Measuring the Behaviour of Stock in the Estimation Window and the Event Window
As its name implies, the estimation window is used to estimate a model of the stock's returns under "normal" circumstances. The most common model used for this purpose is the market model, which is essentially a regression of the stock returns and the returns of the market index.
The market model for a stock i can be expressed as
r_{it} = α_{i} + β_{i}r_{Mt}
Here r_{it} and r_{Mt} represent the stock and the market return on day t. The coefficients α_{i} and β_{i }are estimated by running an ordinary least-square regression over the estimation window. The most common criteria for selecting market and industry indexes are whether the company is listed on NYSE/AMEX or Nasdaq and whether any restrictions are imposed by data availability. In general, the market index should be a broad-based value-weighted index or a float weighted index. The industry index should be Specific to the company being analyzed. For litigation purposes, it is common to construct the industry index instead of using alternative S&P 500 or MSCI indexes (most industry indexes are available from Yahoo).
Given the equation r_{it} = α_{i} + β_{i}r_{Mt} in the estimation window, we can now measure the impact of an event on the stock's return in the event window. For a particular day t in the event window, we define the stock's abnormal return (AR) as the difference between its actual return and the return that would be predicted by the equation
We interpret the abnormal return during the event window as a measure of the impact the event had on the market value of the security. This interpretation assumes that the event is exogenous with respect to the change in the security's market value. The cumulative abnormal return (CAR) is a measure of the total abnormal returns during the event window. The variable CAR_{t} is the sum of all the abnormal returns from the beginning of the event window T_{1} until a particular day t in the window: