Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Taufer, Emanuele 2006. Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions. Journal of Statistical Planning and Inference 136 (4) , pp. 1220-1236. 10.1016/j.jspi.2004.09.011

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Abstract

We provide an asymptotic result for the distribution of functionals of continuous Gaussian processes with long memory. Much of the existing literature on the subject resorts to asymptotic representations based on stochastic integrals. However, the method of proof used here, based on characteristic functions, enables one to extend the class of functionals for which we are able to provide an asymptotic representation. Next, we study the properties of the asymptotic process and finally, as an application, we consider the case of continuous regression where the process of errors follows a Gamma process with long-range dependence.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Gaussian process; Gamma process; Long-range dependence; Characteristic function; Continuous polynomial regression
Publisher:	Elsevier
ISSN:	0378-3758
Last Modified:	20 Oct 2022 07:54
URI:	https://orca.cardiff.ac.uk/id/eprint/26894

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