# Adaptive Lag Walk-Forward: M2 → BTC

## Protocol

This evaluates forward-matured pairs, not the trailing window used to choose a
lag. Every seven days from 2020-01-01, the engine estimates a 30–120 day lag
from the preceding 365 daily observations (minimum 240). It then records the
transformed source at selection time against transformed BTC at the selected
lag's future maturity. Results below use zero assumed source availability delay
because the archive does not include authoritative macro release timestamps.

Each baseline follows the same schedule and scores source at `t` against BTC
at `t + fixed_lag`. Bootstrap intervals use 14-day moving blocks and 500
deterministic resamples.

## Results

| Transform | Adaptive r [95% block CI] | Fixed 45d r [95% block CI] | Adaptive mean lag |
| --- | --- | --- | ---: |
| Levels | +0.708 [+0.593, +0.818] | +0.723 [+0.606, +0.832] | 57.4 |
| First difference | +0.017 [-0.061, +0.084] | +0.035 [-0.056, +0.121] | 67.0 |
| Percentage change | +0.038 [-0.032, +0.107] | +0.091 [-0.027, +0.229] | 66.5 |
| Log return | +0.031 [-0.041, +0.096] | +0.091 [-0.025, +0.227] | 68.4 |

The zero-lag levels baseline is also +0.744, stronger than adaptive levels;
this confirms that level correlations are not evidence of a useful lead. The
return/change results are weak and every interval includes zero. Fixed 45 days
outperforms adaptive for every stationary transform tested, although its own
intervals are also inconclusive.

## Availability-delay sensitivity

The same archive can model conservative availability assumptions by delaying
the displayed source series. Across 0, 7, 14, and 30 day delays, adaptive
correlations stayed weak for every stationary transform:

| Transform | Adaptive r at 0d / 7d / 14d / 30d delay |
| --- | --- |
| First difference | +0.017 / +0.037 / +0.038 / +0.035 |
| Percentage change | +0.038 / +0.031 / +0.012 / +0.001 |
| Log return | +0.031 / +0.035 / +0.052 / +0.004 |

Every adaptive block-bootstrap interval included zero. Several fixed 72/90-day
results at 7–14 day delay were modestly positive (for example log-return fixed
72d at a 7-day delay: `r=+0.134`, 95% interval `[+0.043, +0.278]`), but this
does not validate adaptive selection and needs independent confirmation before
being treated as a signal.

## Decision

Do not promote adaptive lag, fixed lag, or M2 as a trading signal from this
export. The desired criterion—adaptive out-of-sample improvement over both
fixed and zero-lag baselines—was not met.

The archive is sufficient for TradingView-consistent delay sensitivity because
it contains the M2 value visible at each chart bar. Release/vintage data would
be needed only for a stricter external-data study. The stopping point for this
adaptive-lag work is reached: do not implement a Pine consumer or connect it
to trading logic. A separate fixed-lag 72-day hypothesis may be investigated
only as a fresh, independently validated experiment.