The hessian method for models with leverage-like effects

djegnene, barnabe; mccausland. j, william;

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.