Simulation Smoothing for State Space Models: An Extremum Monte Carlo Approach

This paper introduces a novel approach to simulation smoothing for nonlinear and non-Gaussian state space models. It allows for computing smoothed estimates of the states and nonlinear functions of the states, as well as visualizing the joint smoothing distribution. The approach combines extremum estimation with simulated data from the model to estimate the conditional distributions in the backward smoothing decomposition. The method is generally applicable and can be paired with various estimators of conditional distributions. Several applications to nonlinear models are presented for illustration. An empirical application based on a stochastic volatility model with stable errors highlights the flexibility of the approach.