Statistical Conventions and Formula Audit

Market Model (MacKinlay 1997)

The Market Model regresses firm returns on index returns over the estimation window by OLS and defines the abnormal return as the residual in the event window.

Audit result: verified against MacKinlay (1997); two silent-wrong defects fixed 2026-09-24 (items A6). The core OLS/AR/CAR formulas match MacKinlay. The 2026-09-24 re-evaluation found the insufficient-observations guard used a flat n_valid < 2 threshold (too permissive for a 2-parameter OLS fit to be meaningful) and the forecast-error correction’s mean(Rm_est)/SS_market included estimation rows where firm_returns was NA but index_returns was not – rows lm() silently drops via na.omit() but which the correction formula still summed over, biasing the correction away from the fitted model’s own estimation sample. Both are fixed; pinned in test_golden_values.R and test_reeval_statistical_fixes.R against an independent closed-form lm() derivation restricted to complete pairs, at absolute tolerance 1e-10/1e-12.

Citation: MacKinlay, A. C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature, 35(1), 13–39.

Market Adjusted Model

The Market Adjusted (index) model treats the market index itself as the expected return: it fixes alpha = 0 and beta = 1 rather than estimating them, so the abnormal return is simply the firm return minus the index return. It is the restricted market model of MacKinlay (1997) sec. 4.4.2.

Audit result: one silent-wrong defect fixed 2026-09-24 (item A8). The subtraction AR = R - Rm matches the restricted market model. The 2026-09-24 re-evaluation found the forecast-error correction wrongly reused the constant-MEAN formula sigma * sqrt(1 + 1/m) – which is only valid when ONE parameter (a mean) is estimated from the estimation window, as in the Comparison Period Mean Adjusted Model below. MarketAdjustedModel estimates NOTHING (alpha/beta are fixed, not fitted), so its correction factor is exactly 1: forecast_error_corrected_sigma == sigma. Re-pinned in test_golden_values.R and locked in test_reeval_statistical_fixes.R at absolute tolerance 1e-10/1e-12.

Citation: MacKinlay, A. C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature, 35(1), 13–39.

Comparison Period Mean Adjusted Model

The Comparison Period Mean (constant-mean-return) model uses the firm’s own average return over the estimation window as the expected return. It is the constant-mean-return model of Brown & Warner (1985), also described in MacKinlay (1997) sec. 4.4.1.

Audit result: verified, no change. AR, sigma, df, and FEC match the constant-mean-return model. Pinned in test_golden_values.R against a closed-form subtraction against the fixed estimation mean at absolute tolerance 1e-10.

Citation: Brown, S. J., & Warner, J. B. (1985). Using daily stock returns: The case of event studies. Journal of Financial Economics, 14(1), 3–31. MacKinlay (1997).

Fama-French Three-Factor Model

Regresses firm excess returns on the three Fama-French factors – market excess (market_excess), size (smb), and value (hml) – by OLS over the estimation window; the abnormal return is the residual in the event window. All factor models share the LinearFactorModel OLS core.

Audit result: verified, no change (guard strengthened 2026-09-24, item A6). The OLS fit and hat-value FEC match Fama-French (1993). Pinned in test_golden_values.R against an independent lm()/predict() derivation at absolute tolerance 1e-10.

Citation: Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3–56.

Fama-French Five-Factor Model

Extends the three-factor model with profitability (rmw) and investment (cma) factors – Fama & French (2015). Same OLS core, five factors.

Audit result: verified, no change (guard strengthened 2026-09-24, item A6). Pinned in test_golden_values.R against an independent lm()/predict() derivation at absolute tolerance 1e-10.

Citation: Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22.

Carhart Four-Factor Model

Extends the three-factor model with a momentum factor (mom) – Carhart (1997). Same OLS core, four factors.

Audit result: verified, no change (guard strengthened 2026-09-24, item A6). Pinned in test_golden_values.R against an independent lm()/predict() derivation at absolute tolerance 1e-10.

Citation: Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57–82.

Custom Model

The Custom Model inherits the Market Model’s OLS estimation but defines the abnormal return as firm_returns - predict(user_model), plus an optional event-date adjustment loss_market_cap added only on the event date. There is no single published closed-form here – the convention is deliberately “whatever the supplied model predicts.”

Audit result: documented convention (no closed-form pin possible). With loss_market_cap = 0 the Custom Model reduces exactly to the Market Model; that identity is what test_golden_values.R pins (absolute 1e-10). A general user-supplied prediction has no published reference value to pin against.

Citation: Convention is user-defined; the reduction case cites MacKinlay (1997).

BHAR Model (Barber-Lyon 1997)

The Buy-and-Hold Abnormal Return (BHAR) model is for long-horizon studies where compounding matters. Instead of summing daily abnormal returns it compounds firm and benchmark returns separately over the event window and takes the difference.

Audit result: verified, no change. The compounded BHAR, the sigma * sqrt(n) scaling, and the constant-mean forecast-error correction match Barber-Lyon (1997) / Lyon-Barber-Tsai (1999). Pinned in test_golden_values.R against an independent closed-form compounding at absolute tolerance 1e-10.

Citation: Barber, B. M., & Lyon, J. D. (1997). Detecting long-run abnormal stock returns: The empirical power and specification of test statistics. Journal of Financial Economics, 43(3), 341–372. Lyon, J. D., Barber, B. M., & Tsai, C.-L. (1999). Improved methods for tests of long-run abnormal stock returns. Journal of Finance, 54(1), 165–201.

Volume Model

The Volume model runs an event study on trading volume rather than returns. Expected volume is the estimation-window mean of (optionally log-transformed) volume, and abnormal volume is the deviation from that mean. It writes abnormal volume into the abnormal_returns column so the standard test statistics apply.

Audit result: verified, no change. The log-mean expected volume, the deviation-from-mean abnormal volume, and df = m - 1 match the standard abnormal-trading-volume convention. Pinned in test_golden_values.R against a direct log-mean subtraction at absolute tolerance 1e-10.

Citation: Convention follows the abnormal-trading-volume literature (e.g. Campbell & Wasley 1996, log relative volume); the mean-adjusted form is the volume analogue of the constant-mean-return model of Brown & Warner (1985).

Volatility Model

The Volatility model runs an event study on return variance. Expected variance is the estimation-window sample variance, and abnormal volatility is the ratio of each event-window squared return to that variance, minus one (so zero means “as expected”). It writes the measure into abnormal_returns for compatibility.

Audit result: verified, no change. The ratio-to-expected-variance abnormal measure and df = m - 1 match the abnormal-volatility convention. Pinned in test_golden_values.R against a direct ratio computation at absolute tolerance 1e-10.

Citation: The squared-return / expected-variance ratio follows the event-induced-variance literature (Beaver 1968; Patell & Wolfson 1979), adapted to the constant-variance benchmark of the estimation window.

Rolling-Window Model

The Rolling-Window model captures parameter instability by estimating the market model over a rolling OLS window and using the LAST window’s parameters to predict the event window. This yields a time-varying beta without a full GARCH model.

Audit result: one silent-wrong defect fixed 2026-09-24 (item A1). The rolling OLS, last-window prediction, and df = n_complete - 2 are internally consistent once restricted to complete pairs. Pinned in test_golden_values.R on a 30-observation fixture where ws = min(60, 30) = 30 collapses to a single closed-form OLS, and in test_reeval_statistical_fixes.R on a 150-day window with firm-return NAs co-occurring with index outliers every 3rd day (beta, alpha, sigma, and df all match lm() on the complete-pair subset within 1e-10).

Citation: Rolling-window / time-varying market-model estimation is standard practice for capturing beta instability (e.g. Fama & MacBeth 1973 rolling regressions); the underlying market model is MacKinlay (1997).

GARCH Model

The GARCH model fits a GARCH(1,1) mean-variance model to firm returns with the index return as an external regressor in the mean equation (via the optional rugarch package). The abnormal return is the mean-equation residual.

Audit result: verified, no change (identity-pinned). Because rugarch is an optional dependency and its fitted coefficients vary across package and solver versions, pinning a raw fitted constant would be fragile (threat T-26-02). The documented golden-value choice is therefore to pin the STABLE ALGEBRAIC IDENTITY AR = firm - (mu + mxreg1 * index), which holds for any fitted coefficients, in test_golden_values.R guarded by skip_if_not_installed("rugarch") – locking the AR formula without a version-fragile number.

Citation: Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

DCC-GARCH Model

The DCC-GARCH model (via the optional rmgarch package) fits a bivariate Dynamic Conditional Correlation GARCH to firm and market returns, yielding a time-varying beta beta_t = Cov(firm, mkt)_t / Var(mkt)_t. The last conditional beta predicts the event window.

Audit result: verified, no change (identity-pinned). As with GARCH, rmgarch is optional and non-deterministic across versions, so the documented golden-value choice is to pin the stable identity AR = firm - (alpha_last + beta_last * index) in test_golden_values.R guarded by skip_if_not_installed("rmgarch") / ("rugarch"), rather than a fragile fitted constant.

Citation: Bollerslev, T. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model. Review of Economics and Statistics, 72(3), 498–505. Engle, R. F. (2002). Dynamic conditional correlation. Journal of Business & Economic Statistics, 20(3), 339–350.

Multi-event all-NA exclusion (2026-09-24 re-evaluation, item A2)

Every CAR-based multi-event statistic (CSectTTest, PatellZTest, SignTest, GeneralizedSignTest, BMPTest, KolariPynnonenTest) shares one exclusion rule, implemented once in R/contract.R (.exclude_all_na_events()) and applied centrally by calculate_statistics() before any configured statistic runs (so N statistics in one group produce AT MOST ONE warning, not N), and defensively again at the top of each compute() for direct/standalone calls: an event with zero finite event-window abnormal returns is EXCLUDED from the group entirely – not NA-propagated and coalesced to 0 – because cumulating a fully-degenerate event’s abnormal returns as 0 would silently understate the true cross-sectional dispersion (an entirely different failure mode from a normal 0 abnormal return). Excluded events whose model already emitted the one contract warning guaranteed by CONTRACT-04 (an unfitted ModelBase instance) are dropped SILENTLY; any other excluded event is reported once, naming the event_id(s) (strict mode errors instead). This exclusion leaves the pre-existing STATS-03 convention for a PARTIAL gap unchanged: an event with at least one finite event-window abnormal return, but a missing value on some individual day, still contributes 0 to THAT EVENT’s own CAR on the missing day(s) via coalesce(abnormal_returns, 0).

AR / CAR t-tests (ARTTest, CARTTest)

Documented above with the Market Model, since the tracer anchors them together. The AR t-test divides each event-day abnormal return by the model sigma; the CAR t-test divides the cumulative abnormal return by sqrt(L) * sigma. Both are distributed as Student’s t with the model’s residual degrees of freedom and are two-sided by default. Every return model also computes forecast_error_corrected_sigma_car (the FEC’s per-event covariance/hat-value term), but ARTTest/CARTTest INTENTIONALLY do not use it – they keep the simpler constant-sigma approximation (item A11, documented convention, no formula change); forecast_error_corrected_sigma_car exists for consumers that need the full prediction-error covariance structure. Citation: MacKinlay (1997).

BHAR t-test (BHARTTest)

The single-event buy-and-hold abnormal-return t-test. Documented above with the BHAR Model, since the model and its t-test share the same compounded definition and sigma * sqrt(n) scaling. In its general form the statistic is bhar_t = BHAR / (sigma * sqrt(n)), where BHAR = cumprod(1 + firm) - cumprod(1 + index) over the event window, sigma = sd(firm - index) over the estimation window, and n is the day index within the event window. It returns NA (never Inf/NaN) when sigma == 0. Two-sided by default. Citation: Barber & Lyon (1997); Lyon, Barber & Tsai (1999).

Cross-Sectional t-test (CSectTTest)

The cross-sectional t-test evaluates, at each relative event day, whether the average abnormal return across events is zero, using the cross-event dispersion of abnormal returns as the standard error. It is the workhorse parametric test of Brown & Warner (1985).

Audit result: verified against Brown & Warner (1985); two silent-wrong defects fixed 2026-09-24 (items A2, A9). The core sqrt(n_valid_events) * aar / sd(AR) / caar / sd(CAR) construction matches Brown & Warner. The 2026-09-24 re-evaluation found n_pos used >= 0 (so a zero AR silently counted as “positive”) and that a fully-degenerate event (all event-window ARs NA, e.g. an unfitted model) was not excluded from the cumulative CAR-based statistics – its coalesce(AR, 0) silently understated cross-event dispersion instead of being excluded. Both are fixed; pinned in test_golden_values.R and test_reeval_statistical_fixes.R against an independent closed-form cross-sectional computation at absolute tolerance 1e-10/1e-12.

Citation: Brown, S. J., & Warner, J. B. (1985). Using daily stock returns: The case of event studies. Journal of Financial Economics, 14(1), 3–31.

Patell Z-test (PatellZTest)

The Patell (standardized-residual) test standardizes each event’s abnormal return by its own forecast-error-corrected standard deviation before aggregating, which accounts for the fact that event-window prediction errors have larger variance than estimation-window residuals. The aggregate is approximately standard normal.

Audit result: verified against Patell (1976); three silent-wrong defects fixed 2026-09-24 (items A2, A6, A9). The standardization by the forecast-error-corrected sigma and the Q_total = sqrt(sum Q_i) aggregation match Patell. The 2026-09-24 re-evaluation found: (1) k was derived as length(resid) - df instead of read from each model’s own n_params, silently using the WRONG k whenever df reflected an unrelated adjustment; (2) m used the raw estimation-window row count instead of the finite-observation count; (3) n_pos used >= 0; and (4) an all-NA event was not excluded from the statistic. All four are fixed; re-pinned in test_golden_values.R and locked in test_reeval_statistical_fixes.R against an independent closed-form Patell computation at absolute tolerance 1e-10, plus a guard test confirming NA for a single-event group.

Citation: Patell, J. M. (1976). Corporate forecasts of earnings per share and stock price behavior: Empirical tests. Journal of Accounting Research, 14(2), 246–276.

BMP test (BMPTest)

The Boehmer, Musumeci & Poulsen (1991) standardized cross-sectional test combines Patell-style standardization with a cross-sectional variance estimate, making it robust to event-induced increases in return variance (which the plain Patell test does not accommodate). It standardizes abnormal returns by the model sigma, then applies a cross-sectional t-test to the standardized values.

Audit result: verified, no change (all-NA exclusion added 2026-09-24, item A2; roxygen documentation corrected, item A11). The standardization by MODEL sigma (not the forecast-error-corrected sigma – this is the defining contrast with PatellZTest/KolariPynnonenTest) and the cross-sectional t sqrt(N) * mean(SAR) / sd(SAR) match Boehmer, Musumeci & Poulsen (1991). The 2026-09-24 re-evaluation found the roxygen documentation itself INCORRECTLY described the standardization as using the forecast-error-corrected sigma; the formula was always right, only the docstring was fixed (item A11, docs-only). Pinned in test_golden_values.R against an independent closed-form BMP computation on a fixed three-event fixture at absolute tolerance 1e-10.

Citation: Boehmer, E., Musumeci, J., & Poulsen, A. B. (1991). Event-study methodology under conditions of event-induced variance. Journal of Financial Economics, 30(2), 253–272.

Sign test (SignTest)

The sign test is a nonparametric test of whether positive abnormal returns occur more often than the 0.5 that would be expected by chance. Under the null the count of positive abnormal returns is Binomial(N, 0.5), approximated by a normal.

Audit result: verified, no change (all-NA exclusion added 2026-09-24, item A2). The (n_pos - 0.5 N)/(0.5 sqrt(N)) statistic, the strict > 0 positive-count convention, and the N >= 2 guard match the standard sign test. Pinned in test_golden_values.R against a direct binomial-normal computation on the fixed three-event fixture at absolute tolerance 1e-10, plus a guard test confirming NA for a single-event group.

Citation: The binomial sign test for event studies is standard; see Brown & Warner (1980, 1985) and Cowan (1992) for its use alongside the generalized form.

Generalized Sign test (GeneralizedSignTest)

The generalized sign test (Cowan 1992) relaxes the ordinary sign test’s implicit p = 0.5 by estimating the expected fraction of positive abnormal returns from the estimation window, which corrects for asymmetry (skewness) in the return distribution.

Audit result: one silent-wrong defect fixed 2026-09-24 (item A4; all-NA exclusion added, item A2). The (n_pos - N p_hat)/sqrt(N p_hat (1 - p_hat)) statistic and the degenerate- denominator guard match Cowan (1992). The 2026-09-24 re-evaluation found p_hat was estimated by grouping the estimation window by firm_symbol rather than event_id: when a firm recurs across multiple events, its estimation-window abnormal returns from DIFFERENT events were silently pooled into one p_hat, instead of estimating one p_hat per event and averaging those. Fixed to group by event_id; pinned in test_golden_values.R against an independent closed-form computation on the three-event fixture (where the balanced estimation residuals give p_hat = 0.5, so the generalized test reduces to the ordinary sign test) at absolute tolerance 1e-10, and locked in test_reeval_statistical_fixes.R (identical results whether a firm recurs across events or every event has a distinct firm).

Citation: Cowan, A. R. (1992). Nonparametric event study tests. Review of Quantitative Finance and Accounting, 2(4), 343–358.

Rank test (RankTest)

The Corrado (1989) rank test is a nonparametric test that ranks each firm’s abnormal returns across the combined estimation and event windows, then tests whether the event-window ranks are unusually high or low. Ranking makes it robust to non-normality and to event-induced variance.

Audit result: FIXED (broadcast bug), then verified. The centered-rank construction and the mean_rank / S_rank statistic match Corrado (1989). The audit found a genuine implementation error: rank_z was computed with base ifelse(is.finite(S_rank) & S_rank > 0, mean_rank / S_rank, NA_real_). Because S_rank is a scalar, ifelse returned a length-1 result (the length of its condition), collapsing the per-day mean_rank / S_rank vector to its first element, which dplyr::mutate then recycled across every event day – so all event days reported the day-0 z. No published convention makes the rank z identical on every day, so this is a bug, not a convention. It was fixed to guard the scalar S_rank with a plain if() and divide the vector directly; a regression test (test_golden_values.R) locks the corrected per-day values (+1.586, -0.952, +1.269) and asserts they are distinct, preventing the broadcast from silently returning. The fix precedes the golden pin.

2026-09-24 re-evaluation (item A4): ranking/centering was also found to group by firm_symbol instead of event_id, silently pooling a recurring firm’s ranks across its distinct events. Fixed to group by event_id; locked in test_reeval_statistical_fixes.R (identical results whether a firm recurs across events or every event has a distinct firm).

Citation: Corrado, C. J. (1989). A nonparametric test for abnormal security-price performance in event studies. Journal of Financial Economics, 23(2), 385–395.

Calendar-Time Portfolio test (CalendarTimePortfolioTest)

The calendar-time portfolio approach forms, for each relative event day, an equal-weighted portfolio of all event firms’ abnormal returns and tests whether the portfolio’s mean return differs from zero. Aggregating into a portfolio naturally absorbs the cross-sectional dependence that arises when events cluster in calendar time.

Audit result: FIXED (broadcast bug; then Brown-Warner denominator redefinition, item A7; then A9). The equal-weight portfolio construction matches the calendar-time portfolio approach. Three issues were found across two audit rounds:

1. Broadcast bug (original audit). caltime_t / ccaltime_t used base ifelse(is.finite(ts_sd) & ts_sd > 0, ...) with the scalar ts_sd as the condition, collapsing the per-day t vectors to their first element and recycling it across every event day. Fixed by guarding the scalar once with a plain if() and dividing the vectors directly.
2. Self-referential denominator (2026-09-24 re-evaluation, item A7). ts_sd was computed from the EVENT-WINDOW portfolio AAR series itself – the same series aar that appears in the numerator – so a larger event-day shock inflated BOTH the numerator and (via the window’s own dispersion) the denominator, and the statistic was not independent of the event window’s length or contents. This is REDEFINED (not merely a bug fix in the narrow sense) to the Brown-Warner (1980, 1985) crude-dependence adjustment: ts_sd is now the ESTIMATION-window AAR series’s standard deviation, with df = n_estimation_days - 1 exposed via attr(result, "caltime_df") and threaded through to adjust_p_values() and tidy(). This is a genuine convention change (not a silent-input-only fix) – valid-input caltime_t/ccaltime_t values differ from the prior release; see NEWS.md. Locked in test_reeval_statistical_fixes.R: doubling a pure event-day shock exactly doubles caltime_t on that day (proving the denominator no longer depends on the event window).
3. Sign convention (item A9). n_pos used >= 0; fixed to strict > 0.

A regression test locks the corrected per-day broadcast values and asserts they are distinct; the golden values were RE-PINNED for the A7 redefinition (see test_golden_values.R, “re-pinned 2026-09-24: A7”).

Citation: Brown, S. J., & Warner, J. B. (1980). Measuring security price performance. Journal of Financial Economics, 8(3), 205–258. Brown, S. J., & Warner, J. B. (1985). Using daily stock returns: The case of event studies. Journal of Financial Economics, 14(1), 3–31. The calendar-time portfolio approach is also due to Jaffe (1974) and Mandelker (1974), popularized for long-horizon studies by Fama (1998) and Mitchell & Stafford (2000) as a control for cross-sectional dependence.

Kolari-Pynnonen test (KolariPynnonenTest)

The Kolari & Pynnonen (2010) test corrects the BMP standardized cross-sectional test for cross-sectional correlation of abnormal returns. When events share calendar time, their abnormal returns are positively correlated, which biases the BMP variance downward and over-rejects the null; the KP adjustment scales the BMP statistic down by a factor derived from the average pairwise correlation.

Audit result: verified against Kolari & Pynnonen (2010); two silent-wrong defects fixed 2026-09-24 (items A2, A3). The BMP base statistic and the sqrt((1 - r_bar)/(1 + (n_t - 1) r_bar)) adjustment formula match Kolari-Pynnonen. The 2026-09-24 re-evaluation found: (1) a degenerate (all-NA or constant) event’s estimation-window SAR series was silently folded into the r_bar correlation matrix instead of being excluded, and when the adjustment was undefined the code fell back to kp_adj = 1 – silently reporting the UNADJUSTED BMP value as if it were KP-corrected; and (2) the per-day window-size term used only the FIRST day’s n_valid_events, applied uniformly to every day, instead of that day’s own count. Both are fixed; re-pinned in test_golden_values.R against the package pipeline’s own output on the three-event fixture (where the events’ estimation SARs are highly correlated by construction, r_bar ~ 0.983, so kp_adj ~ 0.076 shrinks the BMP t sharply – unaffected here since all three events remain usable and n_valid_events is constant across days in this fixture), and locked in test_reeval_statistical_fixes.R against a 6-event fixture with one constant-estimation-window (non-usable) event and a per-day varying n_valid_events, at absolute tolerance 1e-8.

Citation: Kolari, J. W., & Pynnonen, S. (2010). Event study testing with cross-sectional correlation of abnormal returns. Review of Financial Studies, 23(11), 3996–4025.

PermutationTest (unwired stub)

PermutationTest is exported but its compute() body is empty (returns NULL) and it is not wired into any statistics set or parameter set – it is not on any pipeline path. It is recorded here for completeness; a decision to implement or remove it is deferred (see the audit log).

TestStatisticBase confidence_type (2026-09-24 re-evaluation, item A10)

Every TestStatisticBase subclass accepts confidence_level and confidence_type at construction, but confidence_type was never read by any compute() method – every p-value computed anywhere in EventStudy is two-sided. initialize() now validates confidence_type with match.arg(c("two-sided", "less", "greater")) (an invalid value errors) and emits ONE warning at construction when a non-default value (“less” or “greater”) is supplied, stating that it is currently ignored. The value is still stored (for forward compatibility) but has no effect; one-sided p-values are NOT implemented by this fix. This is a documented convention (no p-value formula changed) with an added validation/warning surface.

Cross-sectional regression (2026-09-24 re-evaluation, item A5)

cross_sectional_regression() regresses per-event CARs on user-supplied firm characteristics. Prior to 2026-09-24 it silently tolerated three sample- integrity hazards:

This is a sample-integrity fix (T-sfl-02 in the threat register), not a formula change: the OLS regression itself, robust-SE handling, and CAR extraction for a fully-matched, non-degenerate window are unchanged.

Wild bootstrap inference (2026-09-24 re-evaluation, item A12)

bootstrap_test() computes bootstrap p-values for AAR/CAAR test statistics. Two silent-wrong defects were found and fixed:

• A12a: observed-vs-draw construction mismatch. observed_caar / caar_t were previously built as cumsum() of the cross-event DAILY mean AR (na.rm = TRUE), while each bootstrap draw built its CAAR as the MEAN over events of each event’s own cumsum(coalesce(AR, 0)). The two constructions coincide only when every event has a fully-observed event window; with a partial gap in ONE event (but not all), they diverge, and only the per-event-CAR-mean construction is the correct STATS-03-consistent comparison for what the bootstrap draws compute. Fixed so observed_caar and caar_t use the SAME per-event coalesce-to-0 CAR construction as the draws; on NA-free input this is numerically identical to the old cumsum(aar) form.
• A12b: NA draws counted as “did not exceed”. A bootstrap draw whose cross-sectional statistic is NA (e.g. a Rademacher sign-flip combination that zeroes the cross-sectional SD) was previously counted as “did not exceed the observed statistic” while still inflating the n_boot + 1 denominator – silently biasing the p-value toward significance (too small) whenever NA draws are common. Fixed to track the number of VALID (finite) draws per day and use p = (exceed + 1) / (n_valid_draws + 1), with NA when the observed statistic is NA or no draw produced a finite statistic.
• A12c: bootstrap clustering unit (REVISED, no change). The bootstrap weights are clustered by firm_symbol (one weight per unique firm per draw, shared across that firm’s events) – a deliberate prior fix; firm-level clusters are the coarser, correlation-robust choice when a firm recurs across multiple events. The 2026-09-24 re-evaluation confirmed this is intentional and made NO change; it is locked with a hand-replication test (test_bootstrap.R).

Audit summary

The original audit covered all 13+ return models and all wired test statistics and found two broadcast-bug implementation errors (RankTest, CalendarTimePortfolioTest). The 2026-09-24 re-evaluation covered the same surface plus bootstrap_test() and cross_sectional_regression(), and found twelve additional silent-wrong-statistic defects (items A1-A9, A11-A12; A10 is a validation/warning addition, no formula change; A11 is docs-only). Every defect is fixed, locked by a regression test that fails on the pre-fix code (test_reeval_statistical_fixes.R), and golden values affected by a genuine redefinition (A7, A8, and the Patell/KP/Rank/GSign pins touched by A2/A3/A4/A6/A9) are re-pinned in test_golden_values.R with an explanatory comment. No valid-input behavior changed for any component NOT listed above as fixed.

2026-09-24 re-evaluation fixes (12 items, A1-A9 + A11-A12; A10 is a validation addition):

1. A1 – RollingWindowModel complete pairs. Rolling-window OLS computed x_bar/ss_xx from ALL index values in a window, including rows where the firm return was NA, biasing beta when NA-firm rows co-occur with index outliers. Fixed to restrict each window to complete pairs.
2. A2 – Multi-event all-NA exclusion. A fully-degenerate event (all event-window ARs NA) was coalesced to 0 in cumulative statistics instead of excluded, silently understating cross-event dispersion. Fixed with a shared exclusion helper applied once per group.
3. A3 – KolariPynnonenTest usable events. A degenerate estimation-window SAR series was folded into r_bar, and an undefined adjustment silently fell back to kp_adj = 1 (the unadjusted BMP value). Fixed to exclude non-usable events from r_bar and return NA (never a silent 1) when the adjustment cannot be computed; also fixed the per-day window-size term (previously the first day’s count applied to every day).
4. A4 – RankTest / GeneralizedSignTest grouping. Ranking and p_hat estimation grouped by firm_symbol, silently pooling a recurring firm’s data across its distinct events. Fixed to group by event_id.
5. A5 – cross_sectional_regression sample integrity. Duplicate event_ids, out-of-range car_windows, and NA-CAR events were silently tolerated. Fixed with explicit errors/warnings and exclusion.
6. A6 – OLS insufficient-observations guard and Patell m/k. The insufficient-obs guard used a flat threshold instead of n_params + 1; Patell’s k was derived as length(resid) - df instead of read from the model; Patell’s m used the raw row count instead of the finite count; MarketModel’s FEC included incomplete-pair rows. All fixed.
7. A7 – CalendarTimePortfolioTest denominator. ts_sd was computed from the event-window portfolio series itself (self-referential with the numerator). Redefined to the Brown-Warner (1980, 1985) estimation-window AAR standard deviation.
8. A8 – MarketAdjustedModel FEC. Wrongly reused the constant-MEAN correction (sigma * sqrt(1 + 1/m)) for a model that estimates NOTHING. Fixed to FEC == sigma exactly.
9. A9 – Sign convention. n_pos used >= 0 in CSectT, Patell, and CalendarTime (inconsistent with SignTest’s > 0). Fixed to strict > 0 everywhere.
10. A11 – BMP/KP roxygen (docs-only). The BMP docstring incorrectly claimed forecast-error-corrected-sigma standardization; both BMP and KP standardize by MODEL sigma. Fixed the docstring; no formula change.
11. A12a/b – bootstrap_test() observed/draw mismatch and NA-draw denominator. observed_caar used a different construction than the draws; NA draws were counted as “did not exceed” while still inflating the denominator. Both fixed.
12. A12c – bootstrap clustering unit (confirmed, no change). Firm-level clustering is deliberate and unchanged; locked with a hand-replication test.

A10 (TestStatisticBase confidence_type validation) adds a construction-time check and a one-time warning; it changes no computed statistic.