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You can treat this "problem" as an statistics one, usign covariance, correlation, p-value, etc...
Using covariance and correlation for knowing if there exists a true (statisctly based) relation between symbols, or in a case that you have multiple, choosing that has the higher correlation.
So, doing an study on your symbols may give you a more statisctial perspective on this problem.
As I continue reading, I can tell you are well versed on this topics (correlation and covariance), so then I will suggest checking more advanced statistical technics such as ARIMA (for forecasting an only symbo) or VAR (for forecasting and checking correlation on multiple symbols) for your correlation problems.
And GARCH or ARCH for variance (volatility).