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NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY

Published online by Cambridge University Press:  01 December 2009

Jiti Gao ,
Maxwell King ,
Zudi Lu  and
Dag Tjøstheim
Jiti Gao*
Affiliation:
University of Adelaide
Maxwell King
Affiliation:
Monash University
Zudi Lu
Affiliation:
University of Adelaide
Dag Tjøstheim
Affiliation:
University of Bergen
*
*Address correspondence to Jiti Gao, School of Economics, University of Adelaide, Adelaide SA 5005, Australia; e-mail: [email protected].
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Abstract

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test statistic. Both the setting and the results differ from earlier work on nonparametric time series regression with stationarity. In addition, we develop a bootstrap simulation scheme for the selection of suitable bandwidth parameters involved in the kernel test as well as the choice of simulated critical values. An example of implementation is given to show that the proposed test works in practice.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009 , pp. 1869 - 1892
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Brockwell, P. & Davis, R. (1990) Time Series Theory and Methods. Springer.Google Scholar
Chen, J., Gao, J., & Li, D. (2008) Semiparametric regression estimation in null recurrent time series. Working paper, University of Adelaide; available at http://www.adelaide.edu.au/directory/jiti.gao.Google Scholar
Chow, Y.S. & Teicher, H. (1988) Probability Theory. Springer-Verlag.Google Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Engle, R.F. & Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation and testing. Econometrica 55, 251–276.Google Scholar
Fan, J. & Yao, Q. (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer.Google Scholar
Fan, Y. & Linton, O. (2003) Some higher-theory for a consistent nonparametric model specification test. Journal of Statistical Planning and Inference 109, 125–154.Google Scholar
Gao, J. (2007) Nonlinear Time Series: Semiparametric and Nonparametric Methods. Chapman & Hall/CRC.Google Scholar
Gao, J. & Gijbels, I. (2008) Bandwidth selection in nonparametric kernel testing. Journal of the American Statistical Association 484, 1584–1594.Google Scholar
Gao, J. & King, M.L. (2004) Adaptive testing in continuous-time diffusion models. Econometric Theory 20, 844–883.CrossRefGoogle Scholar
Gao, J., King, M.L., Lu, Z., & Tjøstheim, D. (2007) Specification Testing in Nonlinear Time Series with Nonstationarity. Working paper, University of Adelaide; available at http://www.adelaide.edu.au/directory/jiti.gao.Google Scholar
Gao, J., Lu, Z., & Tjøstheim, D. (2006) Estimation in semiparametric spatial regression. Annals of Statistics 34, 1395–1435.Google Scholar
Granger, C.W.J. & Newbold, P. (1974) Spurious regressions in econometrics. Journal of Econometrics 2, 111–120.Google Scholar
Granger, C.W.J. & Newbold, P. (1977) Forecasting Economic Time Series. Academic Press.Google Scholar
Granger, C.W.J. & Teräsvirta, T. (1993) Modelling Nonlinear Dynamic Relationships. Oxford University Press.Google Scholar
Hall, P. & Heyde, C. (1980) Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Hong, S.H. & Phillips, P.C.B. (2005) Testing Linearity in Cointegrating Relations with an Application to PPP. Cowles Foundation Discussion Paper 1541, Yale University.Google Scholar
Kapetanios, G., Shin, Y., & Snell, A. (2003) Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359–379.Google Scholar
Karlsen, H., Myklebust, T., & Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration model. Annals of Statistics 35, 252–299.Google Scholar
Karlsen, H. & Tjøstheim, D. (1998) Nonparametric Estimation in Null Recurrent Time Series. Working paper 50, Sonderforschungsbereich series 373, Humboldt University.Google Scholar
Karlsen, H. & Tjøstheim, D. (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372–416.Google Scholar
Kasparis, I. (2007) The Bierens Test for Certain Nonstationary Models. Discussion paper 2007–04, University of Cyprus.Google Scholar
Kasparis, I. (2008) Detection of functional form misspecification in cointegrating relations. Econometric Theory 24, 1373–1403.Google Scholar
Li, Q. (1999) Consistent model specification tests for time series econometric models. Journal of Econometrics 92, 101–147.Google Scholar
Li, Q. & Racine, J. (2007) Nonparametric Econometrics: Theory and Practice. Princeton University Press.Google Scholar
Li, Q. & Wang, S. (1998) A simple consistent bootstrap tests for a parametric regression functional form. Journal of Econometrics 87, 145–165.Google Scholar
Lobato, I. & Robinson, P.M. (1998) A nonparametric test for I(0). Review of Economic Studies 65, 475–95.Google Scholar
Masry, E. & Tjøstheim, D. (1995) Nonparametric estimation and identification of nonlinear ARCH time series. Econometric Theory 11, 258–289.Google Scholar
Masry, E. & Tjøstheim, D. (1997) Additive nonlinear ARX time series and projection estimates. Econometric Theory 13, 214–252.Google Scholar
Park, J. & Phillips, P.C.B. (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–162.Google Scholar
Phillips, P.C.B. (1986) Understanding spurious regressions in econometrics. Journal of Econometrics 33, 311–340.Google Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–302.CrossRefGoogle Scholar
Phillips, P.C.B. (1997) Unit root tests. In Klotz, S. (ed.), Encyclopedia of Statistical Sciences, vol. 1, 531–542.Google Scholar
Phillips, P.C.B. (2007) Local limit theory and spurious regressions. Cowles Foundation Discussion Paper, Yale University.Google Scholar
Phillips, P.C.B. & Park, J. (1998) Nonstationary density estimation and kernel autoregression. Cowles Foundation Discussion Paper 1181, Yale University.Google Scholar
Phillips, P.C.B. & Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.Google Scholar
Phillips, P.C.B. & Xiao, Z. (1998) A primer on unit root testing. Journal of Economic Surveys 12, 423–469.Google Scholar
Robinson, P.M. (1988) Root-N-consistent semiparametric regression. Econometrica 56, 931–964.Google Scholar
Robinson, P.M. (1989) Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of Economic Studies 56, 511–534.Google Scholar
Robinson, P.M. (2003) Efficient tests of nonstationary hypotheses. In Recent Developments in Time Series, vol. 1, pp. 526–43. Elgar Reference Collection. International Library of Critical Writings in Econometrics.Google Scholar
Tong, H. (1990) Nonlinear Time Series: A Dynamical System Approach. Oxford University Press.Google Scholar
Vadim, M. (2008) Nonlinearity nonstationarity and spurious forecasts. Journal of Econometrics 142, 1–27.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.Google Scholar