Forecasting with Weakly Identified Linear State-Space Models.
Sébastien Blais · 2009
Normalizing models in empirical work is sometimes a more difficult task than commonly appreciated. Permutation invariance and local non-identification cause well-documented difficulties for maximum-likelihood and Bayesian inferencein finite mixture distributions. Because these issues arise when some parameters are close to being unidentified, they are best described as weak identification (or empirical underidentification) problems. Although similar difficulties arise in linear state-space models, little is known about how they should be addressed. In this paper, I show that some popular normalizations do not provide global identification and yield parameter point estimators with undesirable finite-sample properties. At the computational level, I propose a novel posterior simulator for Gaussian linear state-space models, which I use to illustrate the relationship between forecasting performance and weak identification. In particular, Monte Carlo simulations show that taking into account parameter uncertainty reduces out-of-sample root mean square forecast errors when some parameters are weakly identified.