Asymptotic inference in some heteroscedastic regression models with long memory design and errors

Annals of Statistics

Volumn 36, Issue 1, 2008, Pages 458-487

  Guo, Hongwen ^a   Koul, Hira L ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Local Whittle estimator; Model diagnostics; Moving average errors; OLS

Indexed keywords

EID: 50649124252     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000686     Document Type: Article

References (35)

1. AN, H. Z. and CHENG, B. (1991). A Kolmogorov-Smirnov type statistic with application to test for nonlinearity in time series. Internat. Statist. Rev. 59 287-307.
2. ANDREWS, D. W. K. (1995). Nonparametric kernel estimation for semiparametric models. Econometric Theory 11 560-596. MR1349935
3. ARCONES, M. (1994). Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probah. 22 2242-2274. MR1331224
4. BERAN, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York. MR 1304490
5. BERMAN, S. (1992). Sojourns and Extremes of Stochastic Processes. Wadsworth and Brooks/Cole, Pacific Grove, CA. MR1126464
6. DAHLHAUS, R. (1995). Efficient location and regression estimation for long range dependent regression models. Ann. Statist. 23 1029-1047. MR1345213
7. DALLA, V., GIRAITIS, L. and HIDALGO, J. (2006). Consistent estimation of the memory parameter for nonlinear time series. J. Time Ser. Anal. 27 211-251. MR2235845
8. DAVYDOV, J. A. (1970). The invariance principle for stationary processes. Theory Probab. Appl. 15 487-498. MR0283872
9. DEHLING, H. and TAQQU, M. S. (1989). The empirical process of some long-range dependent sequences with an application to U-statistics. Ann. Statist. 17 1767-1783. MR1026312
10. FOX, R. and TAQQU, M. (1987). Multiple stochastic integrals with dependent integrators. J. Multivariate Anal. 21 105-127. MR0877845
11. GUO, H. and KOUL, H. L. (2007). Nonparametric regression with heteroscedastic long memory errors. J. Statist. Plann. Inference 137 379-404. MR2298945
12. GIRAITIS, L., KOUL, H. L. and SURGAILIS, D. (1996). Asymptotic normality of regression estimators with long memory errors. Statist. Probab. Lett. 29 3'17-335. MR 1409327
13. HART, J. D. (1997). Nonparametric Smoothing and Lack-of-Fit Tests. Springer, New York. MR1461272
14. HENRY, M. and ROBINSON, P. (1995). Bandwidth choice in Gaussian semiparametric estimation of long range dependence. Athens Conference on Applied Probability and Time Series Analysis II 220-232. Lecture Notes in Statist. 115. Springer, New York. MR1466748
15. HIDALGO, J. and ROBINSON, P. (2002). Adapting to unknown disturbance autocorrelation in regression with long memory. Econometrica 70 1545-1581. MR1929978
16. HO, H. and HSU, N. (2005). Polynomial trend regression with long memory errors. J. Time Ser. Anal. 26 323-354. MR2163286
17. KOUL, H. L. (1992). M-estimators in linear models with long range dependent errors. Statist. Probab. Lett. 14 153-164. MR1173413
18. KOUL, H. L. and MUKHERJEE, K. (1993). Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. Probab. Theory Related Fields 95 535-553. MR1217450
19. KOUL, H. L. (1996). Asymptotics of M-estimators in non-linear regression with long-range dependent errors. Athens Conference on Applied Probability and Time Series Analysis II. Lecture Notes in Statist. 115 272-290. Springer, New York. MR1466752
20. KOUL, H. L., BAILLIE, R. and SURGAILIS, D. (2004). Regression model fitting with a long memory covariate process. Econometric Theory 20 485-512. MR2061725
21. KOUL, H. L. and STUTE, W. (1999). Nonparametric model checks for time series. Ann. Statist. 27 204-237. MR1701108
22. LAHIRI, S. N. (2003). Reampling Methods for Dependent Data. Springer, New York. MR2001447
23. LUENBERGER, D. G. (1979). Introduction to Dynamical Systems: Theory and Applications. Wiley, New York.
24. ROBINSON, P. M. (1995). Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 1630-1661. MR1370301
25. ROBINSON, P. M. (1997). Large-sample inference for nonparametric regression with dependent errors. Ann. Statist. 25 2054-2083. MR1474083
26. ROBINSON, P. and HIDALGO, J. (1997). Time series regression with long-range dependence. Ann. Statist. 25 77-104. MR1429918
27. SOULIER, P. (2001). Moment bounds and central limit theorem for functions of Gaussian vectors. Statist. Probab. Lett. 54 193-203. MR1858634
28. SURGAILIS, D. (1982). Zones of attraction of self-similar multiple integrals. Lithuanian Math. J. 22 327-340. MR0684472
29. STUTE, W. (1997). Nonparametric model checks for regression. Ann. Statist. 25 613-641. MR1439316
30. STUTE, W., THIES, S. and ZHU, L. X. (1998). Model checks for regression: An innovation process approach. Ann. Statist. 26 1916-1934. MR1673284
31. STUTE, W. and ZHU, L. X. (2002). Model checks for generalized linear models. Scand. J. Statist. 29 333-354. MR 1925573
32. TAQQU, M. (1975). Weak convergence to fractional Brownian motion and to Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31287-302. MR0400329
33. YAJIMA, Y. (1988). On estimation of a regression model with long-memory stationary errors. Ann. Statist. 16 791-807. MR0947579
34. YAJIMA, Y. (1991). Asymptotic properties of the LSE in a regression model with long-memory stationary errors. Ann. Statist. 19 158-177. MR1091844
35. ZYGMUND, A. (2002). Trigonometric Series, 3rd ed. Cambridge Univ. Press. MR1963498