Mixed Measurement Dynamic Factor Models

Abstract

We propose a latent dynamic factor model framework for mixed-measurement mixed-frequency panel data. Time series observations may come from different families of parametric distributions, may be observed at different frequencies, and exhibit common dynamics and cross sectional dependence due to shared exposure to latent dynamic factors. As the main complication, the likelihood does not exist in closed form for this class of models. We therefore present three different approaches to parameter and factor estimation in this framework. First, assuming a factor structure for location parameters yields a parameter driven model that can be cast into state space form. Parameters and factors estimation is then accomplished by Monte-Carlo maximum likelihood based on importance sampling. Second, we propose a less complex observation driven alternative to the parameter driven original model, for which the likelihood exists in closed form. Finally, parameter and factor estimates can be obtained by Markov Chain Monte Carlo. We use the new mixed-measurement framework for the estimation and forecasting of intertwined credit and recovery risk conditions for US Moody’s-rated firms from 1982 - 2008. The joint model allows us to construct predictive (conditional) loss densities for portfolios of bank loans and corporate bonds in the presence of non-standard sources of credit risk such as systematic frailty effects and systematic recovery risk.