Elsevier

Journal of Econometrics

Volume 74, Issue 1, September 1996, Pages 3-30
Journal of Econometrics

Fractionally integrated generalized autoregressive conditional heteroskedasticity

https://doi.org/10.1016/S0304-4076(95)01749-6Get rights and content

Abstract

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 T12-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.

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    ∗∗

    The second author is also affiliated with the NBER. Most of this research was completed while the third author was visiting Northwestern University. We gratefully acknowledge the helpful comments received from three anonymous referees, Robin Brenner, Yin-Wong Cheung, Miguel Delgado, Francis X. Diebold, Andrew Harvey, Campbell Harvey, Daniel B. Nelson, Peter M. Robinson, participants at the 1993 workshop on ‘Modern Time Series Analysis in Finance’ at the University of Aarhus, Denmark, the 1994 conference on ‘Asymmetries and Non-Linearities in Dynamic Economic Models’ in Madrid, the 1994 NBER Summer Institute, as well as seminar audiences at the University of Arizona, University of California at Santa Barbara, University of Iowa, University of Minnesota, University of Montreal, University of Texas at Austin, and University of Virginia.

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