Consistent estimation of a general nonparametric regression function in time series

Journal of Econometrics

Volumn 152, Issue 1, 2009, Pages 70-78

  Linton, Oliver ^a   Sancetta, Alessio ^b  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Kernel; Regression; Time series

Indexed keywords

CONDITIONAL DISTRIBUTION; CONSISTENT ESTIMATION; ERGODICITY CONDITION; KERNEL; NONPARAMETRIC REGRESSION FUNCTIONS; REGRESSION; REGRESSION FUNCTION; SMOOTHNESS CONDITIONS; STATIONARITY;

ESTIMATION; TIME SERIES;

REGRESSION ANALYSIS;

EID: 68649125002     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2009.02.006     Document Type: Article

References (43)

1. Algoet P. Universal schemes for prediction, gambling and portfolio selection. Annals of Probability 20 (1992) 901-941
2. Backus, D.K., Gregory, A.W., 1992. Theoretical relations between risk premiums and conditional variances. Working paper EC-92-18, Stern School of Business, NYU
3. Clarkson J.A., and Adams C.R. On definitions of bounded variation for functions of two variables. Transactions of the American Mathematical Society 35 (1933) 824-854
4. Collomb G. Nonparametric time series analysis and prediction: Uniform almost sure convergence. Statistics 2 (1985) 197-307
5. Dawid A.P. In: Kotz S., Read C.B., and Banks D.L. (Eds). Prequential Analysis. Encyclopedia of Statistical Sciences vol. 1 (1997), Wiley 464-470
6. Devroye L. On the almost everywhere convergence of nonparametric regression function estimates. Annals of Statistics 9 (1981) 1310-1319
7. Ferraty F., and Vieu P. Nonparametric Functional Data Analysis (2007), Springer Verlag, Berlin
8. Gennotte G., and Marsh T. Valuations in economic uncertainty and risk premiums on capital assets. European Economic Review 37 (1993) 1021-1041
9. Gennotte, G., Marsh, T., 1998. Valuations in economic uncertainty and risk premiums on capital assets, UC Berkeley, manuscript
10. Gray R. Probability, Random Processes, and Ergodic Properties (1998), Springer, New York. http://www-ee.stanford.edu/~gray/arp.pdf Revised version downloadable: http://www-ee.stanford.edu/~gray/arp.pdf
11. Gyorfi L., Morvai G., and Yakowitz S. Limits to consistent on-line forecasting for ergodic time series. IEEE Transactions on Information Theory 44 (1998) 886-892
12. Gyorfi L., Kohler M., Krzyzak A., and Walk H. A Distribution Free Theory of Nonparametric Regression (2002), Springer-Verlag, New York
13. Härdle W., and Vieu P. Kernel regression smoothing of time series. Journal of Time Series Analysis 13 (1992) 209-232
14. Karlsen H.A., and Tjostheim D. Nonparametric estimation in null recurrent time series. Annals of Statistics 29 (2001) 372-416
15. Linton O., and Mammen E. Estimating semiparametric ARCH(∞) models by kernel smoothing. Econometrica 73 (2005) 771-836
16. Linton O.B., and Nielsen J.P. A kernel method of estimating structured nonparametric regression using marginal integration. Biometrika 82 (1995) 93-100
17. Linton O.B., and Perron B. The shape of the risk premium: Evidence from a semiparametric generalized autoregressive conditional model. Journal of Business & Economic Statistics (2003) 354-367
18. Lu Z., and Linton O.B. Asymptotic distributions for local polynomial nonparametric regression estimators under weak dependence. Econometric Theory 23 (2007) 37-70
19. Mammen E., Linton O.B., and Nielsen J.P. The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of Statistics 27 (1999) 1443-1490
20. Masry E. Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17 (1996) 571-599
21. Masry E., and Fan J. Local polynomial estimation of regression functions for mixing processes. Scandinavian Journal of Statistics 24 (1997) 165-179
22. Masry E. Nonparametric regression for dependent functional data: Asymptotic normality. Stochastic Processes and their Applications 115 1 (2005) 155-177
23. Merton R.C. An intertemporal capital asset pricing model. Econometrica 41 (1973) 867-887
24. Morvai G., Yakowitz S., and Gyorfi L. Nonparametric inference for ergodic stationary time series. Annals of Statistics 24 (1996) 370-379
25. Morvai G., Yakowitz S., and Algoet P. Weakly convergent nonparametric forecasting of stationary time series. IEEE Transation on Information Theory 43 (1997) 483-498
26. Ornstein D.S. Guessing the next output of a stationary process. Israel Journal of Mathematics 30 (1978) 292-296
27. Pagan A.R., and Hong Y.S. Non-parametric estimation and the risk premium. In: Barnett W.A., Powell J., and Tauchen G. (Eds). Nonparametric and Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium in Economic Theory and Econometrics (1990), Cambridge University Press 51-75
28. Pagan A.R., and Hong Y.S. Nonparametric Estimation and the Risk Premium. In: Barnett W., Powell J., and Tauchen G.E. (Eds). Nonparametric and Semiparametric Methods in Econometrics and Statistics (1991), Cambridge University Press
29. Pagan A.R., and Ullah A. The econometric analysis of models with risk terms. Journal of Applied Econometrics 3 (1988) 87-105
30. Phillips, P.C.B., Park, J.Y., 1998. Nonstationary density estimaiton and kernel autoregression. Cowles Foundation Discussion Paper no. 1181
31. Rio E. Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants (2000), Springer, Paris
32. Robinson P.M. Nonparametric estimation for time series models. Journal of Time Series Analysis 4 (1983) 185-208
33. Robinson P.M. On the consistency and finite-sample properties of nonparametric kernel time series regression, autoregression and density estimators. Annals of the Institute of Statistical Mathematics 38 (1986) 539-549
34. Rosenblatt M. Density estimates and Markov processes. In: Puri M.L. (Ed). Nonparametric Techniques in Statistical Inference (1970), Cambridge University Press, Cambridge 199-210
35. Rosenblatt M. Curve estimates. Annals of Mathematical Statistics 42 (1971) 1815-1842
36. Roussas G. Nonparametric estimation in Markov processes. Annals of the Institute of Statistical Mathematics 21 (1967) 73-87
37. K with common marginals. Journal of Theoretical Probability 20 (2007) 371-380 Downloadable: http://arxiv.org/abs/math.PR/0606462
38. Sancetta,, 2007b. Nearest neighbor conditional estimation for harris recurrent Markov chains. Preprint. Downloadable: http://www.sancetta.googlepages.com/academicpublications
39. Seillier-Moiseiwitsch F., and Dawid A.P. On testing the validity of sequential probability forecasts. Journal of American Statistical Association 88 (1993) 355-359
40. Stone C.J. Additive regression and other nonparametric models. Annals of Statistics 13 (1985) 685-705
41. Tong H. Non-linear Time Series: A Dynamical System Approach (1990), Clarendon Press, Oxford
42. Tuan P.D. Nonparametric Estimation of the Drift Coefficient in the Diffusion Equation Statistics (1981), Taylor & Francis
43. Van der Vaart A., and Wellner J.A. Weak Convergence and Empirical Processes. Springer Series in Statistics (2000), Springer, New York