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Fractionally integrated generalized autoregressive conditional heteroskedasticity. (English) Zbl 0865.62085
Summary: The new class of fractionally integrated generalized autoregressive conditionally heteroskedastic (FIGARCH) processes is introduced. The conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations. Unlike I($$d$$) processes for the mean, maximum likelihood estimates (MLE) of the FIGARCH parameters are argued to be $$T^{1/2}$$-consistent. The small sample behavior of an approximate MLE procedure is assessed through a simulation study, which also documents how the estimation of a standard GARCH model tends to produce integrated, or IGARCH, like estimates. An empirical example with daily Deutschmark-U.S. dollar exchange rates illustrates the practical relevance of the new FIGARCH specification.

##### MSC:
 62P20 Applications of statistics to economics 91B84 Economic time series analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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