Identification and Estimation of Initial Conditions in Non-Minimal State-Space Models

In this paper the identification problem is considered for initial conditions in a non-minimal state-space model that includes interpretable state variables generated by non-stationary stochastic processes. In order to solve the identification problem, structural restrictions are imposed on initial conditions in a state-space model with redundant state variables. The corresponding restricted maximum likelihood estimator of initial conditions is derived. The restricted estimator of initial conditions can be used in order to compute uniquely identified realizations of interpretable latent variables. The identification problem is illustrated analytically using a simple structural economic model