On Multivariate Time-Varying Dynamic Models

This dissertation consists of three chapters that contribute to different multivariate time series models with local stationarity; that is, the underlying data generating mechanism of the dynamic process is changing smoothly over time. The first chapter briefly reviews the literature. The second chapter considers a new class of time-varying vector moving average infinity processes. The third chapter introduces a new class of time-varying vector autoregression (VAR) models in which the VAR coefficients and covariance matrix of the error innovations are allowed to change smoothly over time. The fourth chapter considers a wide class of time-varying multivariate causal processes that nests many classic and new examples as special cases. Numerical studies are conducted to illustrate the usefulness of the proposed models and methods.