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New asymptotics applied to functional coefficient regression and climate sensitivity analysis

Author

Listed:
  • Qiying Wang

    (University of Sydney)

  • Peter C. B. Phillips

    (Cowles Foundation, Yale University)

  • Ying Wang

    (Renmin University of China)

Abstract

A general asymptotic theory is established for sample cross moments of nonstationary time series, allowing for long range dependence and local unit roots. The theory provides a substantial extension of earlier results on nonparametric regression that include near-cointegrated nonparametric regression as well as spurious nonparametric regression. Many new models are covered by the limit theory, among which are functional coefficient regressions in which both regressors and the functional covariate are nonstationary. Simulations show finite sample performance matching well with the asymptotic theory and having broad relevance to applications, while revealing how dual nonstationarity in regressors and covariates raises sensitivity to bandwidth choice and the impact of dimensionality in nonparametric regression.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:2365
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    References listed on IDEAS

    as
    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. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    3. Yundong Tu & Ying Wang, 2020. "Adaptive estimation of heteroskedastic functional-coefficient regressions with an application to fiscal policy evaluation on asset markets," Econometric Reviews, Taylor & Francis Journals, vol. 39(3), pages 299-318, March.
    4. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    5. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    6. Jiti Gao & Dag Tjøstheim & Jiying Yin, 2012. "Model Specification between Parametric and Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 18/12, Monash University, Department of Econometrics and Business Statistics.
    7. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    8. Phillips, Peter C.B. & Wang, Ying, 2022. "Functional coefficient panel modeling with communal smoothing covariates," Journal of Econometrics, Elsevier, vol. 227(2), pages 371-407.
    9. Phillips, Peter C.B. & Leirvik, Thomas & Storelvmo, Trude, 2020. "Econometric estimates of Earth’s transient climate sensitivity," Journal of Econometrics, Elsevier, vol. 214(1), pages 6-32.
    10. 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.
    11. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    12. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    13. 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.
    14. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    15. Magnus, Jan R. & Melenberg, Bertrand & Muris, Chris, 2011. "Global Warming and Local Dimming: The Statistical Evidence," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 452-464.
    16. Masayuki Hirukawa & Mari Sakudo, 2018. "Functional-coefficient cointegration models in the presence of deterministic trends," Econometric Reviews, Taylor & Francis Journals, vol. 37(5), pages 507-533, May.
    17. 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.
    18. Wang, Qiying & Phillips, Peter C.B. & Kasparis, Ioannis, 2021. "Latent Variable Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 37(1), pages 138-168, February.
    19. Wang, Qiying & Phillips, Peter C.B., 2011. "Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications," Econometric Theory, Cambridge University Press, vol. 27(2), pages 235-259, April.
    20. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    21. Kunpeng Li & Degui Li & Zhongwen Liang & Cheng Hsiao, 2017. "Estimation of semi-varying coefficient models with nonstationary regressors," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 354-369, March.
    22. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    23. Wang, Qiying & Phillips, Peter C. B., 2016. "Nonparametric Cointegrating Regression With Endogeneity And Long Memory," Econometric Theory, Cambridge University Press, vol. 32(2), pages 359-401, April.
    24. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 143-164, February.
    25. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    26. Wang, Qiying, 2014. "Martingale Limit Theorem Revisited And Nonlinear Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 509-535, June.
    27. Sun, Yiguo & Cai, Zongwu & Li, Qi, 2013. "Semiparametric Functional Coefficient Models With Integrated Covariates," Econometric Theory, Cambridge University Press, vol. 29(3), pages 659-672, June.
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