Before revision:  Finally, the methods are illustrated in two empirical applications motivated from finance. We study time seriesof log-prices and log-volatility from 29 individual US stocks; no evidence of non-semimartingality in asset prices is found, but we do find evidence of non-semimartingality in volatility. This confirms a recently proposed conjecture that stochastic volatility processes of financial assets are rough (Gatheral et al., 2014) .
After revision:  Finally, the methods are illustrated on two time series; one of turbulent velocity flows and one of financial prices .