The highest rated answer to the question on What concepts are the most dangerous ones in quantitative finance work? is this one:
Correlations are notoriously unstable in financial time series [...]
My question is a little bit broader than just about linear dependence, it is:
What is the most stable, non-trivial dependence structure in financial data?
With non-trivial I mean that I don't want answers that are about direct connections, e.g. between derivative and underlying.
The dependence structure can be either cross-sectional or through time with univariate time series, it can also be non-linear.
The context of my question is that I am preparing the documentation for a new machine learning R package I wrote and I am looking for a good showcase in the financial sphere. Now this is not a trivial feat given that correlations are notoriously... see above ;-)