Multivariate local polynomial fitting for martingale nonlinear regression models

Annals of the Institute of Statistical Mathematics

Volumn 51, Issue 4, 1999, Pages 691-706

  Lu, Zhan Qian ^a,b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b Parametric Technology Corporation   (United States)

Author keywords

Confidence intervals; Nonlinearity in time series; Nonparametric estimation; Partial derivative estimation; Sunspots data

Indexed keywords

EID: 6544265018     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004083213922     Document Type: Article

References (14)

1. Castellana, J. V. and Leadbetter, M. R. (1986). On smoothed probability density estimation for stationary processes, Stochastic. Process. Appl., 21, 179-193.
2. Fan, J. and Gijbel, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall, London.
3. Härdle, W. and Tsybakov, A. (1997). Local polynomial estimators of the volatility function in nonparametric autoregression, J. Econometrics, 81, 223-242.
4. Härdle, W., Tsybakov, A. and Yang, L. (1996). Nonparametric vector autoregression, Working Papers, No. 61, Humboldt University, Berlin.
5. Lu, Z. Q. (1996). Multivariate locally weighted polynomial fitting and partial derivative estimation, J. Multivariate. Anal., 59, 187-205.
6. Masry, E. (1996). Multivariate regression estimation: local polynomial fitting for time series, Stochastic. Process. Appl., 65(1), 81-101.
7. Masry, E. and Fan, J. (1997). Local polynomial estimation of regression functions for mixing processes, Scand. J. Statist., 24(2), 165-179.
8. Mills, T. C. (1993). The Econometric Modelling of Financial Time Series, Cambridge University Press, Cambridge.
9. Nychka, D., Ellner, S., McCaffrey, D. and Gallant, A. R. (1992). Finding chaos in noisy systems, J. Roy. Statist. Soc. Ser. B, 54(2), 399-426.
10. Priestley, M. B. (1988). Non-linear and Non-stationary Time Series Analysis, Academic Press, London.
11. Ruppert, D. and Wand, M. P. (1994). Multivariate locally weighted least squares regression, Ann. Statist., 22(3), 1346-1370.
12. Shiryayev, A. N. (1984). Probability, Springer, New York.
13. Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach, Oxford University Press, Oxford.
14. Welsh, A. H. (1996). Robust estimation of smooth regression and spread functions and their derivatives, Statist. Sinica, 6, 347-366.