Forecasting time series with complex seasonal patterns using exponential smoothing
Alysha M De Livera and
Rob Hyndman ()
No 15/09, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics
A 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.
Keywords: Exponential smoothing; Fourier series; prediction intervals; seasonality; state space models; time series decomposition (search for similar items in EconPapers)
JEL-codes: C22 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
References: Add references at CitEc
Citations: View citations in EconPapers (15) Track citations by RSS feed
Downloads: (external link)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:msh:ebswps:2009-15
Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics
Access Statistics for this paper
More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Dr Xibin Zhang ().