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Functional Coefficient Nonstationary Regression

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Abstract
This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960-2009.

Suggested Citation

  • Jiti Gao & Peter C.B. Phillips, 2013. "Functional Coefficient Nonstationary Regression," Cowles Foundation Discussion Papers 1911, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1911
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d19/d1911.pdf
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    References listed on IDEAS

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    19. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
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    Cited by:

    1. Guohua Feng & Jiti Gao & Xiaohui Zhang, 2018. "Estimation of technical change and price elasticities: a categorical time–varying coefficient approach," Journal of Productivity Analysis, Springer, vol. 50(3), pages 117-138, December.
    2. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    3. Connor, G. & Li, S. & Linton, O., 2020. "A Dynamic Semiparametric Characteristics-based Model for Optimal Portfolio Selection," Cambridge Working Papers in Economics 20103, Faculty of Economics, University of Cambridge.
    4. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.
    5. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    6. Yarovaya, Larisa & Matkovskyy, Roman & Jalan, Akanksha, 2021. "The effects of a “black swan” event (COVID-19) on herding behavior in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    7. Biqing Cai & Dag Tjøstheim, 2015. "Nonparametric Regression Estimation for Multivariate Null Recurrent Processes," Econometrics, MDPI, vol. 3(2), pages 1-24, April.
    8. Jiti Gao & Bin Peng & Zhao Ren & Xiaohui Zhang, 2015. "Variable Selection for a Categorical Varying-Coefficient Model with Identifications for Determinants of Body Mass Index," Monash Econometrics and Business Statistics Working Papers 21/15, Monash University, Department of Econometrics and Business Statistics.
    9. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Aggregate consumption; Asymptotic theory; Cointegration; Density; Local time; Nonlinear functional; Nonparametric estimation; Semiparametric; Time series; Varying coefficient model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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