Walk-forward evaluation of recursive yen trend signals

A single testable procedure

The archive specified a recursive yen trend system as one procedure. A constant-level smoother, a straight-line forecast, and dollar-up and dollar-down thresholds were fitted together rather than judged as separate parts.

Walk-forward evaluation was the acceptance step. Parameters from each in-sample window were applied to the next unseen year before the long and short rules were treated as more than an in-sample curve-fit.

Continuous contracts are not live rolls

A continuous yen futures series was built from quarterly contracts by switching on rollover and back-adjusting the price gap so the history looks smooth. That continuous contract remains different from live rolls.

Results on that series cannot match live trading because of rollover costs and execution slippage. Percentage-of-price rules applied to a back-adjusted continuous series can also be distorted, because each rollover difference is written back into earlier prices.

Recursive estimates instead of daily refits

Recursive polynomial fitting updates the next-day price estimate from a few lagged estimates plus the current close. It does not re-solve a least-squares straight line over a large block of past closes each day. That update is a recursive estimate.

Under a constant-level model the recursion reduces to an exponential moving average, a slowly updating mean that treats price as reverting toward a measured level. Under a degree-one linear model the same recursion produces a recursive trendline, treated as a one-step forecast of price if the recent path is a line with a changing slope.

A trend oscillator gated by dollar thresholds

The system oscillator is the gap between that one-step trendline forecast and the exponential moving average. The gap is the trend oscillator used to decide whether a directional move exceeds ordinary daily noise.

The system goes long when the gap exceeds a dollar-up threshold and short when the gap falls below a negative dollar-down threshold. Both entries are taken on the close. Each dollar threshold is the minimum oscillator displacement, up or down, required before a signal is issued.

Walk-forward windows and stable parameters

Walk-forward evaluation fitted three parameters: lookback length converted to a smoothing constant, plus the dollar-up and dollar-down thresholds. Each walk-forward window was a fixed-length in-sample segment. The fit from that segment was then applied to the next unseen year, and those years were merged into one out-of-sample record.

The windows themselves were successive five-year samples. Candidate parameter sets were kept only when nearby values left results nearly unchanged and consecutive losses stayed at four or fewer. An in-sample optimum was treated as a curve-fit until the following year was checked.

Across six successive five-year windows the selected lookback and threshold values changed little. That stability was taken as a check that five years of data were enough to stabilize the next out-of-sample year.

How the walk-forward signals behaved

Charted walk-forward signals held established yen trends once those trends had formed. Sudden reversals, gaps, and choppy stretches produced most of the losses.

Reported drawdown and run-up percentages were computed on full contract notional. The same equity move would appear larger if it were restated against futures margin rather than against the full contract.