Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression

Qiying Wang and Peter C. B. Phillips ()
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Qiying Wang: School of Mathematics and Statistics, University of Sydney

No 1594, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. Our main result is applied to offer an alternative development of the asymptotic theory for non-parametric estimation of a non-linear cointegrating regression involving non-stationary time series. In place of the framework of null recurrent Markov chains as developed in recent work of Karlsen, Myklebust and Tjostheim (2007), the direct local time density argument used here more closely resembles conventional nonparametric arguments, making the conditions simpler and more easily verified.

Keywords: Brownian Local time; Cointegration; Integrated process; Local time density estimation; Nonlinear functionals; Nonparametric regression; Unit root (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2006-12
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Journal Article: ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION (2009)
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