In his book, "Why Stock Markets Crash", Didier Sornette discusses a trading strategy that exploits return correlations.

Consider a return $r$ that occurred at time $t$ and a return $r'$ that occurred at a later time $t'$, where $t$ and $t'$, are multiples of some time unit (say 5 minutes). $r$ and $r'$ can be decomposed into an average contribution and a varying part. We are interested in quantifying the correlation $C(t, t')$ between the uncertain varying part, which is defined as the average of the product of the varying part $r$ and of $r'$ normalized by the variance (volatility) of the returns, so that $C(t, t' = t) = 1$ (perfect correlation between $r$ and itself).

A simple mathematical calculation shows that the best linear predictor $m_t$ for the return at time $t$, knowing the past history $r_{t-1}, \> r_{t-2}, \ldots ,r_i, \ldots,$ is given by

$$m_t\equiv\frac{1}{B(t, t)}\sum_{i<t} B(i, t)r_i,$$

where each $B(i, t)$ is a factor that can be expressed in terms of the correlation coefficient $C(t', t)$ and is usually called the coefficient $(i, t)$ of the inverse correlation matrix. This formula expresses that each past return $r_i$ impacts on the future return $r_t$ in proportion to its value with a coefficient $B(i, t)/B(t, t)$ which is nonzero only if there is nonzero correlation between time $i$ and time $t$. With this formula, you have the best linear predictor in the sense that it will minimize the errors in variance. Armed with this prediction, you have a powerful trading strategy: buy if $m_t \> > 0$ (expected future price increase) and sell if $m_t < 0$ (expected future price decrease).