Okay, so the logarithmic return on a stock is given by:
$$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time.
I have no problem calculating that. My question comes to the following formula:
$$ρ(T) \sim 〈r_τ (t+T) \cdot r_τ (t)〉$$
This is supposedly the autocorrelation function of log-returns. What's the deal with the brackets?