Evaluating trend, breakout, and regression rules by average robustness

A locked comparison of trend measures

Each trend measure in the comparison was limited to one free parameter so that extra rules would not tilt the ranking toward overfitting. Linear regression entered as a slope on ordered prices, and the breakout system bought new highs and sold new lows. Both sat inside a trend-following wrapper that treated entry, exit, and remaining flat as one procedure.

One wrapper and three measures

Trend-following is a complete directional procedure that buys when the measured trend turns up and sells when it turns down, with no separate target or stop, so entry, exit, and staying out are one testable rule.

The breakout system is a one-parameter rule that goes long on a new high and short on a new low and leaves the position unchanged while price stays between those extremes.

Linear regression is a slope fitted to ordered prices over a fixed lookback. The sign of that slope is the forecast that becomes the directional signal.

Every method used the same execution wrapper: buy when the trend turns up, sell when it turns down, fill on the next open, and apply no profit target or protective stop.

Direction-change signals

Signals in the comparison were triggered by a change in trend direction rather than a price cross of the trend line, because the line was treated as the filter for noisy prints. A direction-change signal is an entry or exit taken when the trend measure itself flips, filled on the next open, rather than when price crosses a plotted line.

Calculation period and market grid

The calculation period is the single free lookback applied to each method and swept from 30 to 150 days, the band treated as typical of slower, policy-linked moves.

The grid covered four futures sectors: long-term bonds, the euro, an equity-index contract, and crude oil, from 1991 through March 2018, with a fixed cost charged on each side of a contract.

Average robustness, not a peak window

A single best window was rejected as the ranking statistic because isolated spikes can come from lucky timing around shocks. The average across all windows was used instead.

Robustness is the ability to remain useful across many lookbacks and across markets with unlike noise and path structure, judged from the average of the whole grid rather than from one peak window. The historical test asked the same thing: work across many calculation periods and across markets that represent different sectors and price patterns.

Ranking and risk shape stay separate

Average ranking and risk shape were treated as separate evaluation questions. A moving average tends to cut losses quickly with many small losers, a breakout holds through wide swings with fewer trades, and the regression slope sits between those two profiles.