QuanterLab · Research

Educational research, not investment advice. Every result on this page is simulated; nothing here is a recommendation to buy or sell any security.

This is a Draft Document for tesing the report generation capabilities of the platfrom. Static Vs. Per-Regime Threshold Setting on a Mean Reversion Strategy

A point-in-time walk-forward investigation with sealed hypotheses and a multiple-testing (deflated Sharpe) correction.

By Serhat Girigin

Universe · Nasdaq 100 (point-in-time constituents)

Method · Comparative — Arm A vs Arm B

Manipulated variable · Regime

Step size · 1 year per forward window

In-sample · 2 years before each anchor

Out-of-sample span · 2011-01-03 → 2025-12-31

Compiled · July 24, 2026

Abstract · author’s wording

We seal a hypothesis and walk a strategy forward across Nasdaq 100 in 1-year steps, each tested out-of-sample on data the strategy had never touched, with survivorship-bias-free constituents reconstructed as of every anchor. This study walks the SAME sealed windows on two arms — Arm A and Arm B — identical in every respect except one declared variable: Regime. Paired date by date inside each window (3758 common out-of-sample observations across 15 windows), Arm A compounds at 17.4% a year against 15.4% for Arm B — a gap of 2.0 pp. A seeded block bootstrap of the paired return differences puts the probability that Arm A genuinely beats Arm B at 69.8%. Every attempt made along the way — 15 registered circuits, pruned candidates included — is counted in the correction, so the headline number reflects the true cost of the search.

1 Methodology

We conduct a sealed walk-forward comparison of two trading arms on Nasdaq 100 constituents over 15 annual steps spanning 2011 to 2025. Each arm operates on identical out-of-sample windows but differs in its optimization regime and signal configuration. Both arms begin with the same universe selection process. We score all Nasdaq 100 constituents across three statistical dimensions: Hurst exponent, Ornstein-Uhlenbeck half-life, and augmented Dickey-Fuller stationarity. We retain the top 10 securities by composite score for each year, ensuring our trading pool reflects mean-reverting candidates with strong statistical evidence. Arm A employs a static optimizer. For each annual step, we fit parameters on a 252-day in-sample training window using a single set of optimal RSI(7) thresholds that maximize Sharpe ratio across the entire lookback period. We sweep entry.value across 20 to 40 in five steps and exit.value across 60 to 80 in five steps, yielding 25 candidate parameter pairs per in-sample fit. The winning pair is then held fixed and applied to the subsequent 63-day out-of-sample test window. The signal rule is: enter long when RSI(7) crosses below 30; exit when RSI(7) crosses above 70. Arm B employs a per-regime optimizer. Using the same in-sample window and training objective, we segment historical data by a Gaussian-mixture regime classifier that detects macro states via volatility and return distributions. Within each regime, we optimize RSI(14) entry and exit thresholds independently, sweeping entry.value across 20 to 40 in six steps and exit.value across 60 to 80 in six steps. This yields 36 candidate parameter pairs per regime per step. The signal rule is: enter long when RSI(14) crosses below 30; exit when RSI(14) crosses above 70. The per-regime parameters are then applied forward into the test window, with regime assignment updated as new data arrives. Both arms follow rolling walk-forward discipline: optimize on year N, test on the following 63 days, step forward by 63 days, and repeat. This process unfolds across 15 consecutive annual anchors, ensuring no look-ahead bias and treating each test window as truly out-of-sample. The contrast under test is whether the added complexity of regime conditioning and RSI(14) tuning in Arm B generates better risk-adjusted returns than Arm A's static, simpler RSI(7) approach when both face the same out-of-sample periods. The walk has not yet been scored; performance metrics will be logged once all 15 steps complete.

Transaction costs are not modelled in this study; all results are gross of costs.

2 Results

2.1 Headline

Arm A — pooled deflated

76%

SR 0.68 · 3759 OOS bars

Arm B — pooled deflated

82%

SR 0.69 · 3759 OOS bars

P(Arm A beats Arm B)

69.8%

3758 paired bars · CAGR gap +2.0 pp

Figure 1. Both arms stitched through the identical windows — Arm A (+985.3%), Arm B (+736.4%), benchmark grey (+626.6%). Dotted verticals mark the step boundaries; the dashed horizontal is break-even.

2.2 Per-step results

**Table 1.** One row per surviving step. The deflated Sharpe uses the cumulative trial count at that step, so it falls as the search widens — the decay is the point.
#	Out-of-sample window	N	Arm A SR	defl.	Arm B SR	defl.
1	2011-01-03 → 2011-12-30	1	0.90	83%	1.01	84%
2	2012-01-03 → 2012-12-31	2	-0.55	13%	0.62	54%
3	2013-01-02 → 2013-12-31	3	2.23	94%	1.57	84%
4	2014-01-02 → 2014-12-31	4	0.46	28%	-0.03	14%
5	2015-01-02 → 2015-12-31	5	1.58	66%	0.55	26%
6	2016-01-04 → 2016-12-30	6	1.12	46%	0.27	15%
7	2017-01-03 → 2017-12-29	7	1.35	49%	0.89	30%
8	2019-01-02 → 2019-12-31	8	2.72	90%	2.35	90%
9	2019-01-02 → 2019-12-31	9	2.72	89%	2.35	89%
10	2020-01-02 → 2020-12-31	10	1.41	44%	1.06	30%
11	2021-01-04 → 2021-12-31	11	-0.14	4%	-0.64	1%
12	2022-01-03 → 2022-12-30	12	-0.12	4%	-0.60	1%
13	2023-01-03 → 2023-12-29	13	2.48	79%	3.24	97%
14	2024-01-02 → 2024-12-31	14	1.84	55%	1.23	31%
15	2025-01-02 → 2025-12-31	15	0.03	4%	1.11	25%

Figure 2. Arm A — every step's out-of-sample curve overlaid, each rebased to 1× at its own start. Read alongside Table 1: consistent shape across steps is the walk-forward's evidence; a single lucky leg is not.

Figure 3. Arm B — the same windows, the other arm. Compare shape-for-shape with the previous figure: the two arms trade the identical out-of-sample legs.

2.3 Trial accounting

The search registered 15 circuits in total (pruned candidates included); the correction uses this registered-circuit count, N = 15. The pooled deflated Sharpe is the inferential headline; the per-step deflated track in Table 1 is illustrative, since near-identical variants are correlated and per-step deflation over-penalises.

2.4 The comparison

Both arms trade the same sealed windows, so their returns can be PAIRED: inside each window the two return series are inner-joined date by date and the difference r_{Arm A} − r_{Arm B} is the object under test. Because this is ONE pre-declared contrast — sealed before any window was scored — the paired statistic needs no multiple-testing deflation; the per-arm pooled numbers above are still deflated by the trial count as usual.

**Table 2.** Window-by-window paired comparison. Δ is the growth gap (Arm A − Arm B) over the window's paired dates.
#	Window	Paired bars	Arm A	Arm B	Δ	Leader
1	2011-01-04 → 2011-12-30	251	+28.2%	+21.0%	+7.3 pp	Arm A
2	2012-01-04 → 2012-12-31	249	-37.3%	+9.9%	-47.2 pp	Arm B
3	2013-01-03 → 2013-12-31	251	+22.1%	+22.9%	-0.7 pp	Arm B
4	2014-01-03 → 2014-12-31	251	+8.4%	-1.7%	+10.1 pp	Arm A
5	2015-01-05 → 2015-12-31	251	+35.6%	+7.1%	+28.5 pp	Arm A
6	2016-01-05 → 2016-12-30	251	+24.2%	+3.4%	+20.8 pp	Arm A
7	2017-01-04 → 2017-12-29	250	+22.9%	+19.1%	+3.8 pp	Arm A
8	2019-01-03 → 2019-12-31	251	+45.4%	+12.4%	+33.0 pp	Arm A
9	2019-01-03 → 2019-12-31	251	+45.4%	+12.4%	+33.0 pp	Arm A
10	2020-01-03 → 2020-12-31	252	+52.5%	+32.9%	+19.7 pp	Arm A
11	2021-01-05 → 2021-12-31	251	-16.3%	-29.7%	+13.4 pp	Arm A
12	2022-01-04 → 2022-12-30	250	-17.6%	-29.9%	+12.3 pp	Arm A
13	2023-01-04 → 2023-12-29	249	+56.8%	+183.1%	-126.3 pp	Arm B
14	2024-01-03 → 2024-12-31	251	+49.0%	+39.6%	+9.3 pp	Arm A
15	2025-01-03 → 2025-12-31	249	-5.1%	+20.9%	-26.0 pp	Arm B

Paired Sharpe of the difference track: 0.13 · block bootstrap (2000 paths, block 10, seed 1234): P(Arm A beats Arm B) = 69.8%.

3 The circuit

The strategy is a circuit of platform primitives, frozen when the study is registered. Below is the circuit as wired on the canvas, the objective it encodes and how the search runs through it, followed by the mathematics each primitive actually computes — the same formulas the execution engine runs. The complete parameterisation is preserved in the study ledger (Appendix A).

The hypothesis under test

A COMPARATIVE study — Arm A vs Arm B, walked on the same sealed out-of-sample windows. Arm A: NASDAQ 100, selected by statistical / factor criteria, traded via enter long when RSI (length=7) crosses below 30; exit when RSI (length=7) crosses above 70, with parameters tuned in-sample to sharpe, and validated out-of-sample via walk-forward — the rule set is re-optimized on a rolling in-sample window and tested on the unseen window after it. Arm B: NASDAQ 100, selected by statistical / factor criteria, traded via enter long when RSI (length=14) crosses below 30; exit when RSI (length=14) crosses above 70, conditioned on the wired regime classifier, with parameters tuned in-sample to sharpe, and validated out-of-sample via walk-forward — the rule set is re-optimized on a rolling in-sample window and tested on the unseen window after it. The arms differ in: only in Arm A: Static Optimizer; only in Arm B: Per-Regime Optimizer, GMM Regime; parameters differ on: Signal Module, Walk-Forward (Rolling). The contrast under test: whether Arm A generates better risk-adjusted returns than Arm B over the identical out-of-sample windows.

Figure 4. The frozen circuit — every node a primitive, every wire a typed data-flow; the two arms are colour-coded (Arm A green, Arm B blue, shared feeds neutral).

The objective and the search

Arm A — NASDAQ 100, selected by statistical / factor criteria, traded via enter long when RSI (length=7) crosses below 30; exit when RSI (length=7) crosses above 70, with parameters tuned in-sample to sharpe, and validated out-of-sample via walk-forward — the rule set is re-optimized on a rolling in-sample window and tested on the unseen window after it.

Universe	NASDAQ 100 index constituents.
Selection	composite-scored across Hurst exponent, OU half-life, ADF stationarity → top 10 kept by composite score.
Signal generation	enter long when RSI (length=7) crosses below 30; exit when RSI (length=7) crosses above 70.
In-sample search	In-sample optimization via static (single best params across the in-sample); objective = sharpe; sweeping entry.value ∈ [20, 40] / 5 steps × exit.value ∈ [60, 80] / 5 steps; 252-day in-sample train window.
Validation & out-of-sample	rolling walk-forward (252d optimize / 63d test / 63d step); signal forward test (1y horizon from the anchor).

Arm B — NASDAQ 100, selected by statistical / factor criteria, traded via enter long when RSI (length=14) crosses below 30; exit when RSI (length=14) crosses above 70, conditioned on the wired regime classifier, with parameters tuned in-sample to sharpe, and validated out-of-sample via walk-forward — the rule set is re-optimized on a rolling in-sample window and tested on the unseen window after it.

Universe	NASDAQ 100 index constituents.
Selection	composite-scored across Hurst exponent, OU half-life, ADF stationarity → top 10 kept by composite score.
Signal generation	enter long when RSI (length=14) crosses below 30; exit when RSI (length=14) crosses above 70.
In-sample search	In-sample optimization via per-regime (independent best params per macro state); objective = sharpe; sweeping entry.value ∈ [20, 40] / 6 steps × exit.value ∈ [60, 80] / 6 steps; 252-day in-sample train window.
Validation & out-of-sample	rolling walk-forward (252d optimize / 63d test / 63d step); signal forward test (1y horizon from the anchor).
Regime layer	macro regime detected via Gaussian-mixture vol/return detector.

The manipulated variable — the arms differ in: only in Arm A: Static Optimizer; only in Arm B: Per-Regime Optimizer, GMM Regime; parameters differ on: Signal Module, Walk-Forward (Rolling). Everything else is held identical, so any out-of-sample gap between the arms is attributable to this difference.

No transaction-cost elements are wired into this circuit; results are gross of costs.

3.1 Signal Module

The entry / exit rule — turn indicators into a per-bar trade signal.

Composes indicators (RSI, moving averages, …) with comparison and logic operators into a rule that says enter, exit, or hold each bar. The rule is emitted as a portable config the optimizer tunes and the walk-forward validates — so what you design is exactly what gets traded.

Boolean rule → position state

\text{signal}_t = \begin{cases} +1 & \text{entry rule true} \\ 0 & \text{exit rule true} \\ \text{hold} & \text{otherwise}\end{cases}

e.g. enter when RSI < 30, exit when RSI > 50.

3.2 Static Optimizer

Grid-search one best parameter set over the whole in-sample window.

Sweeps a grid of parameter combinations, backtests each on the in-sample data, and keeps the single combination that scores best on your objective (Sharpe by default). One rule for the whole period — no time variation.

Argmax over the grid

\boldsymbol\theta^* = \arg\max_{\boldsymbol\theta\in\text{grid}} \;\mathcal O\big(\text{backtest}(\boldsymbol\theta)\big)

Objective 𝒪 ∈ {Sharpe, Calmar, Sortino, total return, profit factor, win rate}.

Default objective — Sharpe

\text{Sharpe} = \frac{\bar r - r_f}{\sigma_r}\,\sqrt{252}

3.3 Walkforward Rolling

Walk-forward with a sliding window — fixed-width, always recent.

Same out-of-sample discipline, but the training window is a fixed width that slides forward — each fold trains on the SAME amount of data, just more recent. Better when old regimes hurt and only recent behaviour matters.

Sliding folds

\text{fold}_k:\quad [\,\text{split}_k - W,\;\text{split}_k\,]\ \text{train} \;\to\; [\,\text{split}_k,\;\text{end}_k\,]\ \text{test}

Fixed train width W slides forward. Non-overlapping tests by default (step = test).

3.4 Backtest Validator

Forward-test the winning rule on unseen, out-of-sample data.

Takes the wired rule config (the Walk-Forward validated config wins, else the optimized config, else the raw signal config) and trades it FORWARD on the out-of-sample window to the right of the anchor — data it never saw during optimization — re-deriving the regime as-of each bar. It produces the true out-of-sample equity curve, trades and statistics: the signal-path twin of the Portfolio Forward Test, not an in-sample replay.

Apply the frozen rule forward (OOS)

E_t = E_{t-1}\,(1 + r_t),\qquad \text{Sharpe} = \frac{\bar r - r_f}{\sigma_r}\sqrt{252}

Config frozen from optimization / walk-forward, then replayed bar-by-bar on the forward window it has never seen, with cost + risk overlays applied.

3.5 Universe

The starting set of tickers — resolved point-in-time so there is no survivorship bias.

Before any math, you need a list of stocks. An index preset (S&P 500, Nasdaq-100, Dow 30) is reconstructed as it stood ON your anchor date by replaying the historical add/drop change-log backwards — so a 2018 backtest sees the 2018 membership, not today's winners.

Point-in-time membership

Start from today's constituents and un-apply every membership change after the anchor t:

\mathcal{U}(t) = \mathcal{U}_{\text{now}} \;\ominus\; \{\text{adds after } t\} \;\oplus\; \{\text{drops after } t\}

Constituents resolved from the index change-log; the same point-in-time set the factor + screening modules use.

3.6 Price Loader

Bulk OHLCV fetch for the whole universe — point-in-time, no future bars.

Momentum, volatility, trend — every price-based metric needs history. This loads open/high/low/close/volume for all names in parallel, clipped so nothing after the anchor can leak in. The lookback window is derived automatically from the deepest metric you wired.

The window is derived, not guessed

It loads exactly enough history for the hungriest downstream metric plus a warm-up buffer:

W = \max_k(\text{lookback}_k) + \text{buffer}, \qquad \text{bars} \le \text{anchor } t

3.7 Filter Hurst

The Hurst exponent — is this series trending, random, or mean-reverting?

Rescaled-range (R/S) analysis measures how the spread of a series grows as you look over longer windows. A random walk spreads like √n; trends spread faster, mean-reversion slower. The exponent H captures which.

Rescaled range scales as a power of the window

\mathbb{E}\!\left[\tfrac{R(n)}{S(n)}\right] \sim c\,n^{H} \;\;\Longrightarrow\;\; H = \frac{\log\!\big(R/S\big)}{\log n}

R = range of the cumulative deviation, S = standard deviation, over log-spaced windows n (10 → min(N/4, 200)).

Bias correction

H = \operatorname{clip}\big(\text{slope} - 0.06,\ 0,\ 1\big)

The R/S estimator runs slightly high on finite samples; the −0.06 correction (clamped to [0,1]) matches the Indicator-Strategies scanner exactly — the same ticker reads the same H in both.

Reading it

H < 0.5 → mean-reverting · H ≈ 0.5 → random walk · H > 0.5 → trending. The metric is attached to each stock; ranking + the cut happen in Composite Σ / Top-N.

The exact compute_hurst of the Indicator-Strategies MR scanner (shared scanner_metrics) — same algorithm, same bias correction, same number.

3.8 Composite Score

The composite — turn many metrics into one 0–100 score per stock.

Each wired metric is ranked across all stocks into a 0–100 percentile (you choose whether high or low is "good"), then the percentiles are weight-averaged. Ranking instead of raw values means no single unit dominates and outliers can't blow it up. It scores; it does not drop.

Per-metric cross-sectional percentile

\text{pct}_k(i) = 100 \cdot \frac{\operatorname{rank}_k(i)}{N}

Direction-aware: "low is good" (e.g. Hurst) inverts the rank.

Weighted blend

\text{score}_i = \frac{\sum_k w_k\,\text{pct}_k(i)}{\sum_k w_k} \in [0,100]

Metrics fanned in PARALLEL all contribute; a name missing a metric just omits that term.

3.9 Filter Ou Halflife

Ornstein–Uhlenbeck half-life — how many days a deviation takes to decay by half.

First remove the long-term drift (an OLS trend line fitted to log-price), then fit an AR(1) to what remains. The autoregressive coefficient β says how fast deviations from trend get pulled back; convert it to a half-life in days. Roughly 5–40 days is the tradeable sweet spot for mean reversion.

Detrend log-price first

\log P_t = a + b\,t + \varepsilon_t \quad\Longrightarrow\quad x_t = \log P_t - (a + b\,t)

Without detrending, a drifting stock looks like it never reverts — the AR(1) must see deviations from trend, not the trend itself.

AR(1) on the detrended residual

x_t = \alpha + \beta\,x_{t-1} + \varepsilon_t

Half-life from the decay rate

\text{half-life} = \frac{\ln 2}{\lvert \ln \beta \rvert}

β close to 1 → very slow reversion (long half-life); small β → fast. No mean reversion detected (β outside (0,1)) reports 999 — it ranks last and fails any "keep below" gate.

The exact compute_halflife of the Indicator-Strategies MR scanner (shared scanner_metrics) — detrended log AR(1), same number in both modules.

3.10 Filter Adf

Augmented Dickey–Fuller — a statistical test for stationarity (mean reversion).

Regress the change in price on its lagged level. If the level coefficient is significantly negative, deviations get pulled back — the series is stationary (mean-reverting). A low p-value rejects the "random walk" null.

The test regression

\Delta x_t = \gamma\,x_{t-1} + \sum_{i=1}^{p}\delta_i\,\Delta x_{t-i} + \varepsilon_t

Test H₀: γ = 0 (unit root / random walk) vs γ < 0 (stationary).

Reading it

p < 0.05 → reject the random walk → mean-reverting. The metric carried is the p-value (or the ADF statistic).

3.11 Top N

Keep the best N — rank, then cut.

Sort the survivors by the Composite Σ (or, if none is wired, the last metric in the chain) and keep the top (or bottom) N. The final narrowing from a scored list to a committed basket.

Order statistic cut

\text{Top-}N = \{\, i : \operatorname{rank}(\text{score}_i) \le N \,\}

"Keep highest" for momentum; "keep lowest" for e.g. Hurst (mean reversion).

3.12 Per Regime Optimizer

A separate best parameter set for each regime.

Partitions the in-sample window by a wired regime classifier and optimizes independently within calm, choppy and stressed. The strategy then switches parameters as the regime switches — different behaviour for different weather.

Argmax per regime

\boldsymbol\theta^*_g = \arg\max_{\boldsymbol\theta}\;\mathcal O\big(\text{backtest}(\boldsymbol\theta)\mid \text{regime}=g\big), \quad g\in\{\text{calm},\text{choppy},\text{stressed}\}

3.13 Regime Gmm

Gaussian mixture — cluster days into regimes, count chosen by BIC.

Treats each day as a point in (return, volatility) space and fits a Gaussian mixture; the Bayesian Information Criterion picks how many regimes the data actually support. States are vol-sorted and short runs de-noised. The rigorous detector the Per-Regime and Regression optimizers were designed around.

Mixture density + model selection

p(\mathbf x) = \sum_{k=1}^{K}\pi_k\,\mathcal N(\mathbf x\mid\boldsymbol\mu_k,\boldsymbol\Sigma_k), \qquad K^* = \arg\min_K \text{BIC}(K)

Features x = (log-return, realized-vol). K ∈ {2,3,4} or auto.

4 Sealed-hypothesis record

The integrity of a walk-forward rests on registering each hypothesis before its out-of-sample window is scored — the windows themselves are historical. The order below is the order in which the hypotheses were sealed.

“NASDAQ 100, selected by statistical / factor criteria, traded via enter long when RSI (length=7) crosses below 30; exit when RSI (length=7) crosses above 70, conditioned on the wired regime classifier, with parameters tuned in-sample to sharpe, and validated out-of-sample via walk-forward — the rule set is re-optimized on a rolling in-sample window and tested on the unseen window after it, is expected to generate positive risk-adjusted returns over the forward test window.”

The same hypothesis was sealed independently at every step — registered before each step's out-of-sample window was scored:

**Table 3.** Registration audit — one row per sealed step.
#	Anchor	Registered at
1	2011-01-01	2026-07-24
2	2012-01-01	2026-07-24
3	2013-01-01	2026-07-24
4	2014-01-01	2026-07-24
5	2015-01-01	2026-07-24
6	2016-01-01	2026-07-24
7	2017-01-01	2026-07-24
8	2018-01-01	2026-07-24
9	2019-01-01	2026-07-24
10	2020-01-01	2026-07-24
11	2021-01-01	2026-07-24
12	2022-01-01	2026-07-24
13	2023-01-01	2026-07-24
14	2024-01-01	2026-07-24
15	2025-01-01	2026-07-24

5 Discussion

A discussion interprets empirical findings. Until the walk finishes and logs performance numbers for the two arms against their identical validation windows, there are no results to read. To preserve the integrity of the sealed hypothesis and avoid post-hoc narrative, I will wait for the walk to score before drafting how Arm A (static RSI-7 optimizer) and Arm B (per-regime RSI-14 optimizer with GMM regime detection) actually performed relative to each other.

Pooled deflated Sharpe is the inferential number; the per-step DSR track is illustrative (near-identical variants are correlated, so per-step N over-deflates). N is a conservative upper bound on the multiple-testing penalty, frozen at compile time and taken as the larger of the lineage trial count and the explored-runs count so it cannot understate the search. Integrity rests on sealed hypotheses: each step's submitted_at is the order in which its hypothesis was registered, auditable against when its out-of-sample window was scored. The windows themselves are historical.

Motivation

This study examines whether incorporating regime awareness into the optimization process yields more predictive trading systems than static parameter selection. We deploy a walk-forward framework across 15 steps, spanning from 2011 through 2025, to test this question on the Nasdaq 100 universe.

Arm A employs a static optimizer, tuning RSI parameters with length 7 once per in-sample window and applying those fixed parameters across the subsequent out-of-sample test period. Arm B uses the same RSI signal structure but with length 14, conditioned on a Gaussian-mixture regime classifier that segments market states based on volatility and return patterns. Critically, Arm B re-optimizes its entry and exit thresholds independently within each detected regime, rather than seeking a single best parameter set. Both arms select from the same composite-scored pool of top 10 constituents by Hurst exponent, half-life, and stationarity metrics.

The manipulated variable is the optimization regime itself: Arm A holds parameters static across all market conditions in the test window, while Arm B adapts its parameters to the macro state it observes. This design isolates whether regime-aware parameter tuning produces superior predictive validity—that is, whether accounting for shifts in market structure during in-sample fitting leads to more robust performance when those market states recur out-of-sample. We measure this contrast through rolling walk-forward validation: a 252-day in-sample optimization window followed by a 63-day test window, stepped forward by 63 days, repeated across 15 steps. The out-of-sample results have not yet been scored and will reveal whether the regime-aware system's added complexity translates to measurable improvement in risk-adjusted returns.

References

As provided by QuanterLab

Bailey, D. H., & López de Prado, M. (2014). The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality. Journal of Portfolio Management, 40(5), 94–107.
Gelman, A., & Loken, E. (2013). The garden of forking paths: Why multiple comparisons can be a problem, even when there is no “fishing expedition.” Working paper, Columbia University.
Harvey, C. R., Liu, Y., & Zhu, H. (2016). … and the Cross-Section of Expected Returns. Review of Financial Studies, 29(1), 5–68.
Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36–52.

Appendix A Reproducibility in QuanterLab

Each step is backed by a frozen run report. The study is re-derivable from the ledger below.

#	Commit	Report	Anchor	OOS window
1	66ff2b275849	268	2011-01-01	2011-01-03 → 2011-12-30
2	b62735fc09f0	269	2012-01-01	2012-01-03 → 2012-12-31
3	7aede40fa0dc	270	2013-01-01	2013-01-02 → 2013-12-31
4	b448d206a540	271	2014-01-01	2014-01-02 → 2014-12-31
5	0c51cee24dce	272	2015-01-01	2015-01-02 → 2015-12-31
6	bcafb4f5cb51	273	2016-01-01	2016-01-04 → 2016-12-30
7	69b71a995d79	274	2017-01-01	2017-01-03 → 2017-12-29
8	caf74981ddf2	276	2018-01-01	2019-01-02 → 2019-12-31
9	403f59583278	278	2019-01-01	2019-01-02 → 2019-12-31
10	23aa21afe954	279	2020-01-01	2020-01-02 → 2020-12-31
11	f82540f9abd0	280	2021-01-01	2021-01-04 → 2021-12-31
12	a52d694ce260	281	2022-01-01	2022-01-03 → 2022-12-30
13	b66d0e51cd52	282	2023-01-01	2023-01-03 → 2023-12-29
14	92bba7cc69e9	283	2024-01-01	2024-01-02 → 2024-12-31
15	e6ab5dcff61b	284	2025-01-01	2025-01-02 → 2025-12-31

Appendix B Per-step diagnostics

What each step's run actually did beyond its return: capital allocation across lanes and regimes, the portfolio book's rebalancing and cost drag, and how positions were sized. Harvested from the frozen run reports — present where the circuit produced them.