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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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References

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  1. Palm, F.C. & Nijman, Th., 1982. "Missing observations in the dynamic regression model," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  2. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(02), pages 208-222, April.
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  4. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  5. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
  6. 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).
  7. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
  8. Hafner, C.M., 2004. "Temporal aggregation of multivariate GARCH processes," Econometric Institute Report EI 2004-29, Erasmus University Rotterdam, Econometric Institute.
  9. 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.
  10. Oscar Jorda & Massimiliano Marcellino, 2003. "Time-Scale Transformations of Discrete-Time Processes," Working Papers 32, University of California, Davis, Department of Economics.
  11. 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.
  12. Nijman, Theo E. & Palm, Franz C., 1990. "Predictive accuracy gain from disaggregate sampling in ARIMA models," Open Access publications from Maastricht University urn:nbn:nl:ui:27-5752, Maastricht University.
  13. 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).
  14. 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.
  15. 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.
  16. 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).
  17. 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.
  18. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  19. Tommaso Proietti, 2004. "On the Estimation of Nonlinearly Aggregated Mixed Models," Econometrics 0411012, EconWPA.
  20. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  21. 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.
  22. 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.
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Cited by:
  1. 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.
  2. repec:eca:wpaper:2009_012 is not listed on IDEAS
  3. 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).

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