Event Study Scholes-Williams Beta First Order Autocorrelation

[Calvin Matthew Johnson]

I am trying to calculate Scholes-Williams Betas for my estimation period (I have attached the formula).

I have managed to calculate the betas from the OLS regression of the returns on the lagged and lead market returns; however I am not sure how I calculate an estimated first order autocorrelation coefficient of the return index on stata.

Any help would be appreciated.

Thanks