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Temporal aggregaton of univariate linear time series models

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  • Andrea, SILVESTRINI

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.

Suggested Citation

  • Andrea, SILVESTRINI, 2005. "Temporal aggregaton of univariate linear time series models," Discussion Papers (ECON - Département des Sciences Economiques) 2005044, Université catholique de Louvain, Département des Sciences Economiques.
    • Handle: RePEc:ctl:louvec:2005044
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    File URL: http://sites.uclouvain.be/econ/DP/IRES/2005-44.pdf
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    1. HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Estimation of temporally aggregated multivariate GARCH models," LIDAM Discussion Papers CORE 2003073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    4. 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.
    5. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    6. 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 405-415, October.
    7. Tommaso Proietti, 2004. "On the Estimation of Nonlinearly Aggregated Mixed Models," Econometrics 0411012, University Library of Munich, Germany.
    8. Hafner, Christian M., 2008. "Temporal aggregation of multivariate GARCH processes," Journal of Econometrics, Elsevier, vol. 142(1), pages 467-483, January.
    9. Theo Nijman & Franz Palm, 1990. "Parameter Identification In Arma Processes In The Presence Of Regular But Incomplete Sampling," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 239-248, May.
    10. L. K. Hotta & J. Cardosc Neto, 1993. "The Effect Of Aggregation On Prediction In Autoregressive Integrated Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 261-269, May.
    11. Daniel O. Stram & William W. S. Wei, 1986. "Temporal Aggregation In The Arima Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 279-292, July.
    12. 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.
    13. Òscar 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.
    14. Jörg Breitung & Norman R. Swanson, 2002. "Temporal aggregation and spurious instantaneous causality in multiple time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 651-665, November.
    15. MOULIN, Laurent & SALTO, Matteo & SILVESTRINI, Andrea & VEREDAS, David, 2004. "Using intra annual information to forecast the annual state deficits : the case of France," LIDAM Discussion Papers CORE 2004048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    17. Granger, C. W. J., 1987. "Implications of Aggregation with Common Factors," Econometric Theory, Cambridge University Press, vol. 3(2), pages 208-222, April.
    18. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    19. Clive W. J. Granger, 1988. "Aggregation of time series variables-a survey," Discussion Paper / Institute for Empirical Macroeconomics 1, Federal Reserve Bank of Minneapolis.
    20. 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.
    21. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-1435, November.
    22. 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.
    23. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    24. Clive Granger & Tae-Hwy Lee, 1999. "The effect of aggregation on nonlinearity," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 259-269.
    25. 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.
    26. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-214, July.
    27. Nijman, T.E. & Palm, F.C., 1990. "Parameter identification in ARMA processes in the presence of regular but incomplete sampling," Other publications TiSEM 708ee84d-487f-48a4-8169-0, Tilburg University, School of Economics and Management.
    28. 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.
    29. 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. MOULIN, Laurent & SALTO, Matteo & SILVESTRINI, Andrea & VEREDAS, David, 2004. "Using intra annual information to forecast the annual state deficits : the case of France," LIDAM Discussion Papers CORE 2004048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Phillip A. Cartwright & Natalija Riabko, 2019. "Do spot food commodity and oil prices predict futures prices?," Review of Quantitative Finance and Accounting, Springer, vol. 53(1), pages 153-194, July.
    4. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    5. Cartwright, Phillip A. & Riabko, Natalija, 2015. "Measuring the effect of oil prices on wheat futures prices," Research in International Business and Finance, Elsevier, vol. 33(C), pages 355-369.
    6. Phillip A. Cartwright & Natalija Riabko, 2016. "Further evidence on the explanatory power of spot food and energy commodities market prices for futures prices," Review of Quantitative Finance and Accounting, Springer, vol. 47(3), pages 579-605, October.
    7. Giacomo Sbrana, 2012. "Aggregation and marginalization of GARCH processes: some further results," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 165-172, August.

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    More about this item

    Keywords

    Temporal aggregation; ARIMA; GARCH; seasonality;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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