A Class of Non-Gaussian State Space Models with Exact Likelihood Inference

The likelihood function of a general non-linear, non-Gaussian state space model is a high-dimensional integral with no closed-form solution. In this paper, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that includes stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a non-negative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the likelihood, I also show how to perform filtering and smoothing to estimate the latent variables in the model. The procedures in this paper can be used for either Bayesian or frequentist estimation of the model’s unknown parameters as well as the latent state variables.