This paper considers index models, such as neural network models and smooth transition regressions, with integrated regressors. These are the models that can be ued to analyze various nonlinear relationships among nonstationary economic time series. Asymptotics for the nonlinear least squares (NLS) estimator in such models are fully developed. The estimator is shown to be consistent with a convergence rate that is a mixture of n^(3/4) n^(1/2) and n^(1/4) for neural network models, and of n^(5/4), n, n^(3/4) and n^(1/2) for smooth transition regressions. Its limiting distribution is also obtained. Some of its components are mixed normal, with mixing variates depending upon Brownian local time as well as Brownian motion. However, it also has non-Gaussian components. It is particular shown that applications of usual statistical methods in such models generally yield inefficient estimates and/or invalid tests. We develop a new methodology to efficiently estimate and to correctly test in those models. A simple simulation is conducted to investigate the finite sample properties of the NLS estimators and the newly proposed efficient estimators.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
file. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Institute of Economic Research, Seoul National University in its series Working Paper Series with number
no7.
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)