Pairs trading and correlations

I approach pairs trading with the correlations tool-box and basic algebra. Let's consider two time series, a(t) and b(t). It will be understood that these are taken on a fixed time scale (second, minute, hour, and the like). Most explanations of pair trading fail to communicate the importance of non-zero correlations at non-zero time lags -- let alone the importance of their constructive interference (to be explained). Meanwhile, it is these subtleties that make a difference between just another roulette-like source of random outcomes and a reliable, little-risk source of arbitrage profits.

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