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Temporal aggregation of GARCH processes

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  • Drost, F.C.

    (Tilburg University)

  • Nijman, T.E.

    (Tilburg University)

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 University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-153273.

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Date of creation: 1993
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Publication status: Published in Econometrica (1993) v.61, p.909-927
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-153273

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Web page: http://www.tilburguniversity.edu/

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  1. Nijman, Theo E & Palm, Franz C, 1990. "Predictive Accuracy Gain from Disaggregate Sampling in ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(4), pages 405-15, October.
  2. Palm, F.C. & Nijman, Th., 1982. "Missing observations in the dynamic regression model," Serie Research Memoranda, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  5. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  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, Tilburg University urn:nbn:nl:ui:12-153287, Tilburg University.
  7. Lutkepohl, Helmut, 1986. "Forecasting Vector ARMA Processes with Systematically Missing Observations," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 4(3), pages 375-90, July.
  8. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, Econometric Society, vol. 57(5), pages 1091-1120, September.
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