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LARCH, leverage and long memory

Giraitis, Liudas, Leipus, Remigijus, Robinson, Peter M. and Surgailis, Donatas (2003) LARCH, leverage and long memory. Econometrics; EM/2003/460 (EM/03/460). Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.

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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.

Item Type: Monograph (Discussion Paper)
Official URL:
Additional Information: © 2003 the authors
Divisions: Economics
Subjects: H Social Sciences > HB Economic Theory
JEL classification: C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C22 - Time-Series Models
Date Deposited: 27 Apr 2007
Last Modified: 12 Dec 2020 00:39

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