The event study is one of the most powerful techniques for studying market efficiency. Over a period of time, researchers have made several modifications to the original methodology of Fama, Fisher, Jensen and Roll (1969). Nevertheless, the current methodology continues to suffer from several grave deficiencies. These deficiencies arise due to (a) a failure to take into account the variance covariance structure of the estimated abnormal returns (across time and across securities) and (b) fundamental shortcomings of the moving window technique used to deal with possible changes in the betas in the neighbourhood of the event. Our proposed methodology overcomes these deficiencies and provides statistically efficient estimates. We then extend the analysis to handle nonstationary parameters evolving according to a Kalman Filer model.