Central limit theorem for stationary linear processes

Annals of Probability

Volumn 34, Issue 4, 2006, Pages 1608-1622

  Peliorad, Magda ^a   Utev, Sergey ^b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Central limit theorem; Ergodic theorem; Martingale; Stationary linear process

Indexed keywords

EID: 33750182694     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000179     Document Type: Article

References (24)

1. BILLINGSLEY, P. (1961). The Lindeberg-Lévy theorem for martingales. Proc. Amer. Math. Soc. 12 788-792. MR0126871
2. BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley, New York. MR1700749
3. BRADLEY, R. C. (2002, 2003). Introduction to strong mixing conditions. 1, 2. Technical report, Dept. Mathematics, Indiana Univ., Bloomington. Custom Publishing of I.U., Bloomington.
4. DEDECKER, J. and MERLEVÈDE, F. (2002). Necessary and sufficient conditions for the conditional central limit theorem. Ann. Probab. 30 1044-1081. MR1920101
5. DEDECKER, J. and Rio, E. (2000). On the functional central limit theorem for stationary processes. Ann. Inst. H. Poincaré Probab. Statist. 36 1-34. MR1743095
6. DOUKHAN, P., MASSART, P. and RIO, E. (1994). The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Statist. 30 63-82. MR1262892
7. DURR, D. and GOLDSTEIN, S. (1986). Remarks on the central limit theorem for weakly dependent random variables. Lecture Notes in Math. 1158 104-118. Springer, Berlin. MR0838560
8. GORDIN, M. I. (1969). The central limit theorem for stationary processes. Soviet Math. Dokl. 101174-1176. MR0251785
9. HALL, P. and HEYDE, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York. MR0624435
10. HANNAN, E. J. (1979). The central limit theorem for time series regression. Stochastic Process. Appl. 9 281-289. MR0562049
11. HEYDE, C. C. (1974). On the central limit theorem for stationary processes. Z. Wahrsch. Verw. Gebiete 30 315-320. MR0372955
12. IBRAGIMOV, I. A. (1960). On asymptotic distribution of values of certain sums. Vestnik Leningrad. Univ. 15 55-69. (In Russian.) MR0120679
13. IBRAGIMOV, I. A. (1962). Some limit theorems for stationary processes. Theory Probab. Appl. 7349-382. MR0148125
14. IBRAGIMOV, I. A. (1963). A central limit theorem for a class of dependent random variables. Theory Probab. Appl. 8 83-89. MR0151997
15. IBRAGIMOV, I. A. and LINNIK, YU. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters, Groningen. MR481287
16. kt). Ann. of Math. (2) 4733-49. MR0015548
17. MAXWELL, M. and WOODROOFE, M. (2000). Central limit theorems for additive functionals of Markov chains. Ann. Probab. 28 713-724. MR1782272
18. MCLEISH, D. L. (1977). On the invariance principle for nonstationary mixingales. Ann. Probab. 5616-621. MR0445583
19. PELIGRAD, M. (1981). An invariance principle for dependent random variables. Z. Wahrsch. Verw. Gebiete 57 495-507. MR0631373
20. PELIGRAD, M. and UTEV, S. (1997). Central limit theorem for linear processes. Ann. Probab. 25443-456. MR1428516
21. RIO, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants. Mathém. Appl. SMAI 31. Springer, Berlin. MR2117923
22. VOLNÝ, D. (1993). Approximating martingales and the central limit theorem for strictly stationary processes. Stochastic Process. Appl. 44 41-74. MR1198662
23. WU, W. B. (2002). Central limit theorems for functionals of linear processes and their applications. Statist. Sinica 12 635-649. MR 1902729
24. WU, W. B. and MIN, W. (2005). On linear processes with dependent innovations. Stochastic Process. Appl. 115 939-958. MR2138809