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Functional coefficient cointegration models with Box–Cox transformation

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  • Lin, Yingqian
  • Tu, Yundong

Abstract

This paper considers a functional coefficient cointegration model where the dependent variable is subject to a Box–Cox transformation. A profile method is proposed to estimate the Box–Cox transformation parameter β0. We first approximate the functional coefficients by sieve method assuming that β0 is known. Then an extremum estimator of β0 is proposed based on a loss function which measures the relative variation of the regression residual compared to the variation in the transformed dependent variable. Finally, a plug-in estimator of the functional coefficients is obtained. Asymptotic properties of the proposed estimators are developed. Numerical results demonstrate the nice performance of the estimators and corroborate the theoretical development.

Suggested Citation

  • Lin, Yingqian & Tu, Yundong, 2024. "Functional coefficient cointegration models with Box–Cox transformation," Economics Letters, Elsevier, vol. 234(C).
    • Handle: RePEc:eee:ecolet:v:234:y:2024:i:c:s0165176523004986
    DOI: 10.1016/j.econlet.2023.111472
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    References listed on IDEAS

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    1. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
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    10. Yingqian Lin & Yundong Tu, 2023. "Transformation Models with Cointegrated and Deterministically Trending Regressors," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 207-232, Emerald Group Publishing Limited.
    11. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Box–Cox transformation; Cointegration; Extremum estimation; Functional coefficient; Sieve method;
    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

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