The live method for generalized additive volatility models

Econometric Theory

Volumn 20, Issue 6, 2004, Pages 1094-1139

  Kim, Woocheol ^a,c   Linton, Oliver ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^c The Korea Institute of Public Finance   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9944222383     PISSN: 02664666     EISSN: None     Source Type: Journal    
DOI: 10.1017/s026646660420603x     Document Type: Article

References (46)

1. Andrews, D.W.K. (1994) Empirical process methods in econometrics. In R.F. Engle & D. McFadden (eds.), Handbook of Econometrics, vol. IV, pp. 2247-2294. North-Holland.
2. Auestadt, B. & D. Tjøstheim (1990) Identification of nonlinear time series: First order characterization and order estimation. Biometrika 77, 669-687.
3. Avramidis, P. (2002) Local maximum likelihood estimation of volatility function. Manuscript, LSE.
4. Breiman, L. & J.H. Friedman (1985) Estimating optimal transformations for multiple regression and correlation (with discussion). Journal of the American Statistical Association 80, 580-619.
5. Buja, A., T. Hastie, & R. Tibshirani (1989) Linear smoothers and additive models (with discussion). Annals of Statistics 17, 453-555.
6. Cai, Z. & E. Masry (2000) Nonparametric estimation of additive nonlinear ARX time series: Local linear fitting and projections. Econometric Theory 16, 465-501.
7. Carrasco, M. & X. Chen (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17-39.
8. Chen, R. (1996) A nonparametric multi-step prediction estimator in Markovian structures. Statistical Sinica 6, 603-615.
9. Chen, R. & R.S. Tsay (1993a) Nonlinear additive ARX models. Journal of the American Statistical Association 88, 955-967.
10. Chen, R. & R.S. Tsay (1993b) Functional-coefficient autoregressive models. Journal of the American Statistical Association 88, 298-308.
11. Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987-1008.
12. Fan, J. & Q. Yao (1996) Efficient estimation of conditional variance functions in stochastic regression. Biometrica 85, 645-660.
13. Gozalo, P. & O. Linton (2000) Local nonlinear least squares: Using parametric information in nonparametric regression. Journal of Econometrics 99(1), 63-106.
14. Hall, P. & C. Heyde (1980) Martingale Limit Theory and Its Application. Academic Press.
15. Härdle, W. (1990) Applied Nonparametric Regression. Econometric Monograph Series 19. Cambridge University Press.
16. Härdle, W. & A.B. Tsybakov (1997) Locally polynomial estimators of the volatility function. Journal of Econometrics 81, 223-242.
17. Härdle, W., A.B. Tsybakov, & L. Yang (1998) Nonparametric vector autoregression. Journal of Statistical Planning and Inference 68(2), 221-245.
18. Hardie, W. & P. Vieu (1992) Kernel regression smoothing of time series. Journal of Time Series Analysis 13, 209-232.
19. Hastie, T. & R. Tibshirani (1990) Generalized Additive Models. Chapman and Hall.
20. Hastie, T. & R. Tibshirani (1987) Generalized additive models: Some applications. Journal of the American Statistical Association 82, 371-386.
21. Horowitz, J. (2001) Estimating generalized additive models. Econometrica 69, 499-513.
22. Jones, M.C., S.J. Davies, & B.U. Park (1994) Versions of kernel-type regression estimators. Journal of the American Statistical Association 89, 825-832.
23. Kim, W., O. Linton, & N. Hengartner (1999) A computationally efficient oracle estimator of additive nonparametric regression with bootstrap confidence intervals. Journal of Computational and Graphical Statistics 8, 1-20.
24. Linton, O.B. (1996) Efficient estimation of additive nonparametric regression models. Biometrika 84, 469-474.
25. Linton, O.B. (2000) Efficient estimation of generalized additive nonparametric regression models. Econometric Theory 16, 502-523.
26. Linton, O.B. & W. Hardie (1996) Estimating additive regression models with known links. Biometrika 83, 529-540.
27. Linton, O.B. & J. Nielsen (1995) A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82, 93-100.
28. Linton, O.B., J. Nielsen, & S. van de Geer (2003) Estimating multiplicative and additive hazard functions by kernel methods. Annals of Statistics 31, 464-492.
29. Linton, O.B., N. Wang, R. Chen, & W. Härdle (1995) An analysis of transformation for additive nonparametric regression. Journal of the American Statistical Association 92, 1512-1521.
30. Mammen, E., O.B. Linton, & J. Nielsen (1999) The existence and asymptotic properties of a back-fitting projection algorithm under weak conditions. Annals of Statistics 27, 1443-1490.
31. Masry, E. (1996) Multivariate local polynomial regression for time series: Uniform strong consistency and rates. Journal of Time Series Analysis 17, 571-599.
32. Masry, E. & D. Tjøstheim (1995) Nonparametric estimation and identification of nonlinear ARCH time series: Strong convergence and asymptotic normality. Econometric Theory 11, 258-289.
33. Masry, E. & D. Tjøstheim (1997) Additive nonlinear ARX time series and projection estimates. Econometric Theory 13, 214-252.
34. Nelson, D.B. (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347-370.
35. Newey, W.K. (1994) Kernel estimation of partial means. Econometric Theory 10, 233-253.
36. Opsomer, J.D. & D. Ruppert (1997) Fitting a bivariate additive model by local polynomial regression. Annals of Statistics 25, 186-211.
37. Pollard, D. (1990) Empirical Processes: Theory and Applications. CBMS Conference Series in Probability and Statistics, vol. 2. Institute of Mathematical Statistics.
38. Robinson, P.M. (1983) Nonparametric estimation for time series models. Journal of Time Series Analysis 4, 185-208.
39. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall.
40. Stein, E.M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press.
41. Stone. C.J. (1985) Additive regression and other nonparametric models. Annals of Statistics 13, 685-705.
42. Stone, C.J. (1986) The dimensionality reduction principle for generalized additive models. Annals of Statistics 14, 592-606.
43. Tjøstheim, D. & B. Auestad (1994) Nonparametric identification of nonlinear time series: Projections. Journal of the American Statistical Association 89, 1398-1409.
44. Volkonskii, V. & Y. Rozanov (1959) Some limit theorems for random functions. Theory of Probability and Applications 4, 178-197.
45. Yang, L., W. Härdle, & J. Nielsen (1999) Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis 20, 579-604.
46. Ziegelmann, F. (2002) Nonparametric estimation of volatility functions: The local exponential estimator. Econometric Theory 18, 985-992.