Inference and Robustness: HAC, Bootstrap, and Multiple Testing
In EventStudy: Event Study Analysis

knitr::opts_chunk$set(
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Introduction

Classical event study inference relies on i.i.d. assumptions that are often violated in practice. The EventStudy package provides several tools to strengthen the robustness of your inference:

HAC Standard Errors (Newey-West) for heteroskedasticity- and autocorrelation-consistent coefficient estimation
Kolari-Pynnonen Test that adjusts the BMP test for cross-sectional correlation
Wild Bootstrap inference for AAR and CAAR test statistics
Multiple Testing Corrections (Bonferroni, BH, Holm, etc.) for controlling the family-wise error rate or false discovery rate

HAC Standard Errors

When estimation-window residuals exhibit heteroskedasticity or autocorrelation, OLS standard errors are biased. The use_hac = TRUE option applies Newey-West HAC standard errors via the sandwich package.

library(EventStudy)

task <- EventStudyTask$new(firm_data, index_data, request)

# Enable HAC SEs on the MarketModel
ps <- ParameterSet$new(
  return_model = MarketModel$new(use_hac = TRUE)
)
task <- run_event_study(task, ps)

You can also specify a custom lag for the Newey-West estimator:

ps <- ParameterSet$new(
  return_model = MarketModel$new(use_hac = TRUE, hac_lag = 5)
)

HAC standard errors are also available for factor models:

ps <- ParameterSet$new(
  return_model = FamaFrench3FactorModel$new(use_hac = TRUE)
)

The OLS sigma (used for abnormal return standardization in test statistics) is deliberately unchanged -- HAC only affects coefficient standard errors and p-values.

Kolari-Pynnonen Test

The Boehmer, Musumeci & Poulsen (BMP) test can be oversized when event-window residuals are cross-sectionally correlated. The Kolari-Pynnonen adjustment corrects for this:

$$t_{KP} = t_{BMP} \sqrt{\frac{1 - \bar{r}}{1 + (N-1)\bar{r}}}$$

where $\bar{r}$ is the average pairwise correlation of standardized abnormal returns in the estimation window.

ps <- ParameterSet$new(
  multi_event_statistics = MultiEventStatisticsSet$new(
    tests = list(
      BMPTest$new(),
      KolariPynnonenTest$new()
    )
  )
)
task <- run_event_study(task, ps)

Wild Bootstrap Inference

The wild bootstrap provides distribution-free inference by resampling with random per-firm sign flips. This preserves the cross-sectional dependence structure while testing the null hypothesis of zero abnormal returns.

task <- create_fitted_mock_task()

# Run bootstrap with 999 replications
boot_result <- bootstrap_test(
  task,
  n_boot = 999,
  weight_type = "rademacher",
  seed = 42
)

boot_result
#> # A tibble: 11 x 5
#>    relative_index observed_aar observed_caar boot_p_aar boot_p_caar
#>             <int>        <dbl>         <dbl>      <dbl>       <dbl>
#>  1             -5      0.00123       0.00123      0.842       0.842
#>  ...

Two weight distributions are available:

"rademacher" (default): $w_i \in {-1, +1}$ with equal probability
"mammen": Mammen two-point distribution, better for skewed data

You can also bootstrap only the AAR or CAAR statistic:

boot_aar <- bootstrap_test(task, n_boot = 499, statistic = "aar")
boot_caar <- bootstrap_test(task, n_boot = 499, statistic = "caar")

Multiple Testing Corrections

When testing abnormal returns at many event-window days, the probability of a false positive increases. The adjust_p_values() function applies standard correction methods:

task <- create_fitted_mock_task()

# Benjamini-Hochberg (controls FDR)
result_bh <- adjust_p_values(task, method = "BH", stat_name = "CSectT")

# Bonferroni (controls FWER)
result_bonf <- adjust_p_values(task, method = "bonferroni", stat_name = "CSectT")

# Holm (less conservative than Bonferroni)
result_holm <- adjust_p_values(task, method = "holm", stat_name = "CSectT")

The result includes both raw and adjusted p-values:

result_bh
#> # A tibble: 11 x 8+
#>    relative_index   aar  caar p_raw_aar p_adj_aar p_raw_caar p_adj_caar ...

The function automatically detects the test statistic type (t, z, BMP, etc.) and computes p-values from the appropriate distribution.

You can filter by group:

result <- adjust_p_values(task, method = "BH", stat_name = "CSectT",
                           group = "MyGroup")

Combining Approaches

For maximum robustness, combine multiple approaches:

# 1. Use HAC SEs in the model
ps <- ParameterSet$new(
  return_model = MarketModel$new(use_hac = TRUE),
  multi_event_statistics = MultiEventStatisticsSet$new(
    tests = list(
      CSectTTest$new(),
      KolariPynnonenTest$new()
    )
  )
)
task <- run_event_study(task, ps)

# 2. Apply multiple testing correction
adjusted <- adjust_p_values(task, method = "BH", stat_name = "CSectT")

# 3. Validate with bootstrap
boot <- bootstrap_test(task, n_boot = 999, seed = 42)

References

Kolari, J. W. and Pynnonen, S. (2010). Event study testing with cross-sectional correlation of abnormal returns. Review of Financial Studies, 23(11), 3996-4025.
Newey, W. K. and West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703-708.
Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, 57(1), 289-300.