Simulation Smoothing for Nonlinear non-Gaussian State Space Models using Machine Learning Methods

This paper develops a new simulation smoothing method for nonlinear and non-Gaussian state space models. It can be used to compute full-sample (smoothed) estimates of latent states, nonlinear functions of the states, and their joint density conditional on the data. The simulation smoother can be adopted as an importance sampler for estimating model parameters via Monte Carlo maximum likelihood. The approach relies on simulated data from the model to estimate the conditional distributions in a backward smoothing step. The method is general and can be combined with various estimators of conditional distributions, which enables the use of general machine learning methods. Two empirical applications, one for the volatility index for crypto-currencies (VCRIX) and one for the daily returns for the stock price of Tesla, highlight the flexibility of the method.