Efficient estimation of conditional variance functions in stochastic regression

Biometrika

Volumn 85, Issue 3, 1998, Pages 645-660

  Fan, Jianqing ^a   Yao, Qiwei ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Absolutely regular; ARCH; Conditional variance; Efficient estimator, heteroscedasticity; Local linear regression; Nonlinear time series; Volatility

Indexed keywords

EID: 0000871211     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/85.3.645     Document Type: Article

References (31)

1. AïT-SAHALIA, Y. (1996). Nonparametric pricing of interest rate derivative securities. Econometrica 64, 527-60.
2. ANDERSEN, T. G. & LUND, J. (1997). Estimating continuous time stochastic volatility models of the short term interest rate. J. Economet. 77, 343-77.
3. ANDERSON, T. W. (1971). The Statistical Analysis of Time Series, New York: Wiley.
4. Box, G. E. P. (1988). Signal-to-noise ratios, performance criteria, and transformations. Teclmometrics 30,1-17.
5. CARROLL, R. J. & RUPPERT, D. (1988). Transformations and Weighting in Regression. London: Chapman & Hall.
6. CHAN, K. C., KAROLYI, A. G., LONGSTAFF, F. A. & SANDERS, A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. J. Finance 47, 1209-27.
7. Cox, J. C., INGERSOLL, J. E. & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica 53, 385-467.
8. ENGLE, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of U.K. inflation. Econometrica 50, 987-1008.
9. FAN, J. (1993). Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21, 196-216.
10. FAN, J. & GIJBELS, I. (1992). Variable bandwidth and local linear regression smoothers. Ann. Statist. 20, 2008-36.
11. FAN, J. & GIJBELS, I. (1995). Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J. R. Statist. Soc. B 57, 371-94.
12. FAN, J. & GIJBELS, I. (1996). Local Polynomial Modelling and its Applications. London: Chapman & Hall.
13. FLORENS-ZMIROU, D. (1993). On estimating the diffusion coefficient from discrete observations. J. Appl. Prob. 30, 790-804.
14. GALLANT, A. R. & TAUCHEN, G. (1997). Estimation of continuous time models for stock returns and interest rates. Macroecon. Dyn. I, 135-68.
15. GASSER, T., SROKA, L. & JENNEN-STEINMETZ, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika 73, 625-33.
16. GENON-CATALOT, V. & JACOD, J. (1993). On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Ann. Inst. H. Poincare Prob. Statist. 29, 119-51.
17. HALL, P. & CARROLL, R. J. (1989). Variance function estimation in regression: the effect of estimation of the mean. J. R. Statist. Soc. B 51, 3-14.
18. HALL, P., KAY, J. W. & TITTERINGTON, D. M. (1990). Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika 77, 521-8.
19. HäRDLE, W. & TSYBAKOV, A. (1997). Local polynomial estimators of the volatility function in nonparametric autoregression. J. Economet. 81, 233-42.
20. HASTIE, T. J. & LOADER, C. (1993). Local regression: automatic kernel carpentry (with Discussion). Statist. Sei. 8, 120-43.
21. MüLLER, H. C. & STADTMüLLER, U. (1987). Estimation of heteroscedasticity in regression analysis. Ann. Statist. 15, 610-25.
22. MüLLER, H. G. & STADTMüLLER, U. (1993). On variance function estimation with quadratic forms. J. Statist. Plan. Inf. 35, 213-31.
23. NEUMANN, M. H. (1994). Fully data-driven nonparametric variance estimators. Statistics 25, 189-212.
24. PELIGRAD, M. (1986). Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables. In Dependence in Probability and Statistics, Ed. E. Eberlein and M. S. Taqqu, pp. 193-223. Boston: Birkhäuser
25. RICE, J. (1984). Bandwidth choice for nonparametric kernel regression. Ann. Statist. 12, 1215-30.
26. RUPPERT, D., SHEATHER, S. J. & WAND, M. P. (1995). An effective bandwidth selector for local least squares regression. J. Am. Statist. Assoc. 90, 1257-70.
27. RUPPERT, D. & WAND, M. P. (1994). Multivariate weighted least squares regression. Ann. Statist. 22,1346-70.
28. RUPPERT, D., WAND, M. P., HOLST, U. & HöSSJER, O. (1997). Local polynomial variance function estimation. Teclmometrics 39, 262-73.
29. STANTON, R. (1998). A nonparametric model of term structure dynamics and the market price of interest rate risk. J. Finance. To appear.
30. YAO, Q. & TONG, H. (1994). Quantifying the influence of initial values on nonlinear prediction. J. R. Statist. Soc. B 56, 701-25.
31. YOSHIHARA, K. (1976). Limiting behaviour of U-statistics for stationary absolutely regular processes. Z. Wahr. verw. Geb. 35, 237-52.