Daily returns for stocks listed on the New York Exchange (NYSE) are not serially correlated while order imbalances on the same stocks are highly persistent. These empirical facts can be reconciled if sophisticated investors react to order imbalances within the trading day by undertaking enough countervailing trades to remove serial dependence over a daily horizon. How long does this actually take? The pattern of intra-day serial dependence reveals that it takes more than five minutes but less than sixty minutes.