  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, this
paper proposes a wide class of multivariate dynamic models with time-varying
coefficients, which have a general time-varying vector moving average (VMA)
representation, and nest, for instance, time-varying vector autoregression
(VAR), time-varying vector autoregression moving-average (VARMA), and so forth
as special cases. The paper then develops a unified estimation method for the
unknown quantities before an asymptotic theory for the proposed estimators is
established. In the empirical study, we investigate the transmission mechanism
of monetary policy using U.S. data, and uncover a fall in the volatilities of
exogenous shocks. In addition, we find that (i) monetary policy shocks have
less influence on inflation before and during the so-called Great Moderation,
(ii) inflation is more anchored recently, and (iii) the long-run level of
inflation is below, but quite close to the Federal Reserve's target of two
percent after the beginning of the Great Moderation period.
