Finding if there is big divergence in current values of two variables X& Y wrt their historical values

Question

I have two variables X and Y.

I have historical data about X and Y.

I have quantified correlation between X and Y

My Question is : Given current value for X(= x_current) and Y(=y_current) AND I want to quantify how divergent current (x_current, y_current) value is from historical correlation value between X and Y. How this is solved in practical applications ?

Note: This is not academic question. I am professional and forgotten many of these things taught to me at school and don't even remember technical terms used for defining these questions.

Can u please answer or point to appropriate resource for further research ?

Answer 1

Your question is a little short on details (e.g. are $x_{current}$ or $y_{current}$ single values or sets?), but I'll give two suggestions for what you could do.

1. A statistical approach would be to compare the correlation in a set of old data to that of a set of new ("current") data, using the Fisher transformation ("r-to-z") to do significance testing.

2. Since you tag with machine-learning, you might want to consider using machine learning-based outlier detection approaches (e.g. see here). Basically, you learn a model for the historical data, and then ask it whether the current data is abnormal (a measure which can be quantified), given that model. This is not specifically for correlations though, I suppose.