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Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

  • SBRANA, Giacomo

    ()

    (Université de Strasbourg, BETA, F-67085 Strasbourg, France)

  • SILVESTRINI, Andrea

    ()

    (Bank of Italy, Economics, Research and International Relations Area, Economic and Financial Statistics Department, I-00184 Roma, Italy)

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of exponential smoothing (EWMA) models. Focusing on a vector IMA(1,1) model, we obtain a closed form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. In the framework of EWMA estimates of volatility, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the decay factor in the portfolio volatility equation from the estimated vector IMA(1,1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying the standard univariate RiskMetrics TM methodology.

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File URL: http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2010_39web.pdf
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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 2010039.

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Date of creation: 01 Jul 2010
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Handle: RePEc:cor:louvco:2010039
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  1. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  2. 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, 07.
  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. repec:ner:tilbur:urn:nbn:nl:ui:12-153273 is not listed on IDEAS
  5. 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.
  6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  7. Lutkepohl, Helmut, 1984. "Linear aggregation of vector autoregressive moving average processes," Economics Letters, Elsevier, vol. 14(4), pages 345-350.
  8. Davis, Richard A., 1996. "Gauss-Newton and M-estimation for ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 75-95, October.
  9. Francq, Christian & Zako an, Jean-Michel, 2000. "Estimating Weak Garch Representations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 692-728, October.
  10. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
  11. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
  12. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  13. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  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. repec:ner:tilbur:urn:nbn:nl:ui:12-153287 is not listed on IDEAS
  16. Wang, Jying-Nan & Yeh, Jin-Huei & Cheng, Nick Ying-Pin, 2011. "How accurate is the square-root-of-time rule in scaling tail risk: A global study," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1158-1169, May.
  17. Paolo Zaffaroni, 2008. "Large-scale volatility models: theoretical properties of professionals' practice," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 581-599, 05.
  18. Nijman, T. & Sentana, E., 1993. "Marginalization and Contemporaneous Aggregation in Multivariate Garch Processes," Papers 9312, Tilburg - Center for Economic Research.
  19. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  20. Lutkepohl, Helmut, 1984. "Linear transformations of vector ARMA processes," Journal of Econometrics, Elsevier, vol. 26(3), pages 283-293, December.
  21. repec:ner:tilbur:urn:nbn:nl:ui:12-73202 is not listed on IDEAS
  22. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  23. Jeroen V.K. Rombouts & Marno Verbeek, 2004. "Evaluating Portfolio Value-at-Risk using Semi-Parametric GARCH Models," Cahiers de recherche 04-14, HEC Montréal, Institut d'économie appliquée.
  24. 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.
  25. Alexandre Petkovic & David Veredas, 2010. "Aggregation of linear models for panel data," ULB Institutional Repository 2013/136203, ULB -- Universite Libre de Bruxelles.
  26. John Galbraith & Aman Ullah & Victoria Zinde-Walsh, 2002. "Estimation Of The Vector Moving Average Model By Vector Autoregression," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 205-219.
  27. repec:ner:tilbur:urn:nbn:nl:ui:12-153295 is not listed on IDEAS
  28. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  29. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  30. 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.
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