This article introduces a new efficient simulation smoother and disturbance
smoother for asymmetric stochastic volatility models where there exists a correlation
between today's return and tomorrow's volatility. The state vector is divided
into several blocks where each block consists of many state variables. For each
block, corresponding disturbances are sampled simultaneously from their conditional
posterior distribution. The algorithm is based on the multivariate normal
approximation of the conditional posterior density and exploits a conventional
simulation smoother for a linear and Gaussian state space model. The performance
of our method is illustrated using two examples (1) simple asymmetric
stochastic volatility model and (2) asymmetric stochastic volatility model with
state-dependent variances. The popular single move sampler which samples a
state variable at a time is also conducted for comparison in the first example. It
is shown that our proposed sampler produces considerable improvement in the
mixing property of the Markov chain Monte Carlo chain.
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