Weighted Nonlinear Regression With Nonstationary Time Series

Abstract

: This study investigates a weighted least squares (WLS) estimation in a nonlinear cointegrating regression. In a nonlinear regression model, where the regressors include nearly integrated arrays and stationary processes, we show that the WLS estimator has a mixed Gaussian limit, and the corresponding Studentized statistic converges to a standard normal distribution. The WLS estimator is free of the memory parameter, even when a fractional process is included in the regressors. We also consider an ordinary least squares estimation in a nonlinear cointegrating regression. Compared with the WLS estimator, the limit distribution of the ordinary least squares estimator is non-Gaussian, and depends on the nuisance parameters from the regressors when the regression function is non-integrable.