Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing

• 成果类型: Article
• 署名作者: De Livera, Alysha M.; Hyndman, Rob J.; Snyder, Ralph D.
• 署名单位: University of Melbourne; Monash University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm09771
• 发表日期: 2011
• 页码: 1513-1527
• 关键词: prediction intervals; state; adjustment; likelihood; components

摘要

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 computational burden in the maximum likelihood estimation. The modeling framework is useful for a broad range of applications, its versatility being illustrated in three empirical studies. In addition, the proposed trigonometric formulation is presented as a means of decomposing complex seasonal time series, and it is shown that this decomposition leads to the identification and extraction of seasonal components which are otherwise not apparent in the time series plot itself.