Nonstationary Index Models

Yoosoon Chang () and Joon Y. Park ()

Working Paper Series from Institute of Economic Research, Seoul National University

Abstract: 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.

Keywords: Index model; integrated time series; nonlinear least squares; neural network model; smooth transition regression; Brownian motion; Brownian local time (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 1999-03
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