1. Short interpretation of your results

- Multi‑year, purged CV has now told you something decisive:

- OLD baseline (raw x1) > FIXED (x1×sign(x2)) on both 10‑day and 20‑day.

- The 13‑feature model is clearly better at 10‑day, only marginally better at 20‑day.

- This is exactly what should happen when you go from “single‑year / low‑regime‑diversity” to “multi‑year / multi‑regime” tests: fragile transforms get exposed.

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2. Can sign(x2) correction itself add noise on multi‑regime data?

Yes, यह बिल्कुल genuinely possible है, और यह established statistical intuition के साथ consistent है.

Key points:

1) Theoretical fix was conditional on extra assumptions

Theory “x1 should be used with a sign correction from x2” implicitly requires:

- sign(x2) is economically and statistically stable across regimes, and

- sign(x2) is not itself dominated by high‑frequency noise, and

- x2 is not frequently near 0 (where small noise flips sign).

If any of these fail on the longer, multi‑year sample, then the implementation of a theoretically‑sound idea becomes empirically harmful.

2) Hard sign() is an extremely high‑variance, discontinuous transform

- Around x2≈0, very small perturbations (micro‑noise, microstructure effects, small regime drifts) flip sign(x2) from −1 to +1 or vice‑versa.

- When you multiply x1 × sign(x2), you are effectively letting these tiny perturbations flip the direction of x1 completely.

- On a 1‑year sample where x2 had a more consistent sign/level, this looked good. On a 3‑year sample with more regime shifts, the same transform becomes a random direction flipper.

3) Multi‑regime = mixture of “good” and “bad” application of the fix

If on some regimes x2’s sign correctly indicates “flip x1”, and on other regimes it does not, then:

- On 2024‑only, you may have been mostly in a “good” regime → fix looked great.

- On 2024‑26, you’re averaging over good+bad regimes → fix moves from “helpful” to “net harmful”, as now clearly seen in AUC.

So, yes: even if the original economic theory is qualitatively right, a hard sign(x2) correction can be empirically counter‑productive when x2’s sign is regime‑dependent or noisy. What you’re seeing is exactly what one would expect under sign instability of x2.

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3. Relation to earlier Diagnostic A (subsampling, coefficient‑sign instability)

आपका अभी वाला pattern उसी दिशा का stronger evidence है:

- Earlier, subsampling / bootstrapping showed coefficient‑sign instability for the effect you are trying to capture.

- Now, on extended multi‑year, purged CV data, the structural transform built on that assumption (x1×sign(x2)) is underperforming the naive x1.

Interpretation:

- The model was implicitly assuming a stable sign of the effect captured by x2 across subsamples.

- Diagnostic A had already told you: that sign was not stable.

- Extending the sample (2024–2026) and doing proper purged CV is a much stronger test, and it is confirming that earlier warning.

In other words: yes, यह पहले की finding (sign instability) का एक और, ज़्यादा कठोर रूप है; multi‑year test ने उसी weakness को और साफ़ कर दिया है.

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4. Declining per‑fold AUC for New model [0.58, 0.58, 0.51] with 3 folds

Two parts:

1) Statistically, 3 folds = very low N for pattern detection

- With only 3 ordered time folds, a sequence 0.58, 0.58, 0.51 can be just noise.

- You cannot claim “true structural decay” based solely on 3 points.

2) But time‑ordered CV folds are not exchangeable

- Fold 3 is later calendar time.

- If Fold 3 corresponds to a different regime (e.g., 2026 or a more volatile period), then the drop from 0.58 → 0.51 is a useful diagnostic hint:

- The model may be regime‑specific (works on earlier years, struggles on the most recent).

- Or features that help historically may be mis‑calibrated for the latest regime.

What is “established practice” here?

- Do not over‑interpret a strict “declining trend” from 3 points.

- But it is worth a limited, targeted investigation:

- Which calendar period is Fold 3?

- Does label distribution, volatility, or microstructure look very different there?

- Are some core features’ distributions or importances shifting heavily in Fold 3?

So:

- Over‑fitting a story to 3 folds → avoid.

- A brief regime‑wise breakdown focusing on Fold 3 → worth doing, as a diagnostic, not to rescue the model by arbitrary re‑tuning.

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5. Should you now treat the sign‑correction hypothesis as “failed” and archive it?

Given what you report, the answer is: yes, this specific hard sign(x2) correction for x1 should be treated as a failed hypothesis on this universe/label.

Reasoning:

1) Extended sample + purged CV + clear underperformance vs simpler baseline

- FIXED < OLD across horizons in a proper purged, multi‑year setup.

- That is exactly the kind of test quant teams treat as decisive for killing a transform.

2) Previous “success” was on a narrow window (2024‑only)

- That earlier validation is now clearly revealed as regime‑specific / overfitted once we include 2025–2026.

- Step‑5 style discipline says:

> When robust out‑of‑sample / extended‑sample tests conflict with earlier in‑sample/small‑window success, believe the larger, more robust test.

3) Consistency with diagnostics

- Your subsampling / sign‑instability evidence + current AUC outcomes are aligned:

- The underlying sign assumption is not stable.

- Continuing to tweak around the same exact idea now mostly risks p‑hacking.

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6. Any “last diagnostics” worth doing before you archive?

If you want to be methodical, you can define a small, finite checklist and then commit to closure after that. For example:

(1) Simple stability check on x2 itself (no model re‑tuning)

- Year‑wise (or regime‑wise) correlation of x2 with the target.

- Year‑wise distribution of x2 conditional on label (e.g., y=+1 vs y=−1).

- Rolling correlation / rolling logistic coefficient sign.

If sign of the relationship flips across years or is near zero most of the time, that is a clean explanation: the core assumption behind sign(x2) is violated → hypothesis formally failed.

(2) Ablation on the transform (again, no hyper‑parameter fishing)

Compare on the same purged CV:

- Model A: uses x1 only (OLD).

- Model B: uses x1 and x2 as separate features, no hard sign correction.

- Model C: uses x1, x2, and an interaction x1×sign(x2) (or x1×x2).

If:

- A and B behave fine,

- C is systematically worse,

then the evidence points clearly to this particular transform as harmful, not the general idea that “x2 might contain useful information”.

(3) Implementation sanity check (one‑time)

- Confirm that sign(x2) is computed with correct time alignment, no look‑ahead, correct handling of NaNs/zeros, etc.

This is just to ensure you are not mis‑killing a hypothesis due to a bug. Do this once, then move on.

If these checks confirm what the AUCs already suggest (and they likely will), then by your own Step‑5 standard the correct professional move is:

> Archive this specific hypothesis: “For this universe/label, transforming x1 into x1×sign(x2) improves predictive power.”

Importantly, that does not force you to discard:

- x1 as a feature,

- x2 as a separate feature,

- or the broader conceptual idea of regime‑dependent adjustments.

It only says: this particular, hard, sign‑based correction is not robust on full multi‑year data.

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Summary

- Yes, it is entirely consistent with established theory and practice that a sign(x2) correction which looked good on 2024‑only now becomes net harmful on multi‑year, purged data, especially when x2’s sign is itself unstable/noisy.

- Yes, this aligns with your earlier subsampling evidence of coefficient‑sign instability; multi‑year CV has just made that fragility clearer.

- The declining [0.58, 0.58, 0.51] per‑fold AUC is a weak pattern statistically but a reasonable diagnostic hint; investigate Fold‑3’s regime, but don’t over‑interpret 3 points.

- After a small, clearly defined set of final diagnostics (stability of x2, ablation, sanity‑check), it is methodologically sound to mark this sign‑correction as a failed hypothesis and archive it, exactly as you did with Trend‑Direction‑v2.

If you have any further queries, please connect with us on 022-6290-10141 (Timings : 09.00 AM to 05.00 PM) or you can email us on info@cniinfoxchange.com