- It is shown that interlacing is not needed for the stability and optimality of the direct adaptive minimum variance control based on either the stochastic gradient (SG) or extended least squares (ELS) algorithms. In the least squares case, the authors use the result of L. Guo and H. F. Chen (1990) on the convergence of the adaptive minimum variance control for unit delay systems. The problem of parameter estimation in a regression model with a moving average residual noise is considered. Convergence properties are derived for both SG and ELS algorithms. Based on these properties, the stability and optimality of a direct adaptive MV control is established.