LARCH, leverage and long memory

Liudas Giraitis, Remigijus Leipus, Peter M. Robinson and Donatas Surgailis

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Leverage; long memory; linear ARCH; LARCH; finiteness of moments (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2003-10
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:2020

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