Abstract

This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n 1=4 rate and have mixed normal limit distributions. On the other hand, if the regression functions are homogeneous at innity, the convergence rates are determined by the degree of the asymptotic homogeneity and the limit distributions are non-Gaussian. It is shown that nonlinear least squares generally yields inecient estimators and invalid tests, just as in linear nonstationary regressions. The paper propos...

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