Fractionally integrated generalized autoregressive conditional heteroskedasticity

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.