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Modelling and forecasting time series sampled at different frequencies

Author

Listed:
  • José Casals

    (Universidad Complutense de Madrid, Spain)

  • Miguel Jerez

    (Universidad Complutense de Madrid, Spain)

  • Sonia Sotoca

    (Universidad Complutense de Madrid, Spain)

Abstract

This paper discusses how to specify an observable high-frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high-frequency model, standard state-space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. An example using national accounting data illustrates the practical application of this method. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • José Casals & Miguel Jerez & Sonia Sotoca, 2009. "Modelling and forecasting time series sampled at different frequencies," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(4), pages 316-342.
  • Handle: RePEc:jof:jforec:v:28:y:2009:i:4:p:316-342
    DOI: 10.1002/for.1112
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    File URL: http://hdl.handle.net/10.1002/for.1112
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    References listed on IDEAS

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    1. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
    2. Di Fonzo, Tommaso, 1990. "The Estimation of M Disaggregate Time Series When Contemporaneous and Temporal Aggregates Are Known," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 178-182, February.
    3. Casals, Jose & Jerez, Miguel & Sotoca, Sonia, 2000. "Exact smoothing for stationary and non-stationary time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 59-69.
    4. Santos Silva, J. M. C. & Cardoso, F. N., 2001. "The Chow-Lin method using dynamic models," Economic Modelling, Elsevier, vol. 18(2), pages 269-280, April.
    5. Luis C. Nunes, 2005. "Nowcasting quarterly GDP growth in a monthly coincident indicator model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 575-592.
    6. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    7. Tommaso Proietti, 2006. "Temporal disaggregation by state space methods: Dynamic regression methods revisited," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 357-372, November.
    8. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    9. Tommaso di Fonzo & Marco Marini, 2005. "Benchmarking Systems of Seasonally Adjusted Time Series," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2005(1), pages 89-123.
    10. Pierse, R. G. & Snell, A. J., 1995. "Temporal aggregation and the power of tests for a unit root," Journal of Econometrics, Elsevier, vol. 65(2), pages 333-345, February.
    11. Baffigi, Alberto & Golinelli, Roberto & Parigi, Giuseppe, 2004. "Bridge models to forecast the euro area GDP," International Journal of Forecasting, Elsevier, vol. 20(3), pages 447-460.
    12. Granger, C. W. J. & Siklos, Pierre L., 1995. "Systematic sampling, temporal aggregation, seasonal adjustment, and cointegration theory and evidence," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 357-369.
    13. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    14. Casals J. & Jerez M. & Sotoca S., 2002. "An Exact Multivariate Model-Based Structural Decomposition," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 553-564, June.
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    Cited by:

    1. García-Hiernaux, Alfredo & Guerrero, David E. & McAleer, Michael, 2016. "Market integration dynamics and asymptotic price convergence in distribution," Economic Modelling, Elsevier, vol. 52(PB), pages 913-925.
    2. Aristei, David & Martelli, Duccio, 2014. "Sovereign bond yield spreads and market sentiment and expectations: Empirical evidence from Euro area countries," Journal of Economics and Business, Elsevier, vol. 76(C), pages 55-84.
    3. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    4. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Combination of long term and short term forecasts, with application to tourism demand forecasting," International Journal of Forecasting, Elsevier, vol. 27(3), pages 870-886, July.
    5. Elena Marquez & Belen Nieto, 2011. "Further international evidence on durable consumption growth and long-run consumption risk," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 195-217.

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