Abstract: Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics in this paper, we start our study on a time-varying VMA(infinity) model, develop a time--varying counterpart of the conventional BN decomposition, and establish the inferential theories associated with the trending function. Then, by imposing a more detailed structure on the data generating process (i.e., the time--varying VAR(p) model), we establish theories for the impulse response functions which are of great interest to describe how the economy reacts over time to economic shocks. The asymptotic results are established subject to both short--run timing and long--run restrictions, respectively. Third, we examine the theoretical results through extensive simulated and real data studies.
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