Before revision:  . The estimation of  linear loading spaces of the unit-root factors and the stationary components is achieved by an eigenanalysis of some nonnegative definite matrix , and the separation between the stationary factors and the white noises is based on an eigenanalysis and a projected principal component analysis . Asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n tends to infinity.
After revision:  . The estimation of linear loading spaces of the unit-root factors and the stationary components is achieved by an eigenanalysis of some nonnegative definite matrix , and the separation between the stationary factors and the white noises is based on an eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors, establish asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n tends to infinity.