An Ordinal Pattern Approach to Analyze Dependence Structures Between Real World Time Series

We introduce the concept of ordinal pattern dependence between time series and show in an explorative study that both types of this dependence show up in real world financial data.

The classical way to capture the leverage effect in models for stock markets is to assume a negative correlation between the two datasets which is constant in time (e.g. Barndorff-Nielsen and Shepard (2002)). However, there is strong evidence that this effect is not linear (cf. Whaley (2008)) and that it varies over time. Instead of proposing even more complicated models we introduce a rather simple approach to analyze whether there is a dependence structure between two datasets. In order to capture the zikzak of the datasets we use ordinal patterns.