In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model which is the foundation to initiate the theoretical development. Afterwards, we consider the QMLE estimation approach, and provide both point-wise and simultaneous inferences on the coefficient functions. In addition, we demonstrate the theoretical findings through both simulated and real data examples. In particular, we show the empirical relevance of our study using an application to evaluate the conditional correlations between the stock markets of China and U.S. We find that the interdependence between the two stock markets is increasing over time.