The paper derives the asymptotic variance bound for instrumental variables (IV) estimators, and extends the Gauss-Markov theorem for the regressions with correlated regressors and regression errors. For some special class of models, the usual IV estimator attains the lower bound and becomes the...

This paper considers the cointegrating regression with errors whose variances change smoothly over time. The model can be used to describe a longrun cointegrating relationship, the tightness of which varies along with time. Heteroskedasticity in the errors is modelled nonparametrically and is...

An asymptotic thoery is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and theory covers integrable, asymptotically homeogeneous and explosive functions. Sufficient conditions for weak consistency are given and a...

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit...

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system. The test is based on the Nadaraya-Watson kernel estimate of the Lyapunov exponent. We show that the estimator is consistent: The estimated Lyapunov exponent converges to zero under the...

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...