an:00447131
Zbl 0780.62099
Drost, Feike C.; Nijman, Theo E.
Temporal aggregation of GARCH processes
EN
Econometrica 61, No. 4, 909-927 (1993).
00015441
1993
j
62P20 91B84 62M10
GARCH models; temporal aggregation; financial time-series; ARMA models; low frequency models; conditional heteroskedasticity; conditional variance equation; mean; variance; kurtosis; high frequency model; strongly consistent estimators
Summary: 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.