A Study of the Temporal Aggregation of GARCH Model

TLDR: In this article, the impact of temporal aggregation on the GARCH process was studied. And it was shown that conditional heteroskedasticity disappears if the sampling time interval increases to infinity (Drost and Nijman, 1993).

Abstract: Beginning with the mean variance analysis of portfolio and asset returns, volatility has become central to much of modern finance theory. In recent times, empirical work involving high frequency financial time series data has focused on volatility of asset return. It has been observed that the asset returns exhibit changes, which are not independent over time. Rather, large changes tend to followed by large changes of either sign - small changes tend to be followed by small changes. That is, big shocks are clustered together. GARCH models are used to parameterize conditional heteroskedasticity. It is little known about the impact of temporal aggregation upon GARCH process that conditional heteroskedasticity disappears if the sampling time interval increases to infinity (Drost and Nijman (July 1993). Important applications for persistence variance in GARCH (1,1) model are represented by sum of the coefficients lagged squared disturbance and that of past variance coefficients b1.