Efficient Bayesian inference for univariate and multivariate non linear state space models with univariate autoregressive state equation
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Latent autoregressive processes are a popular choice to model time varying parameters. These models can be formulated as non linear 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 non linear state space models with an univariate autoregressive state equation. We employ an interweaving strategy and elliptical slice sampling to exploit the dependence implied by the autoregressive process. The sampler shows good performance for established models, such as stochastic volatility models with Gaussian and skew Student t errors as well as for dynamic bivariate copula models. Additionally, we use the sampler to estimate the parameters of a proposed bivariate dynamic mixture copula model. This model allows for dynamic asymmetric tail dependence and is employed to model the volatility return relationship. Comparison to relevant benchmark models, such as the DCC-GARCH or a Student t copula model, with respect to log predictive likelihoods shows the superior performance of the proposed approach.
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