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.

Weak convergence of functionals of stationary processes to Rosenblatt-type distributions / Taufer, Emanuele; N., Leonenko. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - STAMPA. - 136:4(2006), pp. 1220-1236.

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

Taufer, Emanuele;
2006-01-01

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.
2006
4
Taufer, Emanuele; N., Leonenko
Weak convergence of functionals of stationary processes to Rosenblatt-type distributions / Taufer, Emanuele; N., Leonenko. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - STAMPA. - 136:4(2006), pp. 1220-1236.
File in questo prodotto:
File Dimensione Formato  
Taufer_3.pdf

Solo gestori archivio

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 168.59 kB
Formato Adobe PDF
168.59 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/19382
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 13
  • OpenAlex ND
social impact