Stochastic technical analysis for decision making on the financial market

We apply the well-known CUSUM and the Girshick-Rubin algorithm as trading strategies involving only mutually exclusive long positions in cash and the DAX at Frankfurt mid-day auction prices. We select optimal pairs of fixed thresholds for up- and down- movements from a pre-defined two-dimensional grid, hence, admitting asymmetric intervals. We show that under three different scenarios for transaction costs, the CUSUM technique not only outperforms the passive investment in the DAX but also the alternative Girshick-Rubin algorithm.