Efficient Bayesian Inference for Nonlinear State Space Models With Univariate Autoregressive State Equation

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.

Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo

“…We set T = 1000 and obtain simulations of the one-day ahead predictive distribution as described above for the first trading day in 2012. Instead of refitting the model for each day we fix parameters that do not change over time (µ, φ, σ, δ, m) at their posterior mode estimates and only update dynamic parameters (S, v) as in Kreuzer and Czado (2019) for the remaining oneday ahead predicitve simulations. For updating only the dynamic parameters we have seen that it is enough to use the last 100 time points and time needed for computation is reduced a lot.…”