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Research design and validation

Research design, model validation, and reproducibility

The test comes before the conclusion. Every investigation declares its question, data, uncertainty, and failure criteria first.

Validation standard

Validation compares a model with pre-specified theoretical and empirical criteria; every conclusion remains conditional on the test design.

Purpose

Determine whether a result is reliable enough to inform a scoped allocation, risk, pricing, or governance decision.

Evidence required

Theoretical anchors, untouched data, uncertainty estimates, failure criteria, versioned artifacts, and reproducible execution.

Result classification

A validated, supported, rejected, or revised claim. The reason and the affected decision are stated.

Boundary

Passing validation does not make the model the market. It does not promise that future data will resemble the test.

Validation protocol

Five stages from research design to publication

  1. 01

    Frame a falsifiable question

    Name the decision and state the claim. Define in advance what evidence would count against it. “Explore the data” is not a falsification criterion.

  2. 02

    Engineer the evidence

    Document selection, dates, transformations, missingness, hashes, and provenance. Separate refreshing data from reproducing an existing experiment.

  3. 03

    Implement against anchors

    Test numerical code against identities, limiting cases, convergence behavior, and independent methods. A stored fixture is not an anchor.

  4. 04

    Test the model

    Use chronological holdouts, calibration tests, stress scenarios, uncertainty intervals, and multiplicity controls appropriate to the claim.

  5. 05

    Publish the boundary

    Report the result, uncertainty, failure modes, data vintage, source commit, and the decision that changes. Rejections and revisions stay published.

Evidence standards

Three conditions for an inspectable result

Traceable data

Sources, dates, transformations, missingness, hashes, and frozen vintages remain attached to the result.

Testable models

Theoretical identities, limiting cases, convergence behavior, holdouts, calibration, and stress tests define what can fail.

Bounded conclusions

Uncertainty, limitations, rejected claims, revisions, and the affected decision are reported together.

Evidence classification

Six classes prevent context from masquerading as proof

Lab measurement

A value generated from declared data, transformations, estimators, and uncertainty procedures.

Numerical validation

Agreement with an identity, limiting case, convergence rate, or independently implemented method.

External empirical evidence

An identified study or dataset evaluated separately from the lab's own measurement.

Institutional record

A dated decision, release, legal instrument, or official account. It establishes chronology and stated action, not causality.

Interpretive synthesis

A bounded connection among measured results, external records, mechanisms, and decision consequences.

Proposed research

A question, baseline, competing explanation, and publication gate declared in advance. No supported result yet.

Reusable resources

Three checklists for analytical work

Model-validation checklist

Use before approving a model for decision support.

  • Name the decision and the model owner.
  • State assumptions explicitly and make each one testable.
  • Anchor the model to theory or an independent method.
  • Prevent leakage by construction, not by inspection.
  • Test calibration and residual behavior.
  • Attach uncertainty to every reported result.
  • Include stress conditions and boundary cases.
  • Declare failure criteria before the comparison runs.
  • Write limitations in decision language.
  • Define monitoring and the revalidation trigger.

Portfolio stress-test checklist

Use before accepting an allocation because it looks diversified.

  • Stress expected returns and estimation error separately.
  • Challenge correlation, not only asset volatility.
  • Measure concentration by weights and risk contribution.
  • Include liquidity, turnover, and transaction costs.
  • Test chronological out-of-sample behavior.
  • Replay dated crises without treating them as bounds.
  • Map activity, inflation, liquidity, and institutional response separately.
  • Compare simple baselines to optimized portfolios.
  • Report drawdown and recovery, not only volatility.
  • State which risks remain outside the scenario set.

Use the Regime Atlas decision protocol →

Research-reproducibility checklist

Use before calling an analytical result reproducible.

  • Pin code to a commit or release.
  • Record data source, vintage, transformations, and hash.
  • Separate data refresh from experiment reproduction.
  • Declare seeds and random-generator family.
  • Document runtime and dependency requirements.
  • Preserve executed artifacts and machine-readable outputs.
  • Test a clean-clone reproduction path.
  • Publish uncertainty and numerical error budgets.
  • Link prose claims to the generating artifact.
  • Keep rejected and revised claims discoverable.

Inspect the record

Inspect implementation and evidence

Full audit trail

The research record preserves how each conclusion changed.

Questions, rejected claims, revisions, data versions, source commits, notebooks, and known limitations remain available for inspection.

Ledger

  1. Investigation 01 · Numerical validation

    Cross-method option-pricing validationValidated

    Question
    Do four independent implementations of European option pricing agree within their distinct, pre-declared numerical error budgets?
    Claim
    Black–Scholes, a CRR tree, a Crank–Nicolson PDE solver, and Monte Carlo will converge to the same arbitrage-free value; put–call parity will hold for every method.
    Assumptions
    • GBM under the risk-neutral measure
    • constant rate and volatility
    • frictionless markets
    • European exercise
    • identical contract inputs across methods.
    Dataset
    Synthetic benchmark contracts with S₀ = 100, r = 5%, σ = 20%, T = 1 year, K ∈ {90, 100, 110}; 200,000 antithetic paths; PCG64 seed 42.
    Method
    Cross-method price comparison, put–call parity, CRR convergence against a 1/n guide, PDE error checks, Monte Carlo standardized error, and implied-volatility round trips.
    Falsifier
    A deterministic method exceeds its discretization tolerance; Monte Carlo differs materially beyond its reported standard error; parity fails; or implied volatility does not round-trip to solver tolerance.
    Result
    The tree and PDE land within roughly 10⁻³ of closed form; Monte Carlo prices are statistically consistent with it; implied volatility returns to about 10⁻⁸. Monte Carlo uncertainty is reported as estimator standard error. Tree and PDE errors remain discretization-dependent.
    Failures
    • Agreement validates numerics, not GBM.
    • Exact terminal sampling flatters Monte Carlo.
    • Barrier, digital, and American contracts stress different weaknesses.
    • Model Greeks do not measure misspecified-dynamics hedging error.
    Record
    Four roads to one price · S₀ = 100, r = 5%, σ = 20%, T = 1
    MethodLargest |error| vs closed formToleranceVerdict
    Black-Scholes0referencepass
    Binomial(1000)0.001999470.01 abspass
    Crank-Nicolson0.0001366850.01 abspass
    Monte Carlo0.03140673.0 × SEpass
    Source
    ad24c49 · evidence ad24c49 · updated
  2. Investigation 02 · Portfolio construction

    Portfolio construction under estimation errorRevised

    Question
    How does portfolio construction change when classical return optimization gives way to uncertainty-aware risk allocation?
    Claim
    Methods that reduce or remove dependence on estimated returns will produce more stable out-of-sample risk profiles than unconstrained maximum-Sharpe optimization.
    Assumptions
    • Long-only, fully invested allocations
    • liquid ETF universe selected in 2026
    • historical moments stand in for future moments
    • identical raw covariance inputs
    • frozen weights during evaluation.
    Dataset
    Frozen adjusted-close snapshot for 15 ETFs, 2,891 daily observations from 2015-01-05 to 2026-07-06. Fit: 2015–2021. Sealed evaluation: 2022–2026. Seed 42.
    Method
    Compare max-Sharpe MVO, box-uncertainty robust MVO, equal-risk-contribution risk parity, and hierarchical risk parity in sample and on one untouched out-of-sample window.
    Falsifier
    The claim fails if return-optimized weights keep their in-sample advantage without added concentration or degradation. It also fails if risk-based portfolios do not reduce realized volatility and drawdown out of sample.
    Result
    MVO Sharpe fell from about 1.12 in sample to 0.44 out of sample. Risk-based portfolios ran at roughly half the volatility and two-thirds the drawdown of optimized books. They did not reliably win on return. Sharpe differences of ±0.2 sit well inside an estimated sampling error near 0.5 for this 4.5-year window. The broad claim was narrowed: risk-based methods delivered risk shape, not superior return.
    Failures
    • One evaluation window
    • survivorship-tilted universe
    • no rolling-origin test
    • frozen weights
    • raw rather than shrunk covariance
    • robust MVO preserved a concentrated ranking and benefited from a specific mega-cap regime.
    Revisions
    • — Published
    • — Editorial framing revised
    • — Underlying investigation last updated
    Source
    ad24c49 · evidence ad24c49 · updated
  3. Investigation 03 · Flagship derivatives study

    Empirical evaluation of constant-volatility dynamicsRejected

    Question
    Are the constant-volatility and Gaussian-return fingerprints required by Black–Scholes compatible with observed equity-index behavior?
    Claim
    If constant-volatility GBM is an adequate description, realized volatility should fluctuate around a stable level, return magnitudes should not remain autocorrelated, standardized returns should be approximately Gaussian, and one implied volatility should price every strike.
    Assumptions
    • SPY is used as an equity-index proxy
    • adjusted daily closes represent the observable return process
    • Heston parameters are illustrative rather than calibrated to a dated option chain.
    Dataset
    Frozen SPY adjusted-close snapshot, approximately 2,900 daily observations from 2015-01 to 2026-07. Seed 42 for simulated Heston paths.
    Method
    Measure rolling realized volatility, skew, kurtosis, extreme standardized moves, and return/absolute-return autocorrelation; then compare flat Black–Scholes volatility with Heston-generated strike and maturity skews.
    Falsifier
    Materially unstable realized volatility, persistent magnitude autocorrelation, fat or asymmetric tails, or a strike-dependent implied-volatility curve rejects the stated GBM fingerprints.
    Result
    The claim was rejected. Realized volatility ranged from roughly 3% to 93%; excess kurtosis was about 14; the worst day was near 10σ under a Gaussian yardstick; lag-1 absolute-return autocorrelation was about 0.35 and persisted. An equity-like Heston specification generated a short-dated skew near 25% to 16%. The rejection holds for this sample. The Heston surface demonstrates a mechanism, not a live market calibration.
    Failures
    • One underlying and one historical window
    • close-to-close returns omit intraday structure
    • parameters treated as constants still drift in practice
    • Heston omits jumps and rough volatility
    • simulation discretization carries bias.
    Revisions
    • — Published
    • — Editorial framing revised
    • — Underlying investigation last updated
    Source
    ad24c49 · evidence ad24c49 · updated
  4. Investigation 04 · Numerical simulation

    Monte Carlo convergence and numerical errorValidated

    Question
    Do the simulation library's errors behave as theory requires, and when does Monte Carlo earn its computational cost?
    Claim
    Exact schemes are free of time-step bias at observation points; Euler bias shrinks with Δt; independent-replication RMSE decays as N⁻¹ᐟ²; and antithetic sampling lowers estimator variance for monotone payoffs.
    Assumptions
    • Specified stochastic processes are the data-generating truth
    • PCG64 pseudorandomness is adequate
    • payoff and scheme comparisons use common random numbers where required.
    Dataset
    Fully synthetic experiments. Primary seed 42; 30 antithetic replications use deterministic seeds 1000 + replicate; convergence replications use 7000 + replicate.
    Method
    Benchmark exact and Euler GBM against closed form, estimate antithetic variance reduction across independent replications, test OU/CIR moments and boundaries, fit the Monte Carlo log–log convergence slope, and price a discretely monitored barrier.
    Falsifier
    Persistent bias from an exact transition, an Euler error that does not shrink with step size, a fitted RMSE slope materially different from −0.5, or confidence intervals that systematically miss known benchmarks.
    Result
    The N⁻¹ᐟ² law was recovered within replication noise; exact GBM remained unbiased across step counts; Euler bias contracted with Δt; antithetic pairing cut empirical standard error by about 30% at the same path budget. Every Monte Carlo estimate retains its reported sampling error.
    Failures
    • CIR and Heston discretization bias was not fully budgeted by step-halving
    • regime parameters were chosen rather than estimated
    • antithetics are weak for some payoff shapes
    • all results share one pseudorandom generator family.
    Revisions
    • — Published
    • — Editorial framing revised
    • — Underlying investigation last updated
    Source
    ad24c49 · evidence ad24c49 · updated
  5. Investigation 05 · Factor research

    ETF factor attribution and multiple-testing controlRevised

    Question
    Do widely held style ETFs load on their advertised factors, and does statistically credible alpha remain after those exposures are controlled?
    Claim
    Each branded ETF should have a positive, economically meaningful loading on its named factor; most apparent excess return should disappear after six-factor attribution.
    Assumptions
    • Linear exposures over each estimation window
    • the Fama–French five factors plus momentum span the relevant systematic effects
    • adjusted-close ETF returns approximate investor experience
    • Newey–West HAC(5) is sufficient for short-range residual dependence.
    Dataset
    2,867 aligned daily observations, 2015-01-05 to 2026-05-29. Factor snapshot ends 2026-05-29, SHA-256 6a8853963fab… ; price snapshot ends 2026-07-06, SHA-256 5dc8433e1c99… .
    Method
    Six-factor time-series OLS for MTUM, VLUE, QUAL, IWM, USMV, and QQQ with Newey–West HAC(5) intervals; 252-observation rolling QQQ betas; chronological 50/50 frozen-coefficient holdout; Holm and Benjamini–Hochberg correction across six alpha tests.
    Falsifier
    The claim fails if an advertised loading is absent, wrongly signed, or economically negligible. It also fails if alpha stays broad, stable, and statistically credible after exposure and multiple-testing controls.
    Result
    The advertised exposures were recovered. QQQ's +3.29% annualized alpha has a raw HAC p-value of 0.024. Its Benjamini–Hochberg q-value is 0.147, so no alpha survives the 5% false-discovery threshold. Frozen-coefficient holdout R² decays by 0.4 to 29.6 percentage points across ETFs; USMV decays most. Confidence intervals and adjusted p-values are published on the factor page.
    Failures
    • The factor menu defines the alpha left behind
    • factor portfolios are not costless tradables
    • eleven years is one historical sample
    • the 50/50 split is only one holdout path
    • HAC lag choice and vendor price adjustments can move inference.
    Revisions
    • — Published
    • — Editorial framing revised
    • — Underlying investigation last updated
    Source
    ad24c49 · evidence ad24c49 · updated
  6. Investigation 06 · Market risk

    Historical VaR coverage and independence backtestRejected

    Question
    Does a rolling 500-observation historical 95% VaR forecast achieve correct unconditional coverage and independent breaches for the cost-aware multi-asset portfolio?
    Claim
    If the model is calibrated, the breach rate should be statistically compatible with 5% and breach arrivals should not cluster.
    Assumptions
    • Fixed strategic weights
    • monthly rebalancing
    • 10bp proportional costs
    • frozen liquid-ETF universe
    • historical shocks are informative but not exhaustive
    • static correlation stress preserves asset volatilities.
    Dataset
    Frozen adjusted-close snapshot through 2026-07-06, SHA-256 5dc8433e1c99… ; 2,640 net backtest returns after warm-up and 2,140 one-step VaR forecasts. Moving-block bootstrap seed 20260803 .
    Method
    Look-ahead-free monthly backtest with 10bp turnover costs; one-day historical VaR/ES; 2,000-replication 21-day moving-block bootstrap; rolling 500-observation VaR; Kupiec coverage and Christoffersen independence/conditional-coverage tests; three date-fixed stress windows.
    Falsifier
    Reject calibration if the Kupiec or Christoffersen conditional-coverage p-value falls below 0.05. Report independence separately, so frequency error stays distinct from clustered failures.
    Result
    Rejected. The model records 135 breaches versus 107 expected (6.31%); Kupiec p = 0.0075, independence p = 0.00025, and conditional-coverage p = 0.000035. VaR95 is 1.079% with a block-bootstrap 95% interval of 0.930%–1.219%; ES95 is 1.718% with interval 1.421%–2.126%. The failure is both excess breach frequency and clustering.
    Failures
    • The bootstrap conditions on one realized history
    • block length is judgmental
    • empirical quantiles adapt slowly after regime changes
    • historical scenarios replay known crises
    • the fixed portfolio and close-to-close prices omit intraday liquidity and dynamic de-risking.
    Revisions
    • — Published
    • — Editorial framing revised
    • — Underlying investigation last updated
    Source
    ad24c49 · evidence ad24c49 · updated