Which Trend is your Friend?

Managed futures funds and commodity trading advisers (CTAs) use heuristics or statistical measures often called “filters” to trade on price trends. Two key statistical measures of trends are “time-series momentum” and “moving-average crossovers.” We show, empirically and theoretically, that these trend indicators are closely related. In fact, they are equivalent representations in their most general forms. They also capture many other types of filters, such as the Hodrick–Prescott (HP) filter, the Kalman filter, and all other linear filters. We show how these filters can be represented through “trend signature plots,” demonstrating their dependence on past prices and returns by horizon.