1. Looking at the extremes in volatile return series
You are going to look at one other feature of a volatile financial return series, and that is the appearance of the extreme values.
2. Extracting the extreme of return series
You will take a longer version of the FTSE daily log-return series spanning the 20-year period from 1991 to 2010.
Then you will select only those days on which the negative value of the log-return exceeds point zero two five. Since log-returns are very close to relative returns, this can be interpreted as the days on which there was approximately a two point five percent fall in the value of the index.
The displayed code selects these days and creates a new time series containing the negative log-returns on those days only. First, a series ftse_losses containing the negative log-returns is created, and then the losses exceeding two point five percent are picked out.
Then the first four extreme values are displayed, and the number of extreme days is counted.
There are 115 days with negative log-returns exceeding point zero two five. However, there are none in the 4-year period 1993 - 1996, as can be seen in the results from the head() command.
3. Plotting the extremes values
Now you can plot this irregular time series.
By using the type="h" option, you can get a plot with vertical bars.
It is also suggested that you switch off the auto.grid feature to prevent the automatic plotting of gridlines.
What you should observe in this picture is that there are long periods of time, including much of the mid-1990s (as already mentioned) and the mid-2000s in which there are no extreme values at all.
On the other hand, there are clusters of extreme values in 1998, in 2002 and then again during the financial crisis of 2008-2009.
The phenomenon of volatility clustering leads to the clustering of extreme values.
This is not the behavior that would be observed in an iid series. In an iid series, the most extreme values occur completely at random, and the times between their appearance can be modeled as being very close to exponentially distributed.
What you are going to see in the next exercise is that the times between the extremes of a real financial return series are far from exponentially distributed. This can also be used as the basis for a test for the presence of serial dependence.
4. Let's practice!
So let's go ahead and work through the next exercise and compare and contrast more closely the behavior of extremes in real financial time series and iid series.
After that, you'll do another exercise in which you study the dependencies not only within individual return series but also across series.