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Forecasting daily time series using periodic unobserved components time series models

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  • Koopman, Siem Jan
  • Ooms, Marius

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 51 (2006)
Issue (Month): 2 (November)
Pages: 885-903

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Handle: RePEc:eee:csdana:v:51:y:2006:i:2:p:885-903

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References

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  1. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May.
  2. A. C. Harvey & Siem Jan Koopman, 2000. "Computing Observation Weights for Signal Extraction and Filtering," Econometric Society World Congress 2000 Contributed Papers 0888, Econometric Society.
  3. Marius Ooms & M. Angeles Carnero & Siem Jan Koopman, 2004. "Periodic Heteroskedastic RegARFIMA models for daily electricity spot prices," Econometric Society 2004 Australasian Meetings 158, Econometric Society.
  4. 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.
  5. Siem Jan Koopman & Marius Ooms, 2001. "Time Series Modelling of Daily Tax Revenues," Tinbergen Institute Discussion Papers 01-032/4, Tinbergen Institute.
  6. Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
  7. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
  8. Holt, Charles C., 2004. "Author's retrospective on 'Forecasting seasonals and trends by exponentially weighted moving averages'," International Journal of Forecasting, Elsevier, vol. 20(1), pages 11-13.
  9. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
  10. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
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Citations

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Cited by:
  1. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
  2. Triantafyllopoulos, K. & Nason, G.P., 2007. "A Bayesian analysis of moving average processes with time-varying parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1025-1046, October.
  3. Cornillon, P.-A. & Imam, W. & Matzner-Lober, E., 2008. "Forecasting time series using principal component analysis with respect to instrumental variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1269-1280, January.
  4. Alonso, Andres M. & Sipols, Ana E., 2008. "A time series bootstrap procedure for interpolation intervals," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1792-1805, January.
  5. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2006. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Tinbergen Institute Discussion Papers 06-101/4, Tinbergen Institute.
  6. Martín Rodríguez, Gloria & Cáceres Hernández, José Juan, 2010. "Splines and the proportion of the seasonal period as a season index," Economic Modelling, Elsevier, vol. 27(1), pages 83-88, January.

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