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Ex post and ex ante prediction of unobserved multivariate time series: a structural-model based approach

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  • Fabio H. Nieto

    (Department of Statistics, National University of Colombia, Bogotá, COLOMBIA)

Abstract

A methodology for estimating high-frequency values of an unobserved multivariate time series from low-frequency values of and related information to it is presented in this paper. This is an optimal solution, in the multivariate setting, to the problem of ex post prediction, disaggregation, benchmarking or signal extraction of an unobservable stochastic process. Also, the problem of extrapolation or ex ante prediction is optimally solved and, in this context, statistical tests are developed for checking online the ocurrence of extreme values of the unobserved time series and consistency of future benchmarks with the present and past observed information. The procedure is based on structural or unobserved component models, whose assumptions and specification are validated with the data alone. Copyright © 2007 John Wiley & Sons, Ltd.

Suggested Citation

  • Fabio H. Nieto, 2007. "Ex post and ex ante prediction of unobserved multivariate time series: a structural-model based approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(1), pages 53-76.
    • Handle: RePEc:jof:jforec:v:26:y:2007:i:1:p:53-76
    DOI: 10.1002/for.1017
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    References listed on IDEAS

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    1. Nieto, Fabio H. & Guerrero, Victor M., 1995. "Kalman filter for singular and conditional state-space models when the system state and the observational error are correlated," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 303-310, March.
    2. Víctor Guerrero & Fabio Nieto, 1999. "Temporal and contemporaneous disaggregation of multiple economic time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 459-489, December.
    3. J. Durbin & B. Quenneville, 1997. "Benchmarking by State Space Models," International Statistical Review, International Statistical Institute, vol. 65(1), pages 23-48, April.
    4. repec:adr:anecst:y:1987:i:6-7:p:12 is not listed on IDEAS
    5. Estela Bee Dagum & Pierre A. Cholette & Zhao‐Guo Chen, 1998. "A Unified View of Signal Extraction, Benchmarking, Interpolation and Extrapolation of Time Series," International Statistical Review, International Statistical Institute, vol. 66(3), pages 245-269, December.
    6. 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 372-375, November.
    7. F. Javier Fernandez Macho & Andrew C. Harvey & James H. Stock, 1987. "Forecasting and Interpolation Using Vector Autoregressions with Common Trends," Annals of Economics and Statistics, GENES, issue 6-7, pages 279-287.
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    Cited by:

    1. Ivonne Caridad Perez Correa & Juan Miguel Martinez Buendia, 2013. "Desagregación multivariada del PIB sectorial del departamento de Bolívar," Revista Economía y Región, Universidad Tecnológica de Bolívar, vol. 7(1), pages 139-167, June.
    2. Kosei Fukuda, 2009. "Related-variables selection in temporal disaggregation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(4), pages 343-357.

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