Bayesian Averaging of Dynamic Linear Models

Meng Xie

In this paper, we assess model Bayesian model averaging techniques for multivariate dynamic linear models (DLMs) with variance matrix discounting. In previous research, the discount factors for the variance matrices and the auto-regressive lag have typically been predetermined and held constant over time. Using posterior model probabilities, we average DLMs employing different discount rates and lag parameters, essentially allowing the discount and lag to be time-varying. We also include an additional discount factor for previous model likelihoods to better model investor decision-making criteria. We apply this model averaging and extension to the daily prices of 9 exchange rates, two commodities, and two stock indices, evaluating 5-day forecasts and portfolio returns. Afterward, we apply the same model to the series of realized returns of the averaged models to create a ``fund of funds'' portfolio. We find that (1) there is shifting of model probabilities over time across both discount factors and lags, (2) the inclusion of likelihood discounting led to higher portfolio returns, and (3) the realized returns of the averaged models show no evidence of auto-regressive structure.