Augmented cointegrating linear models with possibly strongly correlated stationary and nonstationary regressors regressors

Abstract

Since an economic or financial variable may be affected by both stationary and nonstationary variables, this paper proposes a class of augmented cointegrating linear (ACL) models that accommodate these time series of different types. Moreover, the variables are allowed to be strongly correlated in the sense depicted in the paper. The asymptotic limit theory of estimator proposed is established via jointly convergence of the sample variance and covariance that circumvents the existent drawback in the most nonstationary time series literature; also a self-normalized central limit theorem is given to facilitate statistical inference. Monte Carlo simulations confirm the theoretical results. Finally, ACL regression model is applied to the GDP time series in US, for which we show the proposed model is more accurate and competent than some potential models.