Walk-forward velocity filters on noisy intraday trends

The second part of a velocity-based eurodollar study

This article is the second part of a two-part treatment of a velocity-based system applied to eurodollar futures on one-minute bars.

Walk-forward analysis splits the series into many successive in-sample and out-of-sample sections, applies a performance-metric filter to each in-sample optimization, and then tests only those selected inputs on the immediately following out-of-sample section.

Why a full-sample combinatorial search is not enough

A single combinatorial search over the whole series is treated as curve-fitting both repeatable patterns and non-repeating spurious moves, so the best in-sample inputs are not accepted without out-of-sample checks repeated many times.

Walk-forward analysis is a repeated in-sample search and immediately following out-of-sample test that averages many independent windows so chance-fitted noise is not treated as a durable rule.

How the performance-metric filter keeps one row

The walk-forward metric filter used here first requires fewer than 60 in-sample trades so the selected inputs tend to follow the main intraday trend rather than generate more than about three trades a day.

After the trade-count gate, the filter ranks remaining rows by a median runup-minus-final-profit metric and an equity-smoothness term so that one in-sample row, and its inputs, is left for each window.

A performance-metric filter is that rule applied to the in-sample optimization table. It keeps one input row by jointly constraining trade count, runup-to-profit closeness, and equity-path smoothness.

Paired out-of-sample weeks across many windows

That filter is applied across 310 in-sample sections, producing 310 paired out-of-sample weeks whose average and dispersion are used to describe expected weekly results rather than one lucky window.

Under a normal-distribution assumption on weekly results, the reported breakeven horizon for this filter is 33 weeks for a 98 percent chance that cumulative out-of-sample equity is above zero, and the longest stretch without a new equity high is 17 weeks.

Fading-memory velocity that changes with noise

A least squares moving average is a polynomial fit to recent prices whose slope is treated as fading-memory velocity. The polynomial degree can change with how noisy the in-sample window is.

Selected lookback, velocity thresholds, and polynomial degree jump from window to window. Noisier in-sample data is assigned slower first- or second-order velocity, while cleaner data is assigned faster third- or fourth-order velocity.

The trend filter is a gate that lets the velocity-based system trade only when estimated trend strength exceeds an explicit threshold, so noisy one-minute moves do not generate entries.

What the 310-week out-of-sample run reported

After a stated 30-dollar round-trip cost, the 310-week out-of-sample run on one eurodollar contract reports 49421 dollars net equity, a largest losing week of 3550 dollars, a largest drawdown of 4400 dollars, an average of 2.2 trades per week, activity in 188 of 310 weeks, and 60 percent of trades profitable, with no overnight positions.