Larch, Leverage and Long Memory

32 Pages Posted: 21 Jul 2008

See all articles by Liudas Giraitis

Liudas Giraitis

University of York - Department of Mathematics and Economics

Donatas Surgailis

Institute of Mathematics and Informatics, Lithuania

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Date Written: October 2003

Abstract

We consider the long memory and leverage properties of a model for the conditional variance of an observable stationary sequence, where the conditional variance is the square of an inhomogeneous linear combination of past values of the observable sequence, with square summable weights. This model, which we call linear ARCH (LARCH), specializes to the asymmetric ARCH model of Engle (1990), and to a version of the quadratic ARCH model of Sentana (1995), these authors having discussed leverage potential in such models. The model which we consider was suggested by Robinson (1991), for use as a possibly long memory conditionally heteroscedastic alternative to i.i.d. behaviour, and further studied by Giraitis, Robinson and Surgailis (2000), who showed that integer powers, of degree at least 2, can have long memory autocorrelation. We establish conditions under which the cross-autovariance function between volatility and levels decays in the manner of moving average weights of long memory processes. We also establish a leverage property and conditions for finiteness of third and higher moments.

JEL Classification: C16, C53, G12

Suggested Citation

Giraitis, Liudas and Surgailis, Donatas, Larch, Leverage and Long Memory (October 2003). LSE STICERD Research Paper No. EM460, Available at SSRN: https://ssrn.com/abstract=1162622

Liudas Giraitis (Contact Author)

University of York - Department of Mathematics and Economics ( email )

Heslington, York YO10 5DD
United Kingdom

Donatas Surgailis

Institute of Mathematics and Informatics, Lithuania ( email )

Akademijos 4
LT-2600 Vilnius

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