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Temporal Aggregation of Garch Processes

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  • Drost, F.C.
  • Nijman, T.E.

Abstract

The authors derive low frequency, say weekly, models implied by high frequency, say daily, ARMA models with symmetric GARCH errors. They show that low frequency models exhibit conditional heteroskedasticity of the GARCH form as well. The parameters in the conditional variance equation of the low frequency model depend upon mean, variance, and kurtosis parameters of the corresponding high frequency model. Moreover, strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data. The common assumption in applications that rescaled innovations are independent is disputable, since it depends upon the available data frequency. Copyright 1993 by The Econometric Society.
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Suggested Citation

  • Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
    • Handle: RePEc:fth:tilbur:9240
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    3. Verbeek, Marno & Nijman, Theo, 1992. "Testing for Selectivity Bias in Panel Data Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 681-703, August.
    4. Eijffinger, Sylvester & van Rixtel, Adrian, 1992. "The Japanese financial system and monetary policy: a descriptive review," Japan and the World Economy, Elsevier, vol. 4(4), pages 291-309, December.
    5. Marini, Giancarlo & van der Ploeg, Frederick, 1988. "Monetary and Fiscal Policy in an Optimising Model with Capital Accumulation and Finite Lives," Economic Journal, Royal Economic Society, vol. 98(392), pages 772-786, September.
    6. Bomze, I.M. & van Damme, E.E.C., 1990. "A dynamical characterization of evolutionarily stable states," Discussion Paper 1990-45, Tilburg University, Center for Economic Research.
    7. Kapteyn, Arie & Kooreman, Peter & van Soest, Arthur, 1990. "Quantity Rationing and Concavity in a Flexible Household Labor Supply Model," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 55-62, February.
    8. Jurg, A.P. & García-Jurado, I. & Borm, P.E.M., 1992. "On modifications of the concepts of perfect and proper equilibria," Other publications TiSEM b06a7e2d-b824-4a92-b577-9, Tilburg University, School of Economics and Management.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Tim Bollerslev, 1988. "On The Correlation Structure For The Generalized Autoregressive Conditional Heteroskedastic Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(2), pages 121-131, March.
    11. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    12. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    13. Gradus, R.H.J.M. & de Zeeuw, A.J., 1993. "An employment game between government and firms," Other publications TiSEM e4810291-ddd4-4431-8b30-2, Tilburg University, School of Economics and Management.
    14. 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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