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Temporal aggregation of univariate linear time series models

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  • SILVESTRINI, Andrea
  • VEREDAS, David

Abstract

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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File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/109b0a28-62cc-4596-908c-be8d4e095012/coredp_2005_59.pdf
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Bibliographic Info

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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Keywords: temporal aggregation; ARIMA; GARCH; seasonality;

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-35, November.
  3. 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, vol. 13(2), pages 371-402, December.
  4. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
  5. Oscar Jorda & Massimiliano Marcellino, 2003. "Time-Scale Transformations of Discrete-Time Processes," Working Papers 32, University of California, Davis, Department of Economics.
  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. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153273, Tilburg University.
  8. 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.
  9. 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).
  10. Hafner, Christian M., 2008. "Temporal aggregation of multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 142(1), pages 467-483, January.
  11. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  12. HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Estimation of temporally aggregated multivariate GARCH models," CORE Discussion Papers 2003073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  14. 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.
  15. 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).
  16. 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.
  17. Tommaso Proietti, 2004. "On the Estimation of Nonlinearly Aggregated Mixed Models," Econometrics 0411012, EconWPA.
  18. Nijman, T.E. & Palm, F.C., 1990. "Predictive accuracy gain from disaggregate sampling in ARIMA models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153276, Tilburg University.
  19. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
  20. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  21. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
  22. 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.
  23. Palm, F.C. & Nijman, T.E., 1990. "Parameter identification in ARMA-processes in the presence of regular but incomplete sampling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153287, Tilburg University.
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Cited by:
  1. Laurent Moulin & Matteo Sala & Andrea Silvestrini & David Veredas, 2008. "Using intra annual information to forecast the annual state deficit. The case of France," ULB Institutional Repository 2013/136217, ULB -- Universite Libre de Bruxelles.
  2. Andrea Silvestrini & Matteo Salto & Laurent Moulin & David Veredas, 2008. "Monitoring and forecasting annual public deficit every month: the case of France," Empirical Economics, Springer, vol. 34(3), pages 493-524, June.
  3. Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer, vol. 70(2), pages 165-172, August.

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