A cointegration analysis on a triangle of high frequency exchange rates is presented. Market efficiency requires the triangle to be cointegrated and the cointegration term to be a martingale difference sequence. We find empirical evidence against market efficiency for very short time horizons: The cointegration term does not behave like a martingale difference sequence. In an out-of-sample forecasting study the cointegrated vector autoregressive (VAR) model is found to be superior to the naive martingale. Finally, a simple trading strategy shows that the VAR also has a significant forecast value in economic terms even after accounting for transaction costs. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"