Gianna FigÓ-Talamanca, Fabio Bellini
In this work we provide a simple method to locate and measure dependence in the tails of a time series, based on the ''runs test'', a non parametric statistical test for detecting dependence in a 0-1 series.
We plot the p-value of the runs test against several values for the threshold, to construct what we call in the sequel the dependence plot. This allows us not only to measure dependence in a quantitative way, but also to locate at which thresholds the dependence ''turns on''.
The empirical results on daily data reveals a very strong departure from independence; it seems that the effect dies out quickly if we consider returns over longer periods.
We show that in most cases dependence in the tails can be successfully modeled through a two state Markov chain.
A possible interest in this kind of analysis could be found for Value at Risk computation purposes.