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Degrees of Freedom for CAR and BHAR Event-Study Tests

Article Quant Q&A · Author: Felix
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Summary

The document asks how to choose the degrees of freedom for t-tests of mean cumulative abnormal returns (CAR) and mean buy-and-hold abnormal returns (BHAR) across a sample of firms. It gives test-statistic forms that divide each sample mean by its cross-sectional standard error, using the sample standard deviation and the square root of the number of firms. The author wonders whether the critical value should use a degrees-of-freedom count based on the number of CAR observations minus two.

The sole reply does not resolve that statistical question. Instead, it points to several R event-study libraries as comprehensive implementation resources and says one has been briefly reviewed. No derivation, test assumptions, degrees-of-freedom recommendation, or comparison of methods is supplied. The material therefore flags a practical inference issue but does not establish the correct critical value; users would need to consult a statistical treatment or the cited package documentation before relying on a test result.

Key ideas

  • The author tests cross-sectional mean CAR and BHAR using sample standard deviations and the number of firms.
  • The question concerns which degrees of freedom determine the critical t-value.
  • The author proposes subtracting two from the number of observations but receives no confirmation.
  • The reply recommends event-study software libraries without addressing the underlying degrees-of-freedom calculation.
  • No statistical derivation or validation is presented.

Tags

Event-drivenStatisticsBacktesting
Full text
# Event Study t-test finding degrees of freedom for CAR and BHAR


# Event Study t-test finding degrees of freedom for CAR and BHAR












I'm running an event study and calculate the mean cumulative average return and the mean buy-and-hold abnormal return.

The t-test is straightforward: t_CAR = (Mean(CAR_it)) / (sigma(CAR_it) / sqrt(n)) ; and

t_BHAR = (Mean(BHAR_it)) / (sigma(BHAR_it) / sqrt(n))

but how many degrees of freedom do I use for the critical t-values?

I would assume its df= number of CAR - 2 ?

(Note that Mean(CAR_it) and Mean(BHAR_it) are the sample averages and sigma(CAR_it) and sigma(BHAR_it) are the cross-sectional sample standard deviatons of abnormal returns for the sample of n firms (Barber/Lyon 1997))

## Answer by Con Fluentsy (score 1)

https://quant.stackexchange.com/a/66346

In R there is a number of built in event study library routines that are very comprehensive, I have really only had a cursory glance at estudy2 libray link here https://cloud.r-project.org/web/packages/estudy2/estudy2.pdf but here is 2 others https://cloud.r-project.org/web/packages/crseEventStudy/crseEventStudy.pdf; and https://cran.r-project.org/web/packages/EventStudy/EventStudy.pdf They are all thorough and comprehensive and estudy2 is not difficult to implement, I have not tried the others.

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