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Temporal aggregation of univariate linear time series models

  • SILVESTRINI, Andrea
  • VEREDAS, David

In this paper we feature state-of-the-art econometric methodology of temporal aggregation for univariate linear time series, namely ARIMA-GARCH models. We present a unified overview of temporal aggregation techniques for this broad class of processes and we explain in detail, although intuitively, the technical machinery behind the results. An empirical application with Belgian public deficit data illustrates the main issues.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005059.

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Date of creation: 00 Sep 2005
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Handle: RePEc:cor:louvco:2005059
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  1. Drost, F.C. & Werker, B.J.M., 1994. "Closing the GARCH gap : Continuous time GARCH modeling," Discussion Paper 1994-2, Tilburg University, Center for Economic Research.
  2. Nijman, Theo E & Palm, Franz C, 1990. "Predictive Accuracy Gain from Disaggregate Sampling in ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(4), pages 405-15, October.
  3. Nijman, T.E. & Palm, F.C., 1984. "Missing observations in the dynamic regression model," Other publications TiSEM 4d689d7c-4d89-4ab6-b8c3-f, Tilburg University, School of Economics and Management.
  4. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
  5. Hafner, C.M., 2004. "Temporal aggregation of multivariate GARCH processes," Econometric Institute Research Papers EI 2004-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  7. Luiz Hotta & Pedro Pereira & Rissa Ota, 2004. "Effect of outliers on forecasting temporally aggregated flow variables," TEST- An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 371-402, December.
  8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  9. Palm, F.C. & Nijman, T.E., 1990. "Parameter identification in ARMA-processes in the presence of regular but incomplete sampling," Other publications TiSEM 69e84dde-44ef-4592-93a8-8, Tilburg University, School of Economics and Management.
  10. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  12. Hafner, C.M. & Rombouts, J.V.K., 2004. "Estimation of temporally aggregated multivariate GARCH models," Econometric Institute Research Papers EI 2004-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  13. Yue Fang & Sergio G. Koreisha, 2004. "Updating ARMA predictions for temporal aggregates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(4), pages 275-296.
  14. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
  15. Oscar Jordà & Massimiliano Marcellino, 2004. "Time-scale transformations of discrete time processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 873-894, November.
  16. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  17. MOULIN, Laurent & SALTO, Matteo & SILVESTRINI, Andrea & VEREDAS, David, 2004. "Using intra annual information to forecast the annual state deficits : the case of France," CORE Discussion Papers 2004048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  19. Clive Granger & Tae-Hwy Lee, 1999. "The effect of aggregation on nonlinearity," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 259-269.
  20. William W. S. Wei, 1978. "Some Consequences of Temporal Aggregation in Seasonal Time Series Models," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 433-448 National Bureau of Economic Research, Inc.
  21. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  22. Tommaso Proietti, 2004. "On the Estimation of Nonlinearly Aggregated Mixed Models," Econometrics 0411012, EconWPA.
  23. 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.
  24. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  25. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
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