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A Consistent Nonparametric Test On Semiparametric Smooth Coefficient Models With Integrated Time Series

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  • Sun, Yiguo
  • Cai, Zongwu
  • Li, Qi

Abstract

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

Suggested Citation

  • Sun, Yiguo & Cai, Zongwu & Li, Qi, 2016. "A Consistent Nonparametric Test On Semiparametric Smooth Coefficient Models With Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 32(4), pages 988-1022, August.
    • Handle: RePEc:cup:etheor:v:32:y:2016:i:04:p:988-1022_00
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    Citations

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    Cited by:

    1. 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.
    2. Ying Wang & Peter C. B. Phillips & Yundong Tu, 2024. "Limit Theory and Inference in Non-cointegrated Functional Coefficient Regression," Cowles Foundation Discussion Papers 2399, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Heather Anderson & Jiti Gao & Farshid Vahid & Wei Wei & Yang Yang, 2023. "Does Climate Sensitivity Differ Across Regions?," Monash Econometrics and Business Statistics Working Papers 7/23, Monash University, Department of Econometrics and Business Statistics.
    5. 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.
    6. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    7. Ying Wang & Peter C. B. Phillips, 2024. "Limit Theory of Local Polynomial Estimation in Functional Coefficient Regression," Cowles Foundation Discussion Papers 2398, Cowles Foundation for Research in Economics, Yale University.
    8. Li, Li & Tu, Yundong, 2022. "The varying spillover of U.S. systemic risk: A functional-coefficient cointegration approach," Economics Letters, Elsevier, vol. 212(C).

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