Limit theory for the sample autocorrelations and extremes of a GARCH (1,1)process

The asymptotic theory for the sample autocorrelations and extremes of a GAR CH(I, 1) process is provided. Special attention is given to the case when t he sum of the ARCH and GARCH parameters is close to 1, that is, when one is close to an infinite Variance marginal distribution. This situation has be en observed for various financial log-return series and led to the introduc tion 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 squa red time series have nondegenerate limit distributions. We discuss the cons equences for a foreign exchange rate series.