Local polynomial estimators of the volatility function in nonparametric autoregression

Journal of Econometrics

Volumn 81, Issue 1, 1997, Pages 223-242

  Hardle W ^a   Tsybakov, A ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Local polynomials; Nonlinear autoregression; Nonlinear time series; Volatility

Indexed keywords

EID: 0000961658     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(97)00044-4     Document Type: Article

References (34)

1. Ango Nze, P., 1992. Critères d'ergodicité de quelques modèles à représentation markovienne. Comptes Rendus des Seances de l'Academie des Sciences Paris 315, sér 1, 1301-1304.
2. Bossaerts, P., Härdle, W., 1995. Foreign Exchange-rates have surprising volatility. SFB 373 Discussion Paper, available via FTP: amadeus.wiwi.hu.berlin.de (141.20.100.2).
3. Chan, K.S., Tong, H., 1985. On the use of deterministic Lyapunov functions for the ergodicity of stochastic difference equations. Advances in Applied Probability 17, 666-678.
4. Chen, R., Tsay, R.S., 1993a. Nonlinear additive ARX models. Journal of the American Statistical Association 88, 955-967.
5. Chen, R., Tsay, R.S., 1993b. Functional-coefficient autoregressive models. Journal of the American Statistical Association 88, 298-308.
6. Cleveland, W.S., 1979. Robust locally weighted regression and smoothing scatterplots. JASA 74, 829-836.
7. Collomb, 1984. Propriétés de convergence presque complète du prédicteur à noyau. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 66, 441-460.
8. Davydov, Yu.A., 1973. Mixing conditions for Markov chains. Theory of Probability and its Applications 18, 312-328.
9. Diebolt, J., Guégan, D., 1990. Probabilistic properties of the general nonlinear autoregressive process of order one. Technical Report No 128, L.S.T.A., Université Paris VI.
10. n+1. Comptes Rendus des Seances de l'Academie des Sciences Paris, Sér. A 297, 61-64.
11. Doukhan, P., Ghindès, M., 1981. Processus autorégressifs non-linéaires. Comptes Rendus des Seances de l'Academie des Sciences Paris, Sér. A 290, 921-923.
12. Doukhan, P., Tsybakov, A.B., 1993. Nonparametric robust estimation in nonlinear ARX models. Problems of Information Transmission 29, 24-34.
13. Engle, R.F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987-1008.
14. Engle, R.F., Gonzales-Rivera, G., 1989. Semiparametric ARCH Models. U.C.S.D. Discussion Paper.
15. Engle, R.F., Granger, W.J., Rice, J., Weiss, A., 1986. Semiparametric estimates of the relation between weather and electricity sales. Journal of the American Statistical Association 81, 310-320.
16. Fan, J., Gijbels, I., 1996. Local Polynomial Modelling. Chapman and Hall, London.
17. Gouriéroux, Ch., Monfort, A., 1992. Qualitative threshold ARCH models. Journal of Econometrics 52, 159-199.
18. Gregory, A.W., 1989. A nonparametric test for autoregressive conditional heteroscedasticity: a Markov chain approach. Journal of Business and Economic Statistics 7, 107-115.
19. Härdle, W., Klinke, S., Turlach, B., 1995. XploRe - an Interactive Statistical Computing Environment. Springer, Heidelberg.
20. Katkovnik, V.Ya., 1979. Linear and nonlinear methods of nonparametric regression analysis, Automatika, 35-46.
21. Katkovnik, V.Ya., 1985. Nonparametric Identification and Data Smoothing. Nauka, Moscow (in Russian).
22. Liptser, R.Sh., Shirjaev, A.N., 1980. A functional central limit theorem for martingales. Theory of Probability and its Applications 25, 667-688.
23. Lütkepohl, H., 1992. Introduction to Multiple Time Series Analysis. Springer, Heidelberg.
24. McKeague, I.W., Zhang, M.J., 1994. Identification of nonlinear time series from first order cumulative characteristics. Annals of Statistics 22, 495-514.
25. Mokkadem, A., 1987. Sur un modèle autorégressif nonlinéaire. Ergodicité et ergodicité géometrique. Journal of Time Series Analysis 8, 195-204.
26. Müller, H.G., 1988. Nonparametric Regression Analysis of Longitudinal Data, Springer Lecture Notes in Statistics, vol. 46. Springer, New York.
27. Nummelin, E., Tuominen, P., 1982. Geometric ergodicity of Harris-recurrent Markov chains with application to renewal theory. Stochastic Processes and their Applications 12, 187-202.
28. Robinson, P.M., 1983. Nonparametric estimators for time series. J. Time Series Analysis 4, 185-207.
29. Robinson, P.M., 1984. Robust nonparametric autoregression, In: Franke, H., Martin (Eds.), Robust and Nonlinear Time Series Analysis. Springer, Heidelberg.
30. Stone, C.J., 1977. Consistent nonparametric regression. Ann. Statist. 5, 595-645.
31. Tong, H., 1983. Threshold Models in Nonlinear Time Series Analysis, Lecture Notes in Statistics, vol. 21. Springer, Heidelberg.
32. Tweedie, R.L., 1975. Sufficient conditions for ergodicity and geometric ergodicity of Markov chains on a general state space. Stochastic Process and their Applications 3, 385-403.
33. Tsybakov, A.B., 1986. Robust reconstruction of functions by the local-approximation method. Problems of Information Transmission 22, 133-146.
34. Vieu, P., 1995. Order choice in Nonlinear Autoregressive Models. Discussion Paper, Laboratoire de Statistique et Probabilités, Université Toulouse.