Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models

Gao, Jiti (2012): Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models.

Abstract

In this paper, we consider some identification, estimation and specification problems in a class of semi-linear time series models. Existing studies for the stationary time series case have been reviewed and discussed. We also establish some new results for the integrated time series case. In the meantime, we propose a new estimation method and establish a new theory for a class of semi-linear nonstationary autoregressive models. In addition, we discuss certain directions for further research.

• Item Type: MPRA Paper
• Language: English
• Keywords: Asymptotic theory, departure function, kernel method, nonlinearity, nonstationarity, semiparametric model, stationarity, time series
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Chen, J., Gao, J. and Li, D. (2011). Estimation in semiparametric time series models (invited paper). Statistics and Its Interface 4, 243--252.

Chen, J., Gao, J. and Li, D. (2012). Estimation in semiparametric regression with nonstationary regressors Bernoulli 18, 678-702.

Chung, K. L. (1967). Markov Chains with Stationary Transition Probabilities. Springer--Verlag, 2nd Edition.

Fan, J. and Gijbels, I. (1996). Local Polynomial Modeling and Its Applications. Chapman and Hall, London.

Fan, J., Wu, Y. and Feng, Y. (2009). Local quasi-likelihood with a parametric guide. Annals of Statistics 37, 4153--4183.

Fan, J. and Yao, Q. (2003). Nonlinear Time Series: parametric and nonparametric methods. Springer, New York.

Gao, J. (1992) {\em Large Sample Theory in Semiparametric Regression. Doctoral Thesis at the Graduate School of the University of Science and Technology of China, Hefei, China.

Gao, J. (1995). Parametric test in a partially linear model. Acta Mathematica Scientia (English Edition) 15, 1--10.

Gao, J. (2007). Nonlinear Time Series: semi- and non--parametric methods. Chapman and Hall, London.

Gao, J. and Gijbels, I. (2008). Bandwidth selection in nonparametric kernel testing. Journal of the American Statistical Association 484, 1584-1594.

Gao, J., King, M. L., Lu, D. and Tjostheim, D. (2009a). Nonparametric specification testing for nonlinear time series with nonstationarity. Econometric Theory 25, 1869--1892.

Gao, J., King, M. L., Lu, D. and Tjostheim, D. (2009b). Specification testing in nonlinear and nonstationary time series autoregression. Annals of Statistics 37, 3893--3928.

Gao, J. and Phillips, P. C. B. (2011). Semiparametric estimation in multivariate nonstationary time series models. Working paper at http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp17-11.pdf.

Gao, J., Tj{\o}stheim, D. and Yin, J. (2012). Estimation in threshold autoregressive models with a stationary and a unit root regime (http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp21-11.pdf). Forthcoming in Journal of Econometrics 170.

Glad, I. (1998). Parametrically guided nonparametric regression. Scandinavian Journal of Statistics 25, 649--668.

Granger, C. W. J., Inoue, T. and Morin, N. (1997). Nonlinear stochastic trends. Journal of Econometrics 81, 65--92.

H\"{a}rdle, W., Liang, H. and Gao, J. (2000). Partially Linear Models. Springer Series in Economics and Statistics. Physica-Verlag, New York.

Juhl, T. and Xiao, Z. (2005). Partially linear models with unit roots. Econometric Theory 21, 877--906.

Karlsen, H. A. and Tjostheim, D. (2001). Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372--416.

Li, D., Gao, J., Chen, J. and Lin, Z. (2011). Nonparametric estimation and specification testing in nonlinear and nonstationary time series models. Working paper available at www.jitigao.com.

Li, Q. and Racine, J. (2007). Nonparametric Econometrics: theory and practice. Princeton University Press, Princeton.

Martins-Filho, C., Mishra, S. and Ullah, A. (2008). A class of improved parametrically guided nonparametric regression estimators. Econometric Reviews 27, 542--573.

Masry, E. and Tjostheim, D. (1995). Nonparametric estimation and identification of nonlinear ARCH time series. Econometric Theory 11, 258--289.

Nummelin, E. (1984). General Irreducible Markov Chains and Non-negative Operators. Cambridge University Press.

Owen, A. (1991). Empirical likelihood for linear models. Annals of Statistics 19, 1725--1747.

Park, J. Y. and Phillips, P. C. B. (2001). Nonlinear regressions with integrated time series. Econometrica 69, 117--162.

Robinson, P. M. (1988). Root--N--consistent semiparametric regression. Econometrica 56, 931--964.

Terasvirta, T., Tjjstheim, D., Granger, C. W. J. (2010). Modelling Nonlinear Economic Time Series. Oxford University Press, Oxford.

Tong, H. (1990). Nonlinear Time Series: a Dynamical System Approach. Oxford University Press, Oxford.

Wang, Q. Y. and Phillips, P. C. B. (2009). Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710-738.

Wang, Q. Y. and Phillips, P. C. B. (2011). Asymptotic theory for zero energy functionals with nonparametric regression application. Econometric Theory 27, 235--259.

Wang, Q. Y. and Phillips, P. C. B. (2012). Specification testing for nonlinear cointegrating regression. Forthcoming in Annals of Statistics 40.

\item Xia, Y., Tong, H. and Li, W. K. (1999). On extended partially linear single--index models. {\em Biometrika} {\bf 86}, 831--842.