The sample ACF of a simple bilinear process

Bojan Basrak, Richard A. Davis and Thomas Mikosch

Stochastic Processes and their Applications, 1999, vol. 83, issue 1, 1-14

Abstract: We consider a simple bilinear process Xt=aXt-1+bXt-1Zt-1+Zt, where (Zt) is a sequence of iid N(0,1) random variables. It follows from a result by Kesten (1973, Acta Math. 131, 207-248) that Xt has a distribution with regularly varying tails of index [alpha]>0 provided the equation Ea+bZ1u=1 has the solution u=[alpha]. We study the limit behaviour of the sample autocorrelations and autocovariances of this heavy-tailed non-linear process. Of particular interest is the case when [alpha]

Keywords: Sample; autocorrelation; Sample; autocovariance; Heavy; tails; Infinite; variance; Stable; distribution; Convergence; of; point; processes; Mixing; condition; Stochastic; recurrence; equation; Bilinear; process (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (5)

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