Asymptotics for Time-Varying Vector MA(∞) Processes

Moving average infinity (MA(∞)) processes play an important role in modeling time series data. While a strand of literature on time series analysis emphasizes the importance of modeling smooth changes over time and therefore is shifting its focus from parametric models to nonparametric ones, MA(∞) processes with constant parameters are often part of the fundamental data generating mechanism. Along this line of research, an intuitive question is how to allow the underlying data generating mechanism evolves over time. To better capture the dynamics, this paper considers a new class of time-varying vector moving average infinity (VMA(∞)) processes. Accordingly, we establish some new asymptotic properties, including the law of large numbers, the uniform convergence, the central limit theory, the bootstrap consistency, and the long-run covariance matrix estimation for the class of time-varying VMA(∞) processes. Finally, we demonstrate the empirical relevance and usefulness of the newly proposed model and estimation theory through extensive simulated and real data studies.