Test serial dependence before you optimize a mechanical system

The test belongs on the system you already have

The relevant object of an autocorrelation test is the mechanical trading system already under study, not a hypothetical system constructed later from the same analysis. That system's successive results are ordered observations. Serial dependence means one outcome carries information about the next.

Significant dependence can filter later signals

If those successive results show statistically significant interdependence, the finding is treated as unusually strong and potentially usable as a filter on later signals.

One proposed use of detected streaks is a metasystem that accepts signals in the direction suggested by the dependence and rejects opposite signals until the system itself reverses.

Incorporating the dependence should remove it

Once the original system is altered to incorporate the detected interdependence, the serial association that motivated the change is expected to disappear.

Count every later optimization as shrinkage

Rerunning or continuing an experiment after an earlier test reduces the statistical significance of the first result. That reduction is described as optimization shrinkage.

A later optimized result can still exceed an earlier one even after shrinkage is factored in. The mere fact of system optimization does not by itself settle whether optimization was warranted.

The historical argument is not that one should always optimize or never optimize. Any optimization that is performed must be counted and discounted in the evaluation.

Parametric correlation is a practical first measure

Parametric correlation is defended as a practical serial-dependence measure because it is familiar, immediately usable if a metasystem is to be designed, and more sensitive than a nonparametric alternative when dependence takes the form of straightforward serial correlation.

Other forms of dependence exist that parametric correlation may not detect. Dissatisfaction with that measure does not exhaust the statistical options.