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Specification Testing Driven By Orthogonal Series For Nonlinear Cointegration With Endogeneity

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  • Dong, Chaohua
  • Gao, Jiti

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.

Suggested Citation

  • Dong, Chaohua & Gao, Jiti, 2018. "Specification Testing Driven By Orthogonal Series For Nonlinear Cointegration With Endogeneity," Econometric Theory, Cambridge University Press, vol. 34(4), pages 754-789, August.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:04:p:754-789_00
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    Cited by:

    1. Jun Wang & Dianpeng Wang & Yubin Tian, 2022. "Multidimensional specification test based on non-stationary time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 348-372, June.
    2. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    3. Chaohua Dong & Jiti Gao & Yundong Tu & Bin Peng, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Papers 2301.06631, arXiv.org.
    4. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    5. Feng, Guohua & Peng, Bin & Su, Liangjun & Yang, Thomas Tao, 2019. "Semi-parametric single-index panel data models with interactive fixed effects: Theory and practice," Journal of Econometrics, Elsevier, vol. 212(2), pages 607-622.
    6. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Papers 2111.02023, arXiv.org.
    7. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
    8. Chaohua Dong & Jiti Gao & Bin Peng & Yundong Tu, 2021. "Multiple-index Nonstationary Time Series Models: Robust Estimation Theory and Practice," Monash Econometrics and Business Statistics Working Papers 18/21, Monash University, Department of Econometrics and Business Statistics.

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