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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

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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Suggested Citation

  • Koopman, Siem Jan & Ooms, Marius, 2006. "Forecasting daily time series using periodic unobserved components time series models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 885-903, November.
  • Handle: RePEc:eee:csdana:v:51:y:2006:i:2:p:885-903
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
    5. Holt, Charles C., 2004. "Forecasting seasonals and trends by exponentially weighted moving averages," International Journal of Forecasting, Elsevier, vol. 20(1), pages 5-10.
    6. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    7. Siem Jan Koopman & Marius Ooms, 2003. "Time Series Modelling of Daily Tax Revenues," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 439-469.
    8. 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.
    9. Proietti Tommaso, 2004. "Seasonal Specific Structural Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-22, May.
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    Cited by:

    1. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    2. 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.
    3. 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.
    4. 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.
    5. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    6. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    7. Yılmaz, Engin, 2015. "Forecasting tourist arrivals to Turkey," MPRA Paper 68616, University Library of Munich, Germany.
    8. 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.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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