Approximative covariance interpolation with a quadratic penalty

Given output data of a stationary stochastic process estimates of the covariances parameters can be obtained. These estimates can be used to determine ARMA models to approximately fit the data by matching the covariances exactly. However, the estimates of the covariances may contain large errors, especially if they are determined from short data sequences, and thus it makes sense to match the covariances only in an approximative way. Here we consider a convex method for solving an approximative covariance interpolation problem while maximizing the entropy and penalize the quadratic deviation from the nominal covariances.