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

J.Q. Smith and Antonio Santos

6 An empirical demonstration

In this section we intend to demonstrate empirically that the first order APF ap-
proximation is not reliable when applied to a stock return series, namely, when it has
to update the distribution of the states associated with extreme observations. We
use a series of graphs displays and tables of results that try to illustrate that, with
the first order approximation, there are situations where sample impoverishment is
extreme.

Figure 1: Rolls Royce stock returns

We analysed a series of daily returns regarding the Rolls Royce stock, traded on
the London Stock Exchange. In this series we had 3818 observations. This series is
depicted in Figure 1 and shows all the main characteristics found in the majority
of financial time series, e.g., the presence of extreme observations and volatility
clustering. We considered three sub-samples and analysed each one by adjusting an
SV model to fit the data (Table 1). The parameters were estimated as being the

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

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