Testing and estimation of equal variances for correlated variables

For testing the equality of variances for correlated variables, Harris (1985) suggested Wald type test statistics. In this note we show that this test coincides with the generalized least squares statistic employed in the analysis of covariance structures. We derive the generalized least squares estimator of the common variance. This estimator is compared with the average sample variances which is the ordinary least squares estimator for this problem.