Cumulative Abnormal Returns or Structural Change Tests?

In this chapter, it is shown that if the impact of event(s) is considered as permanent, the cumulative abnormal return statistics in event studies coincides with the CUSUM statistics in the tests for parameter changes of regressions such as market models. Namely, the applications for the tests on abnormal returns are closely related with the model specification of normal returns, especially with the regression models assumed for the normal (expected) returns. If the statistical approach is reterospective (where the studies of interest are to identify the possible (permanent) change in parameters within the given history of stock returns), and if the presumed initial date for event window is the correct time period where parameter changes, the hypotheses testings of the conventional CARs and CUSUM statistics are almost identical except for the asymptotic distributions applied. The CARs tests apply the (asymptotic) normality, while CUSUM tests are based on Brownian motion or Brownian bridge.