Abstract
We propose a new method for simulation smoothing in state space models with univariate states and conditional dependence between the observation yt and the contemporaneous innovation of the state equation. Stochastic volatility models with the leverage effect are a leading example. Our method extends the HESSIAN method of McCausland (2012, Journal of Econometrics, 168, 189–206), which required conditional independence between yt and the state innovation. Our generic method is more numerically efficient than the model-specific methods of Omori et al. (2007, J. Fin. Econ., 140, 425–449)—for a stochastic volatility model with Gaussian innovations—and Nakajima and Omori (2009, Comput. Stat. Data Anal., 53, 2335–2353)—for a model with Student's t innovations.
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