Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outlier

J.Q. Smith and Antonio Santos

Table 1: First section: Descriptive Statistics associated with each sub-sample of the series.
Second section: Estimates of the parameters for each sub-sample, which were obtained
as the mean of the posterior distribution defined through MCMC estimation techniques.
Third section: Sample impoverishment figures, which were calculated as the number of
times the range of the filter distribution was less than 0.2.

mean of the posterior distribution, which was obtained using Markov chain Monte
Carlo techniques. By considering three sub-samples we were able to analyse the
particle filter performance for different sets of parameters. A by-product of these
estimation procedures is the smoothing distribution of the states. Despite being
associated with different information sets, it is nonetheless convenient to compare
the smoothed distributions with the filter distributions obtained using algorithms
based on first and second order Taylor approximations to the log-likelihood. We ran

G.E.M.F - F.E.U.C.

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