# Efficient Bayesian inference for nonlinear state space models with univariate autoregressive state equation

## TL;DR

This paper introduces an efficient Gibbs sampler for nonlinear state space models with univariate autoregressive states, improving inference in complex time-varying parameter models, especially in finance applications.

## Contribution

The paper proposes a novel Gibbs sampling method using interweaving and elliptical slice sampling for nonlinear state space models with autoregressive states, enhancing efficiency and applicability.

## Key findings

- Demonstrates improved sampler efficiency in simulation studies
- Achieves superior predictive accuracy over benchmark models
- Effectively models dynamic asymmetric tail dependence in financial data

## Abstract

Latent autoregressive processes are a popular choice to model time varying parameters. These models can be formulated as nonlinear state space models for which inference is not straightforward due to the high number of parameters. Therefore maximum likelihood methods are often infeasible and researchers rely on alternative techniques, such as Gibbs sampling. But conventional Gibbs samplers are often tailored to specific situations and suffer from high autocorrelation among repeated draws. We present a Gibbs sampler for general nonlinear state space models with an univariate autoregressive state equation. For this we employ an interweaving strategy and elliptical slice sampling to exploit the dependence implied by the autoregressive process. Within a simulation study we demonstrate the efficiency of the proposed sampler for bivariate dynamic copula models. Further we are interested in modeling the volatility return relationship. Therefore we use the proposed sampler to estimate the parameters of stochastic volatility models with skew Student t errors and the parameters of a novel bivariate dynamic mixture copula model. This model allows for dynamic asymmetric tail dependence. Comparison to relevant benchmark models, such as the DCC-GARCH or a Student t copula model, with respect to predictive accuracy shows the superior performance of the proposed approach.