Some remarks on the central limit theorem for functionals of linear processes under short-range dependence

• Autorzy: Furmańczyk K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the central limit theorems for functionals G: R^m-> R of one-sided m-dimensional linear processes X_t=∑^∞_r=0 where A_r is a nonrandom matrix mxm and Z_t’s are i.i.d. random vectors in R^m.

Słowa kluczowe

EN

central limit theorem; linear process; time series; short-range dependence; Markov chain; martingale differences

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 2
• Strony: 235--245
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Furmańczyk K.

• Department of Applied Mathematics, University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776 Warszawa, Poland

Bibliografia

• [1] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
• [2] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer, New York-Berlin-Heidelberg 1987.
• [3] Y. A. Davydov, The invariance principle for stationary processes, Theory Probab. Appl. 15 (1970), pp. 487-498.
• [4] L. Giraitis, Central limit theorem for functionals of linear process, Liet. Mat. Rink. 25 (1986), pp. 43-57.
• [5] L. Giraitis and D. Surgailis, Multivariate Appel polynomials and the Central Limit Theorem, in: Dependence in Probability and Statistics: A Survey of Recent Results, Birkhäuser, Boston, MA, 1986, pp. 21-71.
• [6] C. Ho and T. Hsing, On the asymptotic expansion of the empirical process of long memory moving averages, Ann. Statist. 24 (1996), pp. 992-1024.
• [7] C. Ho and T. Hsing, Limit theorems for functional of moving averages, Ann. Probab. 25 (1997), pp. 1636-1669.
• [8] T. Hsing, Linear processes, long-range dependence and asymptotic expansions, Stat. Inference Stoch. Process. 3 (2000), pp. 19-29.
• [9] H. L. Koul and D. Surgailis, Asymptotic expansion of M-estimators with long-memory errors, Ann. Statist. 25 (1997), pp. 818-850.
• [10] H. L. Koul and D. Surgailis, Asymptotics of empirical processes of long memory moving averages with infinite variance, Stochastic Process. Appl. 91 (2001), pp. 309-336.
• [11] M. Woodroofe, A central limit theorem for functionals of a Markov chain with applications to shift, Stochastic Process. Appl. 41 (1992), pp. 33-44.
• [12] W. B. Wu, Central limit theorems for functionals of linear processes and their applications, Statist. Sinica 12 (2002), pp. 635-649.
• [13] W. B. Wu, Additive functionals of infinite-variance moving averages, Statist. Sinica 13 (2003), pp. 1259-1267.