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Martingale Limit Theorem Revisited And Nonlinear Cointegrating Regression

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  • Wang, Qiying

Abstract

For a certain class of martingales, convergence to a mixture of normal distributions is established under convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem, where one generally requires convergence in probability. The extension partially removes a barrier in the applications of the classical martingale limit theorem to nonparametric estimation and inference with nonstationarity and enhances the effectiveness of the classical martingale limit theorem as one of the main tools to investigate asymptotics in statistics, econometrics, and other fields. The main result is applied to investigate limit behavior of the conventional kernel estimator in a nonlinear cointegrating regression model, which improves existing works in the literature.

Suggested Citation

  • Wang, Qiying, 2014. "Martingale Limit Theorem Revisited And Nonlinear Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 509-535, June.
    • Handle: RePEc:cup:etheor:v:30:y:2014:i:03:p:509-535_00
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    Citations

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    Cited by:

    1. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    2. Li, Shaoran & Linton, Oliver, 2021. "When will the Covid-19 pandemic peak?," Journal of Econometrics, Elsevier, vol. 220(1), pages 130-157.
    3. Peng, Zhen & Dong, Chaohua, 2022. "Augmented cointegrating linear models with possibly strongly correlated stationary and nonstationary regressors," Finance Research Letters, Elsevier, vol. 47(PB).
    4. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    5. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.
    6. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    7. Qiying Wang & Peter C.B. Phillips & Ioannis Kasparis, 2017. "Latent Variable Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 3011, Cowles Foundation for Research in Economics, Yale University.
    8. Qiying Wang & Peter C. B. Phillips & Ying Wang, 2023. "New asymptotics applied to functional coefficient regression and climate sensitivity analysis," Cowles Foundation Discussion Papers 2365, Cowles Foundation for Research in Economics, Yale University.
    9. Wang, Qiying & Phillips, Peter C.B. & Kasparis, Ioannis, 2021. "Latent Variable Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 37(1), pages 138-168, February.
    10. Zhishui Hu & Ioannis Kasparis & Qiying Wang, 2020. "Locally trimmed least squares: conventional inference in possibly nonstationary models," Papers 2006.12595, arXiv.org.
    11. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    12. Sepideh Mosaferi & Mark S. Kaiser, 2021. "Nonparametric Cointegrating Regression Functions with Endogeneity and Semi-Long Memory," Papers 2111.00972, arXiv.org, revised Aug 2022.
    13. 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.

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