TEMPORAL AGGREGATION OF GARCH PROCESSES

We derive low frequency, say weekly, models implied by high frequency, say daily, ARMA models with symmetric GARCH errors. Both stock and fl ow variable cases are considered. We show that low frequency models ex hibit conditional heteroskedasticity of the GARCH form as well. The pa rameters in the conditional variance equation of the low frequency mod el depend upon mean, variance, and kurtosis parameters of the correspo nding high frequency model. Moreover, strongly consistent estimators o f the parameters in the high frequency model can be derived from low f requency data in many interesting cases. The common assumption in appl ications that rescaled innovations are independent is disputable, sinc e it depends upon the available data frequency.