Statistics Seminar: Wang -- Local time density estimation

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               *          UNIVERSITY OF SYDNEY              * 
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               *     SCHOOL OF MATHEMATICS & STATISTICS     *
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               *       STATISTICS SEMINAR SERIES - 2007     *
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           Asymptotic theory for local time density estimation 
                and nonparametric cointegrating regression 

                     Qiying Wang (University of Sydney) 
 
                         Friday, 30 March, 2.00pm 

                               Carslaw 173 

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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.  This is a joint work with Prof.  Peter Phillips in Yale
University.  

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