Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Abstract
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others.  Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest.  We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time.  Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain.  The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable.  To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods 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. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).

Joint work with Wen-Hsi Yang and Christopher K. Wikle