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Multivariate dynamic time series models are widely encountered in practicalstudies, e.g., modelling policy transmission mechanism and measuringconnectedness between economic agents. To better capture the dynamics, thispaper proposes a wide class of multivariate dynamic models with time-varyingcoefficients, 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 forthas special cases. The paper then develops a unified estimation method for theunknown quantities before an asymptotic theory for the proposed estimators isestablished. In the empirical study, we investigate the transmission mechanismof monetary policy using U.S. data, and uncover a fall in the volatilities ofexogenous shocks. In addition, we find that (i) monetary policy shocks haveless influence on inflation before and during the so-called Great Moderation,(ii) inflation is more anchored recently, and (iii) the long-run level ofinflation is below, but quite close to the Federal Reserve's target of twopercent after the beginning of the Great Moderation period.

A Class of Time-Varying Vector Moving Average Models: Nonparametric Kernel Estimation and Application