COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1594 Asymptotic Theory for Local Time Density Estimation Qiying Wang and Peter C.B. Phillips December 2006 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. |
