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

Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. The method most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the log-likelihood. We argue in this paper that, for series such as stock return, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, the auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. We demonstrate our results with a typical stock market series.