 LARCH, Leverage and Long MemoryLiudas Giraitis, Remigijus Leipus, Peter M Robinson and Donatas Surgailis STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 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) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:460 Access Statistics for this paper More papers in STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE |
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