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SPECIFICATION TESTING DRIVEN BY ORTHOGONAL SERIES FOR NONLINEAR COINTEGRATION WITH ENDOGENEITY

Published online by Cambridge University Press:  09 June 2017

Chaohua Dong  and
Jiti Gao
Chaohua Dong
Affiliation:
Southwestern University of Finance and Economics
Jiti Gao*
Affiliation:
Monash University
*
*Address correspondence to Jiti Gao, Department of Econometrics and Business Statistics, Monash University, Caulfield East, Victoria 3145, Australia; e-mail: jiti.gao@monash.edu.
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Abstract

This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of bivariate nonlinearly cointegrated time series models with endogeneity and nonstationarity. The first test is proposed for the case where the regression function is integrable, which fills a gap in the literature, and the second test, which nests the first one, deals with regression functions in a quite large function space that is sufficient for both theoretical and practical use. As a starting point of our asymptotic theory, the first test is studied initially and then the theory is extended to the second test. Endogeneity in two general forms is allowed in the models to be tested. The finite sample performance of the tests is examined through several simulated examples. Our experience generally shows that the proposed tests are easily implementable and also have stable sizes and good power properties even when the ‘distance’ between the null hypothesis and a sequence of local alternatives is asymptotically negligible.

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ARTICLES
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Econometric Theory , Volume 34 , Issue 4 , August 2018 , pp. 754 - 789
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

The authors acknowledge the constructive comments from Professor Peter Phillips, the Co–Editor and three referees on the earlier versions. The authors would also like to thank Professor Maxwell King for the proofreading and useful comments on a final version. Thanks also go to Dr Qiying Wang for making an earlier version of Wang and Phillips (2016) available to us while we were writing this paper as well as his constructive comments on an earlier version. The authors would like to acknowledge constructive comments and suggestions from Professor Oliver Linton and Professor Peter Robinson on earlier versions. Thanks from the authors also go to the seminar participants at various seminars for their comments and suggestions. The first author acknowledges financial support from the National Natural Science Foundation of China under Grant No. 71671143 and the second author thanks the Australian Research Council Discovery Grants Program for its support under Grant numbers: DP150101012 & DP170104421.

References

REFERENCES

Cai, Z., Li, Q., & Park, J. (2009) Functional-coefficient cointegration models for nonstationary time series data. Journal of Econometrics 148, 101–113.Google Scholar
Chen, J., Gao, J., & Li, D. (2011) Estimation in semiparametric time series regression. Statistics and its Interface 4, 243–251.Google Scholar
Chen, X. & Shen, X. (1998) Sieve extremum estimates for weakly dependent data. Econometrica 66, 289–314.Google Scholar
Dong, C., Gao, J., & Peng, B. (2015) Semiparametric single-index panel data models with cross-sectional dependence. Journal of Econometrics 188, 301–312.Google Scholar
Dong, C., Gao, J., & Tjøstheim, D. (2016) Estimation for single-index and partially linear single-index nonstationary time series models. Annals of Statistics 44, 425–453.CrossRefGoogle Scholar
Dong, C., Gao, J., Tjøstheim, D., & Yin, J. (2014) Specification testing for nonlinear multivariate cointegrating regressions. Available at http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp08-14.pdf.Google Scholar
Gao, J. (2007) Nonlinear Time Series: Semi- and Non-Parametric Methods. Chapman & Hall/CRC.Google Scholar
Gao, J., King, M., Lu, Z., & Tjøstheim, D. (2009a) Nonparametric specification testing for nonlinear time series with nonstationarity. Econometric Theory 25, 1869–1892.CrossRefGoogle Scholar
Gao, J., King, M., Lu, Z., & Tjøstheim, D. (2009b) Specification testing in nonlinear and nonstationary time series autoregression. Annals of Statistics 37(68), 3893–3928.CrossRefGoogle Scholar
Gao, J. & Phillips, P.C.B. (2013a) Functional Coefficient Nonstationary Regression with Non- and Semi-Parametric Cointegration. 13, 1–56. Working paper. Available at http://ideas.repec.org/p/msh/ebswps/2013-16.html.Google Scholar
Gao, J. & Phillips, P.C.B. (2013b) Semiparametric estimation in triangular system equations with nonstationarity. Journal of Econometrics 176, 59–79.Google Scholar
Gao, J., Tong, H., & Wolff, R. (2002) Model specification tests in nonparametric stochastic regression models. Journal of Multivariate Analysis 83, 324–359.Google Scholar
Gao, J., Wang, Q., & Yin, J. (2011) Specification testing in nonlinear time series with long-range dependence. Econometric Theory 27, 260–284.Google Scholar
Geman, D. & Horowitz, J. (1980) Occupation densities. Annals of Probability 8, 1–67.CrossRefGoogle Scholar
Hall, P., Horowitz, J.L., & Jing, B. (1995) On blocking rules for the bootstrap with dependent data. Biometrika 82, 561–574.CrossRefGoogle Scholar
Hong, S.H. & Phillips, P.C.B. (2010) Testing linearity of cointegriting relations with an application to purchasing power parity. Journal of Business and Economic Statistics 28(1), 96–114.Google Scholar
Horowitz, J. & Spokoiny, V. (2001) An adaptive rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.CrossRefGoogle Scholar
Hualde, J. & Robinson, P.M. (2011) Gaussian pseudo-maximum likelihood estimation of fractional time series models. Annals of Statistics 39, 3152–3181.Google Scholar
Karlsen, H.A., Mykelbust, T., & Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration type model. Annals of Statistics 35, 252–299.Google Scholar
Karlsen, H.A. & Tjøstheim, D. (2001) Nonparametric estimation in null recurrent time series. Annals of Statistics 29, 372–416.Google Scholar
Li, Q. & Wang, S. (1998) A simple consistent bootstrap test for a parametric regression functional form. Journal of Econometrics 87, 145–165.Google Scholar
Marinucci, D. & Robinson, P.M. (2000) Weak convergence of multivariate fractional processes. Stochastic Processes and Their Applications 86, 103–120.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269–298.Google Scholar
Park, J.Y. & Phillips, P.C.B. (2001) Nonlinear regression with integreted time series. Econometrica 69(1), 117–161.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20(2), 971–1001.Google Scholar
Revuz, D. & Yor, M. (2005) Continuous Martingales and Brownian Motion. A Series of Comprehensive Studies in Mathematics, vol. 293. Springer-Verlag.Google Scholar
Wang, Q. & Phillips, P.C.B. (2009a) Asymptotic theory for local time density estimation and nonparametric cointegreting regression. Econometric Theory 25, 710–738.CrossRefGoogle Scholar
Wang, Q. & Phillips, P.C.B. (2009b) Structure nonparametric cointegrating regression. Econometrica 77, 1901–1948.Google Scholar
Wang, Q. & Phillips, P.C.B. (2012) A specification test for nonlinear nonstationary models. Annals of Statistics 40(2), 727–758.Google Scholar
Wang, Q. & Phillips, P.C.B. (2016) Nonparametric cointegrating regression with endogeneity and long memory. Econometric Theory 32, 359–401.Google Scholar
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