Journal article

Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing

Alysha M De Livera, Rob J Hyndman, Ralph D Snyder

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION | AMER STATISTICAL ASSOC | Published : 2011

Abstract

An innovations state space modeling framework is introduced for forecasting complex seasonal time series such as those with multiple seasonal periods, high-frequency seasonality, non-integer seasonality, and dual-calendar effects. The new framework incorporates Box-Cox transformations, Fourier representations with time varying coefficients, and ARMA error correction. Likelihood evaluation and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensive approach to forecasting complex seasonal time series. A key feature of the framework is that it relies on a new method that greatly reduces the comp..

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University of Melbourne Researchers

Grants

Funding Acknowledgements

Alysha M. De Livera is Research Fellow, Faculty of Science, The University of Melbourne, Victoria 3010, Australia (E-mail: alyshad@unimelb.edu.au). Rob J. Hyndman is Professor, Department of Econometrics and Business Statistics, Monash University, Victoria 3800, Australia (E-mail: rob.hyndman@monash.edu). Ralph D. Snyder is Associate Professor, Department of Econometrics and Business Statistics, Monash University, Victoria 3800, Australia (E-mail: ralph.snyder@monash.edu). The first author acknowledges the support provided by the Commonwealth Scientific and Industrial Research Organisation, Australia. The authors thank Dr. Peter Toscas from the Commonwealth Scientific and Industrial Research Organisation, Australia, the editor, the associate editor, and two referees for comments that improved the clarity and quality of the article.