I have a single time series of financial data (stock index returns) and would like to study the autocorrelation among (log-)returns that are classified as "extreme", for example via exceedance of a certain threshold. The threshold could be defined by some quantile (5% for example). From filtering the data I can see that this kind of returns commonly occur in clusters.
- What would be the right method/approach for this type of problem?
- Does it make sense to separate positive and negative "extreme" returns?
- How can I include the temporal distance between "extreme" returns and/or return clusters in this problem?
(I'm familiar with Mathematica and GNU R, so advice in this direction is of course welcome too)
