Time EruptionWaiting timeEruption

Long wait Short wait

Long eruption Short eruption

Short eruption, short wait Long eruption, long wait

Conclusion: The longer the eruption, the longer the wait for the next one

Carbon Dioxide CO 2 Temperature Carbon dioxide concentration is related to the Earth temperature

Carbon dioxide concentration is related to the Earth temperature

Possible solution: Control CO 2 to affect temperature

? Each asset can be described by the (possible) distribution of future values.

Asset A Asset B Portfolio (A+B) ?

Some processes (and random variables) are connected We can measure (or control) one process to predict (or control) another Thus, we need to a) manipulate with several random variables b) establish connections among random variables

Data set “Davis” from package R Outlier

Data set “Davis” from package R Kendall’s  = 0.36 Pearson’s r  = Spearman’s  = 0.49

Kendall’s  = 0.57 Pearson’s r  = 0.9 Spearman’s  = 0.78 Old Faithful geyser data

Kendall’s  = 0.01 Pearson’s r  = 0.01 Spearman’s  = 0.01 Non-monotone trend