Temporal Aggregation of GARCH Processes

Abstract

Abstract 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.