Bayesian Circular Lattice Filters for Computationally Efficient Estimation of Multivariate Time-Varying Autoregressive Models

Abstract: Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. This paper proposes a computationally efficient multivariate Bayesian Circular Lattice Filter to extend the usage of the TV-VAR model to a broader class of high-dimensional problems. Our fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. Our estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of our approach, we conduct a comprehensive comparison with other competing methods through simulation studies and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Finally, we demonstrate our methodology through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.