As part of my analysis of heavy-tailed time series of company returns, I would like to check whether extreme returns exhibit serial dependence, i.e. if extreme events are followed by extreme events.
For now, I am only interested in testing uni-variate time series, i.e. I just want to check if an extreme return of company A has an impact on the returns of company A in the following days.
Since the autocorrelation function (ACF) of a time is looking at the whole return series (not only the extremes), it has limited value in assessing dependence dependence between extreme events.
In my search so far, I have found recent papers about the "extremogram" (http://arxiv.org/abs/1001.1821 and http://www.uis.no/getfile.php/Konferanser/paper_RichardDavis.pdf), something they view as the extreme-value analog of the ACF of a stationary process.
They also write that the extremogram is similar to the tail dependence coefficient of a uni-variate time series. While looking for more information about the tail dependence coefficient, I think tail dependence coefficients are mostly used in the analysis of co-movements in the tails of two distributions - which I am not interested in (for now).
Now finally my question:
- Are there any other methods available for estimating extremal serial dependence?
- Are there any implementations of the extremogram available in R/MATLAB? (Note: I have also contacted the authors and asked if they can share their code with me.)
- If there is no implementation available for the extremogram, are there any other applications available? (e.g. how could I calculate the tail dependence coefficient of a univariate time series in R/MATLAB).
Edit: Author of the extremogram papers replid to me and told me there is no "official" implementation of the extremogram in R/MATLAB yet, but he assured me that it is easy to implement. Will be working on my own implementation for the extremogram then.
