Mean and covariance matrix adaptive estimation for a weakly stationary process. Application in stochastic optimization

Abstract We introduce an adaptive algorithm to estimate the uncertain parameter of a stochastic optimization problem. The procedure estimates the one-step-ahead means, variances and covariances of a random process in a distribution-free and multidimensional framework when these means, variances and covariances are slowly varying on a given past interval. The quality of the approximate problem obtained when employing our estimation of the uncertain parameter is controlled in function of the number of components of the process and of the length of the largest past interval where the means, variances and covariances slowly vary. The procedure is finally applied to a portfolio selection model.