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Functional Coefficient Nonstationary Regression with Non- and Semi-Parametric Cointegration

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  • Jiti Gao

    ()

  • Peter C.B. Phillips

    ()

Abstract

This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endo-geneity 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 with Non- and Semi-Parametric Cointegration," Monash Econometrics and Business Statistics Working Papers 16/13, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2013-16
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    File URL: http://business.monash.edu.au/__data/assets/pdf_file/0020/331049/wp16-13.pdf
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Econometrica, Econometric Society, vol. 75(6), pages 1771-1855, November.
    2. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Joon-Ho Hahm & Douglas G. Steigerwald, 1999. "Consumption Adjustment under Time-Varying Income Uncertainty," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 32-40, February.
    5. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    6. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    7. Gylfason, Thorvaldur, 1981. "Interest Rates, Inflation, and the Aggregate Consumption Function," The Review of Economics and Statistics, MIT Press, vol. 63(2), pages 233-245, May.
    8. Campbell, John Y & Mankiw, N Gregory, 1990. "Permanent Income, Current Income, and Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(3), pages 265-279, July.
    9. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    10. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    11. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    12. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

    More about this item

    Keywords

    fractional Aggregate consumption; Asymptotic theory; cointegration; density; local time; nonlinear functional; nonparametric estimation; semiparametric; time series; varying coefficient model.;

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