Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods

In recent years state space models, particularly the linear Gaussian version, have become the standard framework for analyzing macroeconomic and financial data. However, many theoretically motivated models imply non-linear or non-Gaussian specifications ?or both. Existing methods for estimating such models are computationally intensive, and often cannot be applied to models with more than a few states. Building upon recent developments in precision-based algorithms, we propose a general approach to estimating high-dimensional non-linear non-Gaussian state space models. The baseline algorithm approximates the conditional distribution of the states by a multivariate Gaussian or t density, which is then used for posterior simulation. We further develop this baseline algorithm to construct more sophisticated samplers with attractive properties: one based on the accept-reject Metropolis-Hastings (ARMH) algorithm, and another adaptive collapsed sampler inspired by the cross-entropy method. To illustrate the proposed approach, we investigate the effect of the zero lower bound of interest rate on monetary transmission mechanism.