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

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