Statistical Conventions and Formula Audit

In EventStudy: Event Study Analysis

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Purpose

Every event-study statistic embeds convention choices -- the return type, the forecast-error correction, the degrees of freedom, the p-value sidedness, the Patell denominator, and so on. Two implementations of "the same" test can differ in the last digits (or more) purely because they made different, equally defensible choices. This vignette documents, per return model and per test statistic, exactly which convention EventStudy uses and cites the published source for each. It is the reference that a golden-value regression test is pinned against: a documented convention here matches the assumption annotated in tests/testthat/test_golden_values.R.

Audit methodology

Each model and statistic was audited against its published formula. Findings are classified with a strict two-bucket policy:

• Fix (genuine formula error). If the code computes something no published convention supports, it is a bug. It is fixed in the R source, the fix is locked with a regression test, and the fix precedes the golden pin of that statistic. Such fixes are logged in the "Audit log" section below.
• Document (defensible convention difference). If the code matches a published convention that merely differs from another implementation (for example log vs simple returns, df = m - 2 vs m - 1, one- vs two-sided p), the behavior is not changed -- it is documented here as the chosen convention with its citation. Behavior on valid inputs is frozen for this milestone.

When a discrepancy is ambiguous it is treated as a convention (documented, not changed), because silently altering a valid-input result is the higher-risk error.

Tolerance policy for the golden tests: absolute 1e-10 for exact algebraic identities, absolute 1e-8 as the general default, and relative 1e-6 for any cross-implementation comparison. Each pinned assertion states its provenance, the conventions it assumes, and its tolerance rationale inline.

Return models

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.

| Convention | Choice | Note | |---|---|---| | Return type | Arithmetic (simple) returns | The pipeline's return-calculation strategy is orthogonal; the model consumes whatever firm_returns / index_returns contain. | | Estimation | OLS: firm_returns ~ index_returns | alpha, beta from lm(). | | Abnormal return | AR = R - (alpha + beta * Rm) | MacKinlay (1997) eq. (5). | | Residual sigma | Residual standard error from summary(lm) | Uses df = m - 2 (intercept + slope), m = COMPLETE-PAIR estimation observations. | | Degrees of freedom | m - 2 | m = estimation observations with both firm_returns and index_returns finite. | | Minimum observations | n_valid >= n_params + 1 = 3 | Fewer valid observations route through the degenerate-input contract (NA + one warning, or error in strict mode) rather than fitting an unstable/undefined sigma (needs df >= 1). | | Short-window advisory | One plain warning when 2 < n_valid < 30 | Advisory only (not a degenerate/contract condition) -- the model still fits; 30 is the same recommended minimum as validate_task()'s default. | | statistics$n_params | 2 (intercept + slope) | Consumed by PatellZTest's Q_i adjustment (see below). | | AR t-statistic | AR / sigma | Per-day, constant-sigma approximation. | | CAR t-statistic | CAR / (sqrt(L) * sigma) | L-day cumulative, constant-sigma approximation, MacKinlay (1997). | | Forecast-error correction | sigma * sqrt(1 + 1/m + (Rm_evt - mean(Rm_est))^2 / SS_market) | Patell/MacKinlay prediction-error variance; mean(Rm_est) and SS_market (the estimation-window sum of squares of the index) are computed over COMPLETE PAIRS ONLY, matching exactly the rows lm() used (2026-09-24 re-evaluation item A6: previously included incomplete-pair rows, biasing the mean/SS). Falls back to the constant-mean form sigma * sqrt(1 + 1/m) when the index is constant. | | p-value sidedness | Two-sided by default | confidence_type = "two-sided". |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Whatever firm_returns / index_returns contain | Return-calculation strategy is orthogonal. | | Estimation | None -- alpha = 0, beta = 1 fixed | No OLS parameters estimated. | | Abnormal return | AR = R - Rm | Firm return minus index return. | | Residual sigma | sd(firm - index) over the estimation window | Sample standard deviation of the market-adjusted residual series. | | Degrees of freedom | m - 1 | One parameter consumed by the residual mean in sd(); m = estimation observations. | | statistics$n_params | 0 | Nothing is estimated (alpha/beta are FIXED at 0/1, not fitted). | | Forecast-error correction | forecast_error_corrected_sigma == sigma (correction factor exactly 1) | No regression, no leverage term, and -- since nothing is estimated -- no prediction-error inflation either (2026-09-24 re-evaluation item A8). | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Whatever firm_returns contains | Index returns are unused by this model. | | Estimation | mean(firm_returns) over the estimation window | One parameter (the mean) estimated. | | Abnormal return | AR = R - mean(R_est) | Firm return minus estimation-window mean. | | Residual sigma | sd(firm - mean) over the estimation window | Sample standard deviation of the demeaned residuals. | | Degrees of freedom | m - 1 | The mean consumes one degree of freedom. | | statistics$n_params | 1 | One parameter estimated (the comparison-period mean). | | Forecast-error correction | sigma * sqrt(1 + 1/m) | Constant-mean form. Uses the finite value count (NA rows do not inflate m). Unlike MarketAdjustedModel (A8), this model DOES estimate one parameter, so the constant-mean correction is the correct form here. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Excess returns (excess_return = firm minus risk-free) | Regressed on market_excess + smb + hml. | | Estimation | OLS via lm(excess_return ~ market_excess + smb + hml) | k = 3 factors plus intercept. | | Abnormal return | AR = excess_return - predicted | predicted from the fitted OLS coefficients. | | Residual sigma | Residual standard error from summary(lm) | -- | | Degrees of freedom | m - (k + 1) = m - 4 | Intercept plus three factor slopes. | | Minimum observations | n_valid >= n_params + 1 = 5 | n_params = length(all.vars(formula)) = 4 (response + 3 factors, i.e. intercept + 3 slopes); fewer valid observations route through the degenerate-input contract (2026-09-24 item A6). | | Short-window advisory | One plain warning when 4 < n_valid < 30 | Same advisory convention as the Market Model. | | statistics$n_params | 4 | Consumed by PatellZTest's Q_i adjustment. | | Forecast-error correction | sigma * sqrt(1 + h_t), h_t = x_t' (X'X)^{-1} x_t | Full multi-factor hat-value (leverage) form using the estimation design matrix. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Excess returns (excess_return) | Regressed on market_excess + smb + hml + rmw + cma. | | Estimation | OLS on five factors plus intercept | k = 5. | | Abnormal return | AR = excess_return - predicted | -- | | Residual sigma | Residual standard error | -- | | Degrees of freedom | m - (k + 1) = m - 6 | -- | | Minimum observations | n_valid >= n_params + 1 = 7 | n_params = 6 (intercept + 5 factors); 2026-09-24 item A6. | | statistics$n_params | 6 | Consumed by PatellZTest's Q_i adjustment. | | Forecast-error correction | sigma * sqrt(1 + h_t) | Multi-factor hat-value form. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Excess returns (excess_return) | Regressed on market_excess + smb + hml + mom. | | Estimation | OLS on four factors plus intercept | k = 4. | | Abnormal return | AR = excess_return - predicted | -- | | Residual sigma | Residual standard error | -- | | Degrees of freedom | m - (k + 1) = m - 5 | -- | | Minimum observations | n_valid >= n_params + 1 = 6 | n_params = 5 (intercept + 4 factors); 2026-09-24 item A6. | | statistics$n_params | 5 | Consumed by PatellZTest's Q_i adjustment. | | Forecast-error correction | sigma * sqrt(1 + h_t) | Multi-factor hat-value form. | | p-value sidedness | Two-sided by default | -- |

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."

| Convention | Choice | Note | |---|---|---| | Return type | Whatever the supplied model consumes | User-defined. | | Estimation | Inherited from the Market Model (OLS) | The fitted object is user-supplied via the pipeline. | | Abnormal return | AR = R - predict(model) (+loss_market_cap on the event date) | The event-date term lets a user inject a known shock. | | Residual sigma / df | Inherited from the underlying OLS fit (df = m - 2) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Return type | Arithmetic returns compounded multiplicatively | cumprod(1 + R). | | Estimation | None estimated for the AR itself; the benchmark is the index | sigma is estimated from the estimation window for the t-test. | | Abnormal return | BHAR = cumprod(1 + firm) - cumprod(1 + index) | Barber & Lyon (1997) buy-and-hold definition; compounded within each event window separately. | | Residual sigma | sd(firm - index) over the estimation window | Sample SD of the one-period market-adjusted residual series. | | Degrees of freedom | m - 1 | Finite-pair count via .finite_residual_df() (NA rows do not inflate m). | | BHAR standard error | sigma * sqrt(n) | n is the day index within the event window -- the random-walk sqrt-of-horizon scaling of Lyon, Barber & Tsai (1999). | | BHAR t-statistic | BHAR / (sigma * sqrt(n)) | Returns NA when sigma == 0 (degenerate guard), never Inf/NaN. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Measure | log(firm_volume + 1) by default (log_transform = TRUE) | The +1 avoids log(0); set log_transform = FALSE for raw volume. | | Estimation | mean(log(volume + 1)) over the estimation window | One parameter (the mean). | | Abnormal measure | AR = log(volume + 1) - expected | Deviation from the estimation-window log-mean. | | Residual sigma | sd(residuals) over the estimation window | -- | | Degrees of freedom | m - 1 | Finite value count (NA/non-finite rows excluded). | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Measure | Squared return relative to estimation variance | -- | | Estimation | est_var = var(estimation firm_returns) | Sample variance, df = m - 1. | | Abnormal measure | AR = firm_returns^2 / est_var - 1 | Zero when the squared return equals the expected variance. | | Residual sigma | sd(residuals) of the ratio series over the estimation window | -- | | Degrees of freedom | m - 1 | Finite value count. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Estimation | Rolling OLS firm ~ index over windows of window_size (default 60), requiring min_obs (default 30) finite pairs | Last window's alpha, beta used for prediction. | | Effective window | ws = min(window_size, n_est) | When n_est <= window_size there is a single window equal to the full sample; n_est is the estimation window's ROW span (not a valid-pair count). | | Within-window pairs | Each ws-row window restricts x_bar/y_bar/ss_xx/ss_xy/residuals/sigma to COMPLETE PAIRS (both firm and index finite) | 2026-09-24 re-evaluation item A1: previously x_bar/ss_xx were computed from ALL index values in the window, including rows where the firm return was NA -- if those NA-firm rows are not missing-at-random in the index (e.g. an index outlier co-occurring with a missing firm observation), this silently biases beta away from what lm() on the complete-pair subset would produce. | | Abnormal return | AR = firm - (alpha_last + beta_last * index) | Uses the most recent (last) rolling parameters. | | Residual sigma | Last-window residual SE, denom = max(n_complete_last - 2, 1) | n_complete_last = complete pairs in the LAST window (not a freshly recomputed valid-count that could disagree with the actual last-window row span). | | Degrees of freedom | max(n_complete_last - 2, 1) | fit() and calculate_statistics() share the SAME complete-pair count (stored in private$.rolling_params$n_completes), so the reported df always matches the sigma that was actually estimated. | | statistics$n_params | 2 (alpha, beta) | Consumed by PatellZTest's Q_i adjustment. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Backend | rugarch::ugarchfit, sGARCH, garchOrder default c(1, 1), normal errors | Optional dependency, guarded by requireNamespace. | | Mean equation | firm = mu + mxreg1 * index + e_t | Index return as an external regressor. | | Abnormal return | AR = firm - (mu + mxreg1 * index) | The fitted mean-equation residual. | | Residual sigma | Mean conditional sigma from the GARCH fit | Falls back to sd(residuals) if non-finite. | | Degrees of freedom | max(length(cond_sigma) - length(coefs), 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Backend | rmgarch::dccfit, univariate sGARCH(1,1), DCC order default c(1, 1), multivariate normal | Optional dependency, guarded by requireNamespace. | | Time-varying beta | beta_t = H[firm, mkt]_t / H[mkt, mkt]_t | From the conditional covariance array; non-finite / zero-variance entries yield NA and fall back to the last valid beta. | | Intercept | alpha_last = mean(firm - beta_last * index) over the estimation window | Mean-equation intercept implied by the last beta. | | Abnormal return | AR = firm - (alpha_last + beta_last * index) | Uses the last conditional beta. | | Residual sigma | mean(conditional firm sigma) | -- | | Degrees of freedom | max(n_t - 4, 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

Test statistics

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).

| Convention | Choice | Note | |---|---|---| | Point statistic | aar_t = sqrt(N) * aar / sd(AR) | aar = mean AR across events; sd(AR) = cross-event sample SD (denominator N - 1). | | Cumulative statistic | caar_t = sqrt(N) * caar / sd(CAR) | caar = mean of per-event cumulative ARs; sd(CAR) = cross-event sample SD of the per-event CARs. | | Sample size | N = number of valid (non-NA) events at that day | NA abnormal returns are excluded from both the mean and the SD. | | Distribution | Student's t with N - 1 degrees of freedom | -- | | Standardization | None -- raw abnormal returns | Unlike Patell/BMP, ARs are not divided by a per-event sigma; the cross-event SD is the only scale. | | Positive count | n_pos = sum(AR > 0) -- STRICT inequality | 2026-09-24 item A9: an AR exactly 0 counts as NON-positive (n_neg = sum(AR <= 0)), matching the SignTest convention. | | All-NA event exclusion | An event with ZERO finite event-window ARs is excluded from every multi-event statistic (once per group, one contract warning/error) | 2026-09-24 item A2; see "Multi-event all-NA exclusion" below. A PARTIAL gap (one missing AR mid-window in an otherwise-valid event) still contributes 0 to that event's own CAR (STATS-03, unchanged). | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Standardization | SAR = AR / forecast-error-corrected sigma | Uses the per-event, per-day FEC sigma, not the raw model sigma (this is the defining feature vs. BMP). | | Patell denominator | Q_total = sqrt(sum_i Q_i), Q_i = (m - k) / (m - k - 2) | m = number of FINITE estimation-window abnormal returns for event i (2026-09-24 item A6: NOT the raw row count -- NA rows in the estimation window must not inflate m). k = event i's model's statistics$n_params (MarketModel 2, FF3 4, Carhart4 5, FF5 6, CPMA 1, MarketAdjusted 0), read explicitly rather than derived as length(resid) - df (the pre-2026-09-24 derivation silently produced the WRONG k whenever df already reflected an unrelated correction, e.g. HAC). Q_i inflates the variance of the standardized sum for the estimation-error in each sigma. | | Q_i fallback | Q_i = 1 when m <= k + 2 | Insufficient observations for the adjustment; avoids a negative/undefined denominator. | | AAR statistic | aar_z = sum_i SAR_i / Q_total | Sum (not mean) of standardized abnormal returns over the Patell denominator. | | CAAR statistic | caar_z = (1 / sqrt(N)) * sum_i (cumsum(SAR_i) / sqrt(n * Q_i)) | Per-event cumulative SAR scaled by sqrt(n * Q_i) where n is the day count, then averaged. | | Positive count | n_pos = sum(AR > 0) -- STRICT inequality | 2026-09-24 item A9: matches SignTest/CSectTTest. | | Degenerate-event handling | Events with all-NA FEC sigma are excluded from Q_total (WR-01); events with ZERO finite event-window ARs are excluded from the WHOLE statistic (2026-09-24 item A2) | Prevents a Q_i = 1 fallback (or a coalesced-to-0 CAR contribution) from a degenerate event distorting valid-event z-scores. | | N >= 2 guard | aar_z / caar_z are NA when n_valid_events <= 1 (STATS-04) | A single event gives a statistically invalid z; NA is returned rather than a finite-but-wrong number. | | Distribution | Approximately N(0, 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Standardization | SAR = AR / model sigma | Uses the per-event MODEL sigma (contrast: Patell uses the forecast-error-corrected sigma). | | Point statistic | bmp_t = sqrt(N) * mean(SAR) / sd(SAR) | Cross-sectional t of the standardized abnormal returns; sd(SAR) is the cross-event sample SD (this cross-sectional SD is what makes BMP robust to event-induced variance). | | Cumulative statistic | cbmp_t = sqrt(N) * mean(cumsum(SAR)) / sd(cumsum(SAR)) | Same cross-sectional t applied to per-event cumulative SARs. | | Join key | event_id (one sigma per event) | A firm_symbol join would be many-to-many when a firm recurs across events. | | All-NA event exclusion | An event with ZERO finite event-window ARs is excluded (2026-09-24 item A2) | See "Multi-event all-NA exclusion" below. | | Distribution | Approximately t_{N-1} | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Positive count | n_pos = sum(AR > 0) -- STRICT inequality | A zero abnormal return counts as NON-positive (n_neg = sum(AR <= 0)). This is the > 0 (not >= 0) convention; it is the conservative choice, treating an exact zero as evidence against a positive effect. | | Point statistic | sign_z = (n_pos - 0.5 N) / (0.5 sqrt(N)) | Binomial-normal approximation with p = 0.5; N = valid events at that day. | | Cumulative statistic | csign_z = (n_pos_car - 0.5 N) / (0.5 sqrt(N)) | Same form applied to the count of positive per-event CARs. | | N >= 2 guard | sign_z / csign_z are NA when n_valid_events < 2 (STATS-04, WR-02) | A single observation gives a finite-but-meaningless z; NA is returned instead. | | All-NA event exclusion | An event with ZERO finite event-window ARs is excluded (2026-09-24 item A2) | See "Multi-event all-NA exclusion" below. | | Distribution | Approximately N(0, 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Expected proportion | p_hat = mean over EVENTS of mean(estimation AR > 0) | Estimated PER EVENT from the estimation window, then averaged (2026-09-24 item A4: previously grouped by firm_symbol, which silently pooled a recurring firm's estimation windows ACROSS its distinct events -- each event is fit independently, so this mixed unrelated data). Replaces the ordinary test's fixed 0.5. | | Positive count | n_pos = sum(AR > 0) | Same strict > 0 convention as the sign test. | | Point statistic | gsign_z = (n_pos - N p_hat) / sqrt(N p_hat (1 - p_hat)) | Cowan (1992) generalized sign statistic. | | Cumulative statistic | cgsign_z = (n_pos_car - N p_hat) / sqrt(N p_hat (1 - p_hat)) | Same form on positive per-event CAR counts. | | Degenerate guard | NA when the denominator is non-finite or zero (p_hat in {0, 1}) | -- | | All-NA event exclusion | An event with ZERO finite event-window ARs is excluded (2026-09-24 item A2) | See "Multi-event all-NA exclusion" below. | | Distribution | Approximately N(0, 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Ranking scope | Ranks computed within each EVENT over the COMBINED estimation + event window | ar_rank = rank(AR), T = combined observations for that event (2026-09-24 item A4: previously grouped by firm_symbol, silently pooling a recurring firm's ranks ACROSS its distinct events). | | Centered rank | K = rank / (T + 1) - 0.5 | Corrado's mean-zero centered rank; na.last = "keep" so missing ARs do not receive a rank. | | Rank SD | S_rank = sd(per-day mean centered rank across ALL combined days) | The scale is estimated from the full combined window, not just the event window. | | Point statistic | rank_z = mean_rank_day / S_rank | Per event day, the cross-firm mean centered rank divided by S_rank. | | Degenerate guard | rank_z is NA when S_rank is non-finite or zero | Guarded once on the scalar S_rank, then the per-day vector is divided directly. | | Distribution | Approximately N(0, 1) | -- | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Portfolio | Equal-weighted mean abnormal return per relative day (aar) | -- | | Time-series scale | ts_sd = sd(aar) over the ESTIMATION-window days | 2026-09-24 item A7 (Brown-Warner crude-dependence adjustment): ts_sd is the standard deviation of the cross-event AAR series computed OVER THE ESTIMATION WINDOW, not over the (much shorter, event-specific) event window. This makes the denominator independent of the event window and of any event-day shock magnitude. | | Estimation-window AAR days | n_estimation_days = number of FINITE estimation-window AAR observations | Exposed as attr(result, "caltime_df"). | | Point statistic | caltime_t = aar / ts_sd | Time-series t of the portfolio AAR under H0: E[AAR] = 0; aar is still the EVENT-window per-day portfolio mean. | | Cumulative statistic | ccaltime_t = caar / (ts_sd sqrt(L)) | L = day index within the event window; random-walk sqrt-of-horizon scaling of the cumulative portfolio return. | | Degrees of freedom | n_estimation_days - 1 | Brown-Warner time-series df, NOT a cross-sectional N - 1; adjust_p_values() and tidy() both read attr(result, "caltime_df") rather than deriving a df of their own. | | Positive count | n_pos = sum(AR > 0) -- STRICT inequality | 2026-09-24 item A9: matches SignTest/CSectTTest. | | Degenerate guard | Both t's are NA when ts_sd is non-finite/zero or n_estimation_days < 2 | One contract warning/error (not a silent NA) when the estimation-window AAR series cannot support a standard deviation. | | p-value sidedness | Two-sided by default | -- |

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.

| Convention | Choice | Note | |---|---|---| | Base statistic | BMP cross-sectional t (SAR = AR / model sigma, bmp_t = sqrt(N) mean(SAR)/sd(SAR)) | Identical to BMPTest; KP scales it. | | Usable events | An event contributes to r_bar only if its estimation-window SAR series has >= 2 finite values, a finite model sigma, AND a strictly positive (non-constant) SAR standard deviation | 2026-09-24 item A3: a NON-usable event is excluded (once, with a contract warning/error naming it) -- never silently folded into the correlation matrix as a degenerate (constant or all-NA) series. | | Average correlation | r_bar = average off-diagonal pairwise correlation of estimation-window SARs, over the USABLE events only | r_bar = (sum(cor) - n_usable) / (n_usable (n_usable - 1)); events (not firms) are the cross-sectional units, so the SAR matrix is pivoted by event_id. Numerically identical to the pre-2026-09-24 formula when every event is usable. | | Adjustment factor | kp_adj_t = sqrt((1 - r_bar) / (1 + (n_t - 1) r_bar)) PER DAY | Kolari-Pynnonen (2010) correction; n_t is THAT DAY's n_valid_events (2026-09-24 item A3: previously a single scalar n <- aar_stats$n_valid_events[1] -- the FIRST day's count -- was applied uniformly to every day, silently wrong whenever the per-day valid-event count varies). kp_adj < 1 when r_bar > 0, shrinking the statistic toward zero. | | Point statistic | kp_t = bmp_t * kp_adj_t | -- | | Cumulative statistic | ckp_t = cbmp_t * kp_adj_t' | kp_adj_t' uses the cumulative SAR's own per-day n_valid (from cum_sar), not the AAR-level n_valid_events. | | Degenerate guard | kp_t/ckp_t are NA (NEVER kp_adj = 1) when fewer than 2 usable events remain, an off-diagonal correlation is non-finite, or the adjustment's numerator/denominator is invalid | 2026-09-24 item A3: the pre-fix fallback silently substituted kp_adj = 1 (i.e. the UNADJUSTED BMP value) whenever the correction was undefined -- indistinguishable from "no correlation correction needed" when it actually meant "the correction could not be computed". Exactly one warning/error per compute() call covers both the usable-event exclusion and this NA substitution (never two). | | All-NA event exclusion | An event with ZERO finite event-window ARs is excluded from the whole statistic (2026-09-24 item A2) | See "Multi-event all-NA exclusion" below; distinct from the estimation-window "usable events" check above (A3) -- an event can have valid event-window ARs but a non-usable estimation-window SAR series, or vice versa. | | Distribution | Approximately t_{N-1} | -- | | p-value sidedness | Two-sided by default | -- |

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:

| Hazard | Behavior now | |---|---| | Duplicated event_id in the data argument | Errors (eventstudy_error_bad_argument) naming the duplicated id(s) -- a duplicate would otherwise inflate the join many-to-many. | | car_window extending outside the event window of any event | Errors (eventstudy_error_bad_argument) naming the window, the available range, and the offending event(s), instead of silently summing over rows that do not exist for that event. | | A task event with no matching row in data | One warning listing the count/ids, then dropped (unchanged: an empty match set still errors). | | A missing abnormal return inside car_window for an otherwise-matched event | That event's CAR is NA (.extract_cars() no longer uses na.rm = TRUE, so ANY missing AR in the window makes the whole-window CAR NA, not the sum of the finite subset) and it is excluded from the regression with one warning listing the event(s). car_by_group(), car_quantiles(), and plot_car_distribution() inherit the same NA-CAR semantics from the shared .extract_cars() helper WITHOUT an additional warning (their own na.rm = TRUE summary statistics already tolerate NA rows silently, as documented). |

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 log

| Component | Result | Citation | |---|---|---| | Market Model + AR/CAR t | FIXED 2026-09-24 (A6: insufficient-obs guard now n_params-based; FEC restricted to complete pairs) | MacKinlay (1997) | | Market Adjusted Model | FIXED 2026-09-24 (A8: FEC == sigma exactly, correction factor 1) | MacKinlay (1997) | | Comparison Period Mean Adjusted Model | verified, no change | Brown-Warner (1985); MacKinlay (1997) | | Fama-French Three-Factor Model | FIXED 2026-09-24 (A6: insufficient-obs guard strengthened) | Fama-French (1993) | | Fama-French Five-Factor Model | FIXED 2026-09-24 (A6: insufficient-obs guard strengthened) | Fama-French (2015) | | Carhart Four-Factor Model | FIXED 2026-09-24 (A6: insufficient-obs guard strengthened) | Carhart (1997) | | Custom Model | documented convention (user-supplied prediction; reduces to Market Model when loss_market_cap = 0) | MacKinlay (1997) | | BHAR Model + BHARTTest | verified, no change | Barber-Lyon (1997); Lyon-Barber-Tsai (1999) | | Volume Model | verified, no change | Campbell-Wasley (1996); Brown-Warner (1985) | | Volatility Model | verified, no change | Beaver (1968); Patell-Wolfson (1979) | | Rolling-Window Model | FIXED 2026-09-24 (A1: complete-pair restriction inside each rolling window) | Fama-MacBeth (1973); MacKinlay (1997) | | GARCH Model | verified, no change (identity-pinned, skip-guarded on rugarch) | Engle (1982); Bollerslev (1986) | | DCC-GARCH Model | verified, no change (identity-pinned, skip-guarded on rmgarch) | Bollerslev (1990); Engle (2002) | | AR / CAR t-tests (ARTTest, CARTTest) | verified, no change (documented: forecast_error_corrected_sigma_car intentionally unused, A11) | MacKinlay (1997) | | BHAR t-test (BHARTTest) | verified, no change | Barber-Lyon (1997); Lyon-Barber-Tsai (1999) | | Multi-event all-NA exclusion (shared mechanism) | FIXED 2026-09-24 (A2: all-NA events excluded from every CAR-based multi-event statistic, once per group) | -- | | Cross-Sectional t-test (CSectTTest) | FIXED 2026-09-24 (A2 exclusion; A9: strict n_pos > 0) | Brown-Warner (1985) | | Patell Z-test (PatellZTest) | FIXED 2026-09-24 (A2 exclusion; A6: m/k redefinition; A9: strict n_pos > 0) | Patell (1976) | | BMP test (BMPTest) | FIXED 2026-09-24 (A2 exclusion; A11: roxygen corrected, docs-only) | Boehmer-Musumeci-Poulsen (1991) | | Sign test (SignTest) | FIXED 2026-09-24 (A2 exclusion) | Brown-Warner (1985); Cowan (1992) | | Generalized Sign test (GeneralizedSignTest) | FIXED 2026-09-24 (A2 exclusion; A4: p_hat grouped by event_id) | Cowan (1992) | | Rank test (RankTest) | FIXED (original audit: rank_z broadcast); FIXED 2026-09-24 (A4: grouped by event_id) | Corrado (1989) | | Calendar-Time Portfolio test (CalendarTimePortfolioTest) | FIXED (original audit: caltime_t/ccaltime_t broadcast); FIXED 2026-09-24 (A7: Brown-Warner estimation-window denominator, redefinition; A9: strict n_pos > 0) | Brown-Warner (1980, 1985); Jaffe (1974); Fama (1998) | | Kolari-Pynnonen test (KolariPynnonenTest) | FIXED 2026-09-24 (A2 exclusion; A3: usable-events r_bar, per-day adjustment, never kp_adj = 1 fallback) | Kolari-Pynnonen (2010) | | PermutationTest | unwired stub -- empty compute(), not on pipeline path; deferred | -- | | bootstrap_test() | FIXED 2026-09-24 (A12a: observed/draw CAAR construction aligned; A12b: NA draws excluded from denominator; A12c: clustering unit confirmed, no change) | -- | | cross_sectional_regression() | FIXED 2026-09-24 (A5: duplicate-id error, out-of-range car_window error, unmatched/NA-CAR warnings+exclusion) | -- | | TestStatisticBase$confidence_type | FIXED 2026-09-24 (A10: validated, warns once when non-default; no formula change) | -- |

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.

EventStudy documentation built on Oct. 31, 2026, 1:07 a.m.