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Nonlinear Cointegrating Power Function Regression With Endogeneity

Author

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  • Hu, Zhishui
  • Phillips, Peter C.B.
  • Wang, Qiying

Abstract

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. A new test for linear cointegration against nonlinear departures is developed based on a simple linearized pseudo-model that is very convenient for practical implementation and has standard normal limit theory in the strictly exogenous regressor case. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semimartingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.

Suggested Citation

  • Hu, Zhishui & Phillips, Peter C.B. & Wang, Qiying, 2021. "Nonlinear Cointegrating Power Function Regression With Endogeneity," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1173-1213, December.
    • Handle: RePEc:cup:etheor:v:37:y:2021:i:6:p:1173-1213_4
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    Cited by:

    1. Lin, Yingqian & Tu, Yundong, 2021. "On transformed linear cointegration models," Economics Letters, Elsevier, vol. 198(C).
    2. Qiying Wang & Peter C. B. Phillips, 2022. "A General Limit Theory for Nonlinear Functionals of Nonstationary Time Series," Cowles Foundation Discussion Papers 2337, Cowles Foundation for Research in Economics, Yale University.
    3. Sun, Xiaojun & Lei, Yalin & Wang, Xue-Chao & Zhao, Jun & Varbanov, Petar Sabev, 2024. "Directional nature of technological progress in the petrochemical industry prompting energy marginal substitution," Energy, Elsevier, vol. 310(C).
    4. Ayman Mnasri & Zouhair Mrabet & Mouyad Alsamara, 2023. "A new quadratic asymmetric error correction model: does size matter?," Empirical Economics, Springer, vol. 65(1), pages 33-64, July.
    5. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?," Papers 2009.02262, arXiv.org, revised Dec 2021.
    6. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
    7. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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