Naslov
The sample ACF of a simple bilinear process

Autori
Basrak, Bojan ; Davis, Richard A. ; Mikosch, Thomas

Izvornik
Stochastic processes and their applications (0304-4149) 83 (1999), 1; 1-14

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
sample autocorrelation ; sample autocovariance ; heavy tails ; infinite variance ; stable distribution ; convergence of point processes ; mixing condition ; stochastic recurrence equation ; bilinear process

Sažetak
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 greek small letter alpha>0 provided the equation E|a+bZ1|u=1 has the solution u=greek small letter 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 greek small letter alpha<4. If greek small letter alphaset membership, variant(0, 2) we prove that the sample autocorrelations converge to non-degenerate limits. If greek small letter alphaset membership, variant(2, 4) we prove joint weak convergence of the sample autocorrelations and autocovariances to non-normal limits.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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