Abstract: This paper studies the predictability of ultra high-frequency stock returns and durations to relevant events, using machine learning methods. We find that, contrary to low frequency and long horizon returns, where predictability is rare and inconsistent, predictability in high frequency returns and durations is large, systematic and pervasive. We identify the relevant predictors and examine what determines the variation in predictability across different stocks and market environments. Next, we compute how the predictability varies with the timeliness of the data on a scale of milliseconds. Finally, we determine the value of getting a (short-lived and imperfect) peek at the incoming order flow, an ability that is often attributed to the fastest high frequency traders, in terms of improving the predictability.