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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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Bibliographic Info

Paper provided by Tilburg - Center for Economic Research in its series Papers with number 9066.

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Length: 27 pages
Date of creation: 1990
Date of revision:
Handle: RePEc:fth:tilbur:9066

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Postal: TILBURG UNIVERSITY, CENTER FOR ECONOMIC RESEARCH, 5000 LE TILBURG THE NETHERLANDS.
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Web page: http://center.uvt.nl/
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Keywords: economic models ; heteroskedasticity;

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References

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  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. Nijman, T.E. & Palm, F.C., 1987. "Predictive accuracy gain from disaggregate sampling in ARIMA-models," Research Memorandum 273, Tilburg University, Faculty of Economics and Business Administration.
  5. 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.
  6. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-35, November.
  7. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  8. 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.
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