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Temporal Aggregation of GARCH Processes

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  • Drost, Feike C
  • Nijman, Theo 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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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 61 (1993)
Issue (Month): 4 (July)
Pages: 909-27

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Handle: RePEc:ecm:emetrp:v:61:y:1993:i:4:p:909-27

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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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  3. Lutkepohl, Helmut, 1986. "Forecasting Vector ARMA Processes with Systematically Missing Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(3), pages 375-90, July.
  4. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  5. 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.
  6. 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.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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