A Flexible State Space Model and its Applications

The standard state space model (SSM) treats observations as imprecise measures of the Markov latent states. Our flexible SSM treats the states and observables symmetrically, which are simultaneously determined by historical observations and up to first-lagged states. The only distinction between the states and observables is that the former are latent while the latter have data. Despite the conceptual difference, the two SSMs share the same Kalman filter. However, when the flexible SSM is applied to the ARMA model, mixed frequency regression and the dynamic factor model with missing data, the state vector is not only parsimonious but also intuitive in that low-dimension states are constructed simply by stacking all the relevant but unobserved variables in the structural model.