I am looking for a dataset of 'real-life' time series that exhibits non-comonotonic / non-countermonotonic dependence.
I am not looking for the textbook X^2 correlation, but interesting yet real non-linear association between variables.
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1$\begingroup$ Did you take a look at the UCR Time Series Classification Archive? cs.ucr.edu/~eamonn/time_series_data $\endgroup$– Vladislavs DovgalecsCommented May 3, 2016 at 22:29
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$\begingroup$ I had a quick look indeed. Not had time to run an analysis on the whole batch yet... $\endgroup$– micCommented May 3, 2016 at 22:33
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The predator-prey relationship is also a standard textbook example of a real-life, non-linear, lagged relationship between predator and prey population in a closed environment (see 1). As you can see, the predator and prey time series exhibit correlations, and their relationship is highly non-linear:
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$\begingroup$ Thanks. Yes, indeed. Have you also examples of non-lagged non-linear correlations? $\endgroup$– micCommented May 3, 2016 at 22:32
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$\begingroup$ Generally, I think lags are inevitable in real world examples, as correlations often have causal interpretations, which introduces a lag at some timescale. However, you can think of two time series -- a sine wave and cosine wave -- as an example of a non-linear relationship between two time series, and work backwards to see what physical processes might exhibit such behaviour. (Example: temperature during the day and time of day, etc.) $\endgroup$– VimalCommented May 3, 2016 at 22:41