Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 1993, Volume 61, Issue 4

Temporal Aggregation of Garch Processes<909:TAOGP>2.0.CO;2-2
p. 909-927

Feike C. Drost, Theo E. Nijman

We derive low frequency, say weekly, models implied by high frequency, say daily, ARMA models with symmetric GARCH errors. Both stock and flow variable cases are considered. We 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 in many interesting cases. The common assumption in applications that rescaled innovations are independent is disputable, since it depends upon the available data frequency.

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