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

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In this paper we consider the central limit theorems for functionals G: Rm-> R of one-sided m-dimensional linear processes Xt=∑r=0 where Ar is a nonrandom matrix mxm and Zt’s are i.i.d. random vectors in Rm.
Twórcy
  • Department of Applied Mathematics, University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776 Warszawa, Poland, konfur@wp.pl
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.
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  • [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.
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