Nonparametric arch with additive mean and multiplicative volatility: A new estimation procedure

Statistica e Applicazioni

Volumn 7, Issue 1, 2009, Pages 63-76

  Bagnato, Luca ^a  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Additive mean; Backfitting; Local polynomial regression; Multiplicative volatility; Residual based estimator

Indexed keywords

EID: 84858009056     PISSN: 18246672     EISSN: 22836659     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Ango Nze P. (1992). Criteria of ergodicity for some models with a markovian representation. Comptes Rendus de l'Académie des Sciences, Série I: Mathématique, 315(12), 1301-1304.
2. Bellman R. (1961). Adaptive Control Process. Princeton University Press, Princeton.
3. Diebolt J., Guégan D. (1993). Tail behaviour of the stationary density of general non-linear autoregressive processes of order 1. Journal of Applied Probability, 30, 315-329.
4. Fan J., Yao Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645-660.
5. Gourieroux C., Monfort A. (1992). Qualitative threshold ARCH models. Journal of Econometrics, 52, 159-199.
6. Härdle W., Tsybakov A. (1997). Local polynomial estimators of the volatility function in nonparametric autoregression. Journal of Econometrics, 81, 223-242.
7. Jianqing F., Qiwei Y. (2003). Nonlinear time series: nonparametric and parametric methods. Springer, New York.
8. Mammen E., Linton O., Nielsen J. (1999). The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. The Annals of Statistics, 27(5), 1443-1490.
9. Masry E., Tjstheim D. (1992). Non-parametric estimation and identification of arch and arx nonlinear time series: convergence properties and rates. Preprint, Department of Mathematics, University of Bergen.
10. Mokkadem A. (1987). On a non linear autoregressive model, ergodicity and geometric ergodicity (French). Journal of Time Series Analysis, 8, 195-204.
11. Nelson D. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59, 347-370.
12. Nummelin E., Tuominen P. (1982). Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stochastic Processes and their Applications, 12, 187-202.
13. Tjøstheim D. (1990). Non-linear time series and Markov chains. Advances in Applied Probability, 22, 587-611.
14. Tjstheim D., Auestad, B. (1999). Nonparametric identification of nonlinear time series: Selecting significant lags. Journal of the American Statistical Association, 89, 1410-1419.
15. Tweedie R.L. (1975). Sufficient conditions for regularity, recurrence and ergodicity of Markov processes (STMA V20 561). Mathematical Proceedings of the Cambridge Philosophical Society, 78, 125-136.
16. Vieu P. (1994). Choice of regressors in nonparametric estimation. Computational Statistics & Data Analysis, 17, 575-594.
17. Yang L., Hardle W., Nielsen J.P. (1999). Nonparametric autoregression with multiplicative volatility and additive mean. Journal of Time Series Analysis, 20, 579-604.