Limit Theory for the Sample Autocorrelations and Extremes of a Garch(1,1) Process
نویسنده
چکیده
The asymptotic theory for the sample autocorrelations and extremes of a GARCH(1; 1) process is provided. Special attention is given to the case when the sum of the ARCH and GARCH parameters is close to one, i.e. when one is close to an innnite variance marginal distribution. This situation has been observed for various nancial log{return series and led to the introduction of the IGARCH model. In such a situation the sample autocorrelations are unreliable estimators of their deterministic counterparts for the time series and its absolute values, and the sample autocorrelations of the squared time series have non{degenerate limit distributions. We discuss the consequences for a foreign exchange rate series.
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