# Account for empirical relationship between signal and market data

I have two monthly time series : one is a 'signal', on which I will base my decision to buy or short-sell, and the second one is the time serie of a given asset's price.

I have implemented this extremely naive algorithm : if the signal at time t is positive, buy at t-1, sell at t, if it is negative, short at t-1, buy at t. Testing several (signal, asset) pairs, I find that for some of them I make significant cumulative profit over the years, and for some other, I don't.

So I want to explain why this works for some pairs and not for others (or, instead of causality, find a criteria or a quantity that would be characteristic of "good pairs"). Purely investment-wise, it might (but not more than "might") be enough, but I can't be satisfied with it, and it's not rigorous.

So far, I have (with Python/pandas):

• computed the correlation (Spearman, Kendall and Pearson) between the signal time serie and the asset price / returns, but the results are low for the good pairs
• tried to perform a linear regression the returns against the signal, but the $\beta$ are insignificants and $R^{2}$ very low, which points (as far as I understand) to at least no linear relationship between the two time series

I would like to know what other leads to explore (I gladly accept books/articles references as well, if this is an extensively discussed question !)

• First of all, how do you know a "good" pair is good rather than lucky? – John M Jun 7 '16 at 19:12
• @JohnM : By "good", I meant that my naive strategy produces significant results, but I'd say that my whole point : how can I know whether these discrepancies between the results are due to mere luck or if here is a stronger-than-luck relationship ? – B2000 Jun 8 '16 at 6:48