Local linear fitting under near epoch dependence

Econometric Theory

Volumn 23, Issue 1, 2007, Pages 37-70

  Lu, Zudi ^a   Linton, Oliver ^b  

^a CURTIN UNIVERSITY   (Australia)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947416610     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S0266466607070028     Document Type: Article

References (55)

1. Andrews, D.W.K. (1984) Non-strong mixing autoregressive processes. Journal of Applied Probability 21, 930-934.
2. Andrews, D.W.K. (1995) Nonparametric kernel estimation for semiparametric models. Econometric Theory 11, 560-596.
3. Bandi, F. (2004) On Persistence and Nonparametric Estimation (with an application to stock return predictability). Working paper, Graduate School of Business, University of Chicago.
4. Bierens, H. (1981) Robust Methods and Asymptotic Theory. Lecture Notes in Economics and Mathematical Systems 192. Springer.
5. Billingsley, P. (1968) Convergence of Probability Measures. Wiley.
6. Bollerslev, T. (1986) Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307-327.
7. Carrasco, M. & X. Chen (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17-39.
8. Cleveland, W.S. (1979) Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74, 829-836.
9. Cleveland, W.S. & C. Loader (1996) Smoothing by local regression: Principles and methods. In W. Härdle & M.G. Schimek (eds.), Statistical Theory and Computational Aspects of Smoothing, 10-49. Physica-Verlag.
10. Cline, D.B.H. & H.M.H. Pu (1999) Geometric ergodicity of nonlinear time series. Statistica Sinica 9, 1103-1118.
11. Craven, P. & G. Wahba (1979) Smoothing noise data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerical Mathematics 31, 377-403.
12. Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.
13. Deo, C.M. ( 1973) A note on empirical processes of strong mixing sequences. Annals of Probability 1, 870-875.
14. Devroye, L. & L. Györfi (1985) Nonparametric Density Estimation: The LI View. Wiley.
15. Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of United Kingdom inflation. Econometrica 50, 987-1007.
16. Fan, J. (1992) Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998-1004.
17. Fan, J. & I. Gijbels (1992) Variable bandwidth and local linear regression smoothers. Annals of Statistics 20, 2008-2036.
18. Fan, J. & I. Gijbels (1995) Data-driven bandwidth selection in local polynomial fitting: Variable bandwidth and spatial adaption. Journal of the Royal Statistical Society, Series B 57, 371-394.
19. Fan, J. & I. Gijbels (1996) Local Polynomial Modeling and Its Applications. Chapman and Hall.
20. Fan, J. & Q. Yao (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag.
21. Gallant, A.R. (1987) Nonlinear Statistical Models. Wiley.
22. Gallant, A.R. & H. White (1988) A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. Blackwell.
23. Goródetskii, V.V. (1977) On the strong mixing properties for linear sequences. Theory of Probability and Its Applications 22, 411-413.
24. Hastie, T. & C. Loader (1993) Local regression: Automatic kernel carpentry. Statistical Science 8, 120-143.
25. Ibragimov, I.A. (1962) Some limit theorems for stationary processes. Theory of Probability and Its Applications 1, 349-382.
26. Ibragimov, I.A. & Y.V. Linnik (1971) Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff.
27. Karlsen, H.A. & D. Tjøstheim (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372-416.
28. Ling, S. & W.K. Li (1997) On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association 92, 1184-1194.
29. Lu, Z. (1996a) A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model. Statistics and Probability Letters 30, 305-311.
30. Lu, Z. (1996b) Geometric ergodicity of a general ARCH type model with applications to some typical models. Chinese Science Bulletin 41, 1630.
31. Lu, Z. (1998) On geometric ergodicity of a non-linear autoregressive (AR) model with an autoregressive conditional heteroscedastic (ARCH) term. Statistica Sinica 8, 1205-1217.
32. Lu, Z. (2001) Asymptotic normality of kernel density estimators under dependence. Annals of the Institute of Statistical Mathematics 53, 447-468.
33. 1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term. Statistics and Probability Letters 51, 121-130.
34. Masry, E. (1986) Recursive probability density estimation from weakly dependent processes. IEEE Transactions on Information Theory IT-32, 254-267.
35. Masry, E. & J. Fan (1997) Local polynomial estimation of regression functions for mixing processes. Scandinavian Journal of Statistics 24, 165-179.
36. Masry, E. & D. Tjøstheim (1995) Nonparametric estimation and identification of nonlinear ARCH time series. Econometric Theory 11, 258-289.
37. McLeish, D.L. (1975a) A maximal inequality and dependent strong laws. Annals of Probability 3, 826-836.
38. McLeish, D.L. (1975b) Invariance principles for dependent variables. Zeitschrift fur Wahrscheinlichskeittheorie und verwandte Gebiete 32, 165-178.
39. McLeish, D.L. (1977) On the invariance principle for nonstationary mixingales. Annals of Probability 5, 616-621.
40. Moloche, G. (2000) Local Nonparametric Estimation of Scalar Diffusions. Working paper, Department of Economics, MIT.
41. Nakhapetyan, B.S. (1987) An approach to proving limit theorems for dependent random variables. Theory of Probability and Its Applications 32, 535-539.
42. Nze, P.A., P. Bühlmann, & P. Doukhan (2002) Weak dependence beyond mixing and asymptotics for nonparametric regression. Annals of Statistics 30, 397-430.
43. Nze, P.A. & P. Doukhan (2004) Weak dependence: Models and applications to econometrics. Econometric Theory 20, 995-1045.
44. Pham, T.D. (1986) The mixing properties of bilinear and generalized random coefficient autoregressive models. Stochastic Processes and Their Applications 23, 291-300.
45. Pham, D.T. & L.T. Tran (1985) Some strong mixing properties of time series models. Stochastic Processes and Their Applications 19, 297-303.
46. Phillips, P.C.B. & J.Y. Park (1998) Nonstationary Density Estimation and Kernel Autoregression. Cowles Foundation Discussion paper 1181.
47. Robinson, P.M. (1983) Nonparametric estimators for time series. Journal of lime Series Analysis 4, 185-207.
48. Ruppert, D. & M.P. Wand (1994) Multivariate locally weighted least squares regression. Annals of Statistics 22, 1346-1370.
49. Saikkonen, P. (2001) Stability Results for Nonlinear Vector Autoregressions with an Application to a Nonlinear Error Correction Model. Discussion papers of Interdisciplinary Research Project 373, http://sfb.wiwi.hu-berlin.de/.
50. Stone, C.J. (1977) Consistent nonparametric regression. Annals of Statistics 5, 595-620.
51. Stone, C.J. (1980) Optimal rates of convergence for nonparametric estimators. Annals of Statistics 8, 1348-1360.
52. Tjøstheim, D. (1990) Nonlinear time series and Markov chains. Advances in Applied Probability 22, 587-611.
53. Tong, H. (1990) Nonlinear Time Series: A Dynamical System Approach. Oxford University Press.
54. Wahba, G. (1977) A survey of some smoothing problems and the method of generalized cross-validation for solving them. In P.R. Krisnaiah (ed.), Applications of Statistics, pp. 507-523. North-Holland.
55. Weiss, A.A. (1984) ARMA model with ARCH errors. Journal of Time Series Analysis 5, 129-143.