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

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

J. Q. Smith and Antonio A. F. Santos*

Abstract

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 sec-
ond order approximation appears to perform well in these circumstances. We
demonstrate our results with a typical stock market series.

Keywords: Particle filters; Second order approximations; State space mod-
els; Stochastic volatility.

1 Introduction

Of the two most reported characteristics associated with financial returns time series
the first is the fat tails in the unconditional distribution of returns. More observa-

* University of Warwick(Department of Statistics) and Faculty of Economics at the University
of Coimbra.

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