Inferring Time Varying Dynamic Linear Model Parameters from a Mixture Model

Abstract

Non-stationary time series are extremely challenging to model. We propose a Bayesian mixture model framework for obtaining time varying parameters for a dynamic linear model. We discuss on-line estimation of time varying DLM parameters by means of a dynamic mixture model composed of constant parameter DLMs. For time series with low signal-to-noise ratios, we propose a novel method of constructing model priors. We calculate model likelihoods by comparing forecast distributions with observed values. We utilize computationally efficient moment matching Gaussians to approximate exact mixtures of path dependent posterior densities. The effectiveness of our approach is illustrated by extracting insightful time varying parameters for an ETF returns model in a period spanning the 2008 financial crisis; and, by demonstrating the superior performance in a statistical arbitrage application.