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On transformed linear cointegration models

Author

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  • Lin, Yingqian
  • Tu, Yundong

Abstract

This paper proposes a transformed linear cointegration model of the form Λ(yt,β0)=xt⊤θ10+zt⊤θ20+ut, where Λ is a monotonic function, xt is the nonstationary vector regressor, zt is the stationary regressor, ut is the regression error, and β0,θ10,θ20 are unknown parameters. This model offers a flexible nonlinear cointegration via the monotonic transformation of the dependent variable, and includes the conventional linear cointegration model as a special case. Asymptotic properties of the proposed estimators are established. Simulations demonstrate that the estimators perform well in small samples. A real data example on the purchasing power parity illustrates the practical merits of our model.

Suggested Citation

  • Lin, Yingqian & Tu, Yundong, 2021. "On transformed linear cointegration models," Economics Letters, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:ecolet:v:198:y:2021:i:c:s0165176520304468
    DOI: 10.1016/j.econlet.2020.109686
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    References listed on IDEAS

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    1. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    2. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
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    5. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
    6. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    7. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    8. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    9. 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.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cointegration; Nonlinear regression; Purchasing power parity; Transformation model;
    All these keywords.

    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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