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Uniform Convergence Rates over Maximal Domains in Structural Nonparametric Cointegrating Regression

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  • James A. Duffy

    (Institute for New Economic Thinking, Oxford Martin School, and Economics Department, University of Oxford)

Abstract

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than has been previously considered, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring only that it satisfy certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

Suggested Citation

  • James A. Duffy, 2015. "Uniform Convergence Rates over Maximal Domains in Structural Nonparametric Cointegrating Regression," Economics Papers 2015-W03, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1503
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    References listed on IDEAS

    as
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    3. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1433-1445, October.
    4. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(5), pages 911-952, October.
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    6. Chan, Nigel & Wang, Qiying, 2014. "Uniform Convergence For Nonparametric Estimators With Nonstationary Data," Econometric Theory, Cambridge University Press, vol. 30(5), pages 1110-1133, October.
    7. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
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