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Functional Coefficient Cointegration Models Subject to Time–Varying Volatility with an Application to the Purchasing Power Parity

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  • Yundong Tu
  • Ying Wang

Abstract

This paper analyses functional coefficient cointegration models with both stationary and non‐stationary covariates, allowing time‐varying (unconditional) volatility of a general form. The conventional kernel weighted least squares (KLS) estimator is subject to potential efficiency loss, and can be improved by an adaptive kernel weighted least squares (AKLS) estimator that adapts to heteroscedasticity of unknown form. The AKLS estimator is shown to be as efficient as the oracle generalized kernel weighted least squares estimator asymptotically, and can achieve significant efficiency gain relative to the KLS estimator in finite samples. An illustrative example is provided by investigating the Purchasing Power Parity hypothesis.

Suggested Citation

  • Yundong Tu & Ying Wang, 2019. "Functional Coefficient Cointegration Models Subject to Time–Varying Volatility with an Application to the Purchasing Power Parity," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(6), pages 1401-1423, December.
    • Handle: RePEc:bla:obuest:v:81:y:2019:i:6:p:1401-1423
    DOI: 10.1111/obes.12309
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    Cited by:

    1. Phillips, Peter C.B. & Wang, Ying, 2023. "When bias contributes to variance: True limit theory in functional coefficient cointegrating regression," Journal of Econometrics, Elsevier, vol. 232(2), pages 469-489.
    2. 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.
    3. 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.
    4. Haiqi Li Author-Name-First: Haiqi & Jing Zhang & Chaowen Zheng, 2023. "Estimating and Testing for Functional Coefficient Quantile Cointegrating Regression," Economics Discussion Papers em-dp2023-07, Department of Economics, University of Reading.
    5. 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.
    6. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    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.

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