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

Abstract

The likelihood function for general non-linear, non-Gaussian state space models 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 maximum likelihood estimator, I also show how to perform filtering and smoothing to estimate the latent variables in the model. Finally, it is also possible to take random draws from the joint posterior distribution of the latent states conditional on the data and the model's parameters, which is valuable for inference of more complex models.

Keywords: state space models, filtering, Markov-switching, stochastic intensity, stochastic volatility, Bayesian inference, autoregressive-gamma process

JEL Classification: C11, C15, C32, C58