Unified Mixture Sampler for State-Space Models: Application to Stochastic Conditional Duration Models

We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each specific distribution, our approach dynamically adapts the standard ten-component mixture from Omori et al. (2007) through a deterministic re-centering and rescaling algorithm. Applying this to the stochastic conditional duration (SCD) model, we demonstrate that the proposed sampler can efficiently handle unknown shape parameters - such as those in Weibull or Gamma distributions - by updating mixture components near-instantaneously during MCMC iterations. The UMS not only simplifies implementation but also ensures exact inference via a lightweight Metropolis-Hastings step. Numerical examples show that our method substantially outperforms the conventional slice sampling approach, significantly reducing autocorrelation in MCMC samples while maintaining high computational efficiency. This unified framework encompasses a wide range of applications, including logit, Poisson, and various SCD model specifications, providing a highly efficient alternative to model-specific samplers.