Before revision:  For a p-dimensional unit-root process , we assume that each component consists of a set of common factors, which may be unit-root non-stationary, and a set of stationary components, which contain the cointegrations among the unit-root processes. To further reduce the dimensionality, we also postulate that the stationary part of the series is a nonsingular linear transformation of certain common factors and idiosyncratic white noise components as in Gao and Tsay (2019a, b)
After revision:  For a p-dimensional unit-root process , we assume that each component consists of a set of common factors, which may be unit-root non-stationary, and a set of stationary common factors, which are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal-dependence and the idiosyncratic white noise components as in Gao and Tsay (2019a, b)