080/02664760701592125
Abstract
This paper provides a formulation for the additive Holt–Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the method by applying it to the series of monthly total UK air passengers collected by the Civil Aviation Authority, a long time series from 1949 to the present day, and compares the resulting forecasts with those obtained in previous studies.Keywords
This publication has 11 references indexed in Scilit:
- Improving demand forecasting accuracy using nonlinear programming softwareJournal of the Operational Research Society, 2006
- A state space framework for automatic forecasting using exponential smoothing methodsInternational Journal of Forecasting, 2002
- A spreadsheet modeling approach to the Holt–Winters optimal forecastingEuropean Journal of Operational Research, 2001
- Forecasting models and prediction intervals for the multiplicative Holt–Winters methodInternational Journal of Forecasting, 2001
- Long lead-time forecasting of UK air passengers by Holt–Winters methods with damped trendInternational Journal of Forecasting, 2001
- The M3-Competition: results, conclusions and implicationsInternational Journal of Forecasting, 2000
- Estimation and Prediction for a Class of Dynamic Nonlinear Statistical ModelsJournal of the American Statistical Association, 1997
- A Limited Memory Algorithm for Bound Constrained OptimizationSIAM Journal on Scientific Computing, 1995
- Prediction intervals for the Holt-Winters forecasting procedureInternational Journal of Forecasting, 1990
- Multivariate ObservationsWiley Series in Probability and Statistics, 1984