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Modelling and forecasting time series sampled at different frequencies

  • José Casals

    (Universidad Complutense de Madrid, Spain)

  • Miguel Jerez

    (Universidad Complutense de Madrid, Spain)

  • Sonia Sotoca

    (Universidad Complutense de Madrid, Spain)

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.

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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

Volume (Year): 28 (2009)
Issue (Month): 4 ()
Pages: 316-342

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Handle: RePEc:jof:jforec:v:28:y:2009:i:4:p:316-342
DOI: 10.1002/for.1112
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  1. Robert B. Litterman, 1983. "A random walk, Markov model for the distribution of time series," Staff Report 84, Federal Reserve Bank of Minneapolis.
  2. Granger, C.W.J. & Siklos, P.L., 1993. "Systematic Sampling, Temporal Aggregation, Seasonal Adjustment, and Cointegration: Theory and Evidence," Working Papers 93001, Wilfrid Laurier University, Department of Economics.
  3. 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.
  4. 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.
  5. 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.
  6. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-36, January.
  7. 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.
  8. Fernandez, Roque B, 1981. "A Methodological Note on the Estimation of Time Series," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 471-76, August.
  9. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-75, November.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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 178-82, February.
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