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On the autocorrelation properties of long-memory GARCH processes. (English) Zbl 1051.62076

The authors consider a class of long-memory GARCH processes that belong to the family of conditionally heteroscedastic processes. These processes are very closely related to the fractionally integrated GARCH processes, and share some of the features of fractional ARIMA processes. Such processes have been found to describe well the observed autocorrelation structure of many real-life financial time series. In this paper the autocorrelation function of the square values of long-memory GARCH processes is derived. As an empirical illustration the authors examine properties of continuously compounded daily rates of return for the Deutschmark exchange rate vis-à-vis the US Dollar.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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