Second-order filter distribution approximations for financial time series with extreme outliers

Particle filters are regularly used to obtain the filter distributions associated with state-space financial time series. The most common use today is the auxiliary particle filter (APF) method in conjunction with a first-order Taylor expansion of the log-likelihood. We argue that for series such as stock returns, which exhibit fairly frequent and extreme outliers, filters based on this first-order approximation can easily break down. However, an APF based on the much more rarely used second-order approximation appears to perform well in these circumstances. To detach the issue of algorithm design from problems related to model misspecification and parameter estimation, we demonstrate the lack of robustness of the first-order approximation and the feasibility of a specific second-order approximation using simulated data.