In a college course I try to measure the abnormal returns (the returns that are below or over the returns of the market) of a companies stock after a specific event based on linear OLS regression. When interpreting the results with t-statistic and corresponding p-value, the professor of the course told me that these abnormal returns I observe have to be normally distributed. Otherwise the t-test would lead to miss specified results. If I am not mistaken, OLS assumes the normal distribution of the error terms. Unfortunately I don’t really get why the effect I would like to observe has to be normally distributed in order to get unbiased results. What Problems arise when the data i observe are not normally distriuted? Do I have to work with approach in this case (not OLS regression)? Thanks in advance
what you care about is the distribution of the sample mean of the errors. This is where the central limit theorem helps, because even if your individual errors are not normally distributed, the mean of say 100 (ie the number of datapoints) of them will be.
the p-value is calculated based on an assumption that the (sample mean) of the underlying data is normally distributed, if its not, then you would have to use a different formula to calculate probability. [however, as I say, I don't believe it should be a problem, assuming your t-statistic is calculated from a large enough sample]