A Class of Non-Gaussian State Space Models With Exact Likelihood Inference
提出了一类非高斯状态空间模型，包括随机强度、随机波动率和随机持续时间模型，并展示了如何精确计算其似然函数，同时实现滤波和平滑以估计潜在变量，适用于贝叶斯或频率推断。
The likelihood function of a general nonlinear, non-Gaussian state space model is a high-dimensional integral with no closed-form solution. In this article, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that include stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a nonnegative 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 article can be used for either Bayesian or frequentist estimation of the model’s unknown parameters as well as the latent state variables. Supplementary materials for this article are available online.