High Frequency Returns Sign-Based Robust Inference

We derive the limit of infill asymptotic distribution for the sum of positive returns of prices or log-prices in a given period of time. The framework is multivariate and quite general: it allows for the presence of leverage effects and jumps with finite activity. In a second step, the results are used to estimate the drifts (or rather, the Sharpe ratios) of the continuous part of the processes.