Forecasting daily time series using periodic unobserved components time series models
This discussion paper resulted in a publication in Computational Statistics & Data Analysis (2006). Vol. 51, issue 2, pages 885-903. We explore a periodic analysis in the context of unobserved components time series models that decompose time series into components of interest such as trend and seasonal. Periodic time series models allow dynamic characteristics to depend on the period of the year, month, week or day. In the standard multivariate approach one can interpret periodic time series modelling as a simultaneous analysis of a set of, traditionally, yearly time series where each series is related to a particular season, with a time index in years. Our analysis applies to monthly vector time series related to each day of the month. We focus on forecasting performance and the underlying periodic forecast function, defined by the in-sample observation weights for producing (multi-step) forecasts. These weights facilitate the interpretation of periodic model extensions. We take a statistical state space approach to estimate our model, so that we can identify stochastic unobserved components and we can deal with irregularly spaced time series. We extend existing algorithms to compute observation weights for forecasting based on state space models with regressor variables. Our methods are illustrated by an application to time series of clearly periodic daily Dutch tax revenues. The dimension of our model is large as we allow the time series for each day of the month to be subject to a changing seasonal pattern. Nevertheless, even with only five years of data we find that increased periodic flexibility helps help in simulated out-of-sample forecasting for two extra years of data.
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- M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003.
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- Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
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- Marius Ooms & Björn de Groot & Siem Jan Koopman, 1999. "Time-Series Modelling of Daily Tax Revenues," Computing in Economics and Finance 1999 312, Society for Computational Economics.
- Siem Jan Koopman & Marius Ooms, 2001. "Time Series Modelling of Daily Tax Revenues," Tinbergen Institute Discussion Papers 01-032/4, Tinbergen Institute.
- Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
- Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May. Full references (including those not matched with items on IDEAS)
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