Return trajectory and the forecastability of bitcoin returns

This paper tests the extent to which the ability to correctly predict subsequent bitcoin (BTC) return signs is dependent upon historic BTC return trajectories. Using topological data analysis ball mapper (TDABM), we demonstrate that the performance of random forest and logit regression models varies according to return trajectory. A novel use of TDABM as a forecast model shows that mapping historic return trajectories can also produce more accurate directional return forecasts. Our approach highlights how the predictability of BTC price change direction is dependent on return trajectories. Visualizing historic return trajectories when forming and evaluating return forecasts is imperative.