Forecasting time series with complex seasonal patterns using exponential smoothing
AbstractA new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 15/09.
Length: 28 pages
Date of creation: 12 Dec 2009
Date of revision:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-10 (All new papers)
- NEP-ECM-2010-01-10 (Econometrics)
- NEP-ETS-2010-01-10 (Econometric Time Series)
- NEP-FOR-2010-01-10 (Forecasting)
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RePEc Biblio mentionsAs found on the RePEc Biblio, the curated bibliography for Economics:CitEc Project, subscribe to its RSS feed for this item.
- Alysha M De Livera, 2010. "Automatic forecasting with a modified exponential smoothing state space framework," Monash Econometrics and Business Statistics Working Papers 10/10, Monash University, Department of Econometrics and Business Statistics.
- Harvey, A. & Luati, A., 2012. "Filtering with heavy tails," Cambridge Working Papers in Economics 1255, Faculty of Economics, University of Cambridge.
- Taylor, James W., 2010. "Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles," International Journal of Forecasting, Elsevier, vol. 26(4), pages 627-646, October.
- Kolassa, Stephan, 2011. "Combining exponential smoothing forecasts using Akaike weights," International Journal of Forecasting, Elsevier, vol. 27(2), pages 238-251, April.
- Shaun P Vahey & Elizabeth C Wakerly, 2013. "Moving towards probability forecasting," BIS Papers chapters, in: Bank for International Settlements (ed.), Globalisation and inflation dynamics in Asia and the Pacific, volume 70, pages 3-8 Bank for International Settlements.
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