Before revision:  Assuming Brownian market self-similarity, the market return  memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior and a long-time tail similar to the empirical observations .
After revision:  Assuming Brownian market self-similarity, the market return memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior with a long-time tail similar to the empirical observations .