Estimating smooth structural change in cointegration models
This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down i...
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sg-smu-ink.soe_research-29422020-01-27T10:05:17Z Estimating smooth structural change in cointegration models Peter C. B. PHILLIPS, LI, Degui GAO, Jiti This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to reorient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression. (C) 2016 Elsevier B.V. All rights reserved. 2017-01-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/1943 info:doi/10.1016/j.jeconom.2016.09.013 https://ink.library.smu.edu.sg/context/soe_research/article/2942/viewcontent/em22052014.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Cointegration Endogeneity Kernel degeneracy Nonparametric regression Super-consistency Time varying coefficients Econometrics |
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Cointegration Endogeneity Kernel degeneracy Nonparametric regression Super-consistency Time varying coefficients Econometrics Peter C. B. PHILLIPS, LI, Degui GAO, Jiti Estimating smooth structural change in cointegration models |
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This paper studies nonlinear cointegration models in which the structural coefficients may evolve smoothly over time, and considers time-varying coefficient functions estimated by nonparametric kernel methods. It is shown that the usual asymptotic methods of kernel estimation completely break down in this setting when the functional coefficients are multivariate. The reason for this breakdown is a kernel induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature. Some new techniques are developed to address the degeneracy and resolve the asymptotics, using a path-dependent local coordinate transformation to reorient coordinates and accommodate the degeneracy. The resulting asymptotic theory is fundamentally different from the existing kernel literature, giving two different limit distributions with different convergence rates in the different directions of the (functional) parameter space. Both rates are faster than the usual root-nh rate for nonlinear models with smoothly changing coefficients and local stationarity. In addition, local linear methods are used to reduce asymptotic bias and a fully modified kernel regression method is proposed to deal with the general endogenous nonstationary regressor case, which facilitates inference on the time varying functions. The finite sample properties of the methods and limit theory are explored in simulations. A brief empirical application to macroeconomic data shows that a linear cointegrating regression is rejected but finds support for alternative polynomial approximations for the time-varying coefficients in the regression. (C) 2016 Elsevier B.V. All rights reserved. |
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Peter C. B. PHILLIPS, LI, Degui GAO, Jiti |
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Peter C. B. PHILLIPS, LI, Degui GAO, Jiti |
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Peter C. B. PHILLIPS, |
title |
Estimating smooth structural change in cointegration models |
title_short |
Estimating smooth structural change in cointegration models |
title_full |
Estimating smooth structural change in cointegration models |
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Estimating smooth structural change in cointegration models |
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Estimating smooth structural change in cointegration models |
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estimating smooth structural change in cointegration models |
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Institutional Knowledge at Singapore Management University |
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2017 |
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https://ink.library.smu.edu.sg/soe_research/1943 https://ink.library.smu.edu.sg/context/soe_research/article/2942/viewcontent/em22052014.pdf |
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