State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models

Implications to signal extraction that arise from specifying unobserved components (UC) models with correlated or orthogonal innovations have been well-investigated. In contrast, an analogous statement for forecasting evaluation cannot be made. This paper attempts to fill this gap in light of the recent resurgence of studies adopting UC models for forecasting purposes. In particular, four correlation structures are entertained: orthogonal, correlated, perfectly correlated innovations as well as a novel approach which combines features from two contrasting cases, namely, orthogonal and perfectly correlated innovations. Parameter space restrictions associated with different correlation structures and their connection with forecasting are discussed within a Bayesian framework. Introducing perfectly correlated innovations, however, reduces the covariance matrix rank. To accommodate that, a Markov Chain Monte Carlo sampler which builds upon properties of Toeplitz matrices and recent advances in precision-based algorithms is developed. Our results for several measures of U.S. inflation indicate that the correlation structure between state variables has important implications for forecasting performance as well as estimates of trend inflation.