Walk-forward evaluation for fading-memory velocity systems

Withholding trades inside the noise band

The fading-memory adaptive polynomial velocity procedure treats polynomial order, the number of prices used to estimate coefficients, and two velocity thresholds as unknown inputs, and it issues a trade only after those thresholds leave the noise band. Untrended price meandering can be treated as noise, with trading withheld until estimated trend velocity rises above a minimum noise threshold.

Fading-memory velocity as the trend encoding

A fading-memory polynomial is a polynomial fit that down-weights older price errors so recent bars dominate the estimated path and its velocity. That weighting differs from an equal-weight least-squares polynomial. The zero-order case reduces to an exponential moving average.

Higher-order fading-memory velocity includes acceleration-like terms, so second- through fourth-order velocity can change faster than first-order straight-line velocity. The search is allowed to choose the degree.

One procedure for entry, exit, and abstention

A velocity threshold is a noise gate that withholds long or short signals until estimated velocity leaves a deadband around zero. Trading stays withheld while estimated trend velocity remains inside that noise band.

The stated rules buy when velocity exceeds an upside threshold, sell when velocity falls below a separate downside threshold, ignore signals before 7:00 am, and flatten at 1:50 pm so no position is held overnight.

System optimization as one procedure

System optimization is a grid search over polynomial degree, memory length, and velocity thresholds so entry, exit, and abstention are tested as one procedure. It is specified over four inputs: polynomial degree, the exponential decay weight alpha, the long velocity threshold, and the short velocity threshold.

The in-sample search grid covers degree 1 through 4, memory length N from 20 to 70 in steps of 10, and both velocity thresholds from 0.25 to 3 in steps of 0.25, producing 3456 input combinations in each window.

Walk-forward analysis on unused weeks

Walk-forward analysis is a rolling split that ranks inputs on a recent in-sample window and then scores the locked rules on the next unused out-of-sample week. The in-sample window is the stretch of bars used only to rank candidate input sets. The out-of-sample window is the unused stretch reserved to test inputs chosen from the prior in-sample window.

The specified design uses 30-calendar-day in-sample windows followed by the next one-week unused window, rolled week by week across 314 weeks of one-minute eurodollar futures bars to create 310 paired files.

Robustness testing after in-sample ranking

Robustness testing is a check that inputs chosen from in-sample rankings are not accepted until they are examined on later bars that were not used to select them. In-sample rankings after that search are treated as mostly curve-fit, so the later unused bars are the check on whether those chosen inputs still hold.