Variance Component Estimation of Autoregressive Model Based on Variable Projection Method

In the autoregressive (AR) model, random errors in the observation vector are homologous to those in the coefficient matrix. In view of the unreasonable distribution of the observation weight matrix and the inaccuracy of the random model, the random quantities in the augmented matrix consisting of the coefficient matrix and the observation vector are extracted by the variable projection method. Then, we transform the errors-in-variables (EIV) model into the nonlinear Gauss-Helmert (GH) model and propose a structural total least squares (STLS) algorithm by the nonlinear least squares adjustment theory. Combined with the least squares variance component estimation (LS-VCE) method, the variance component estimation method of STLS problem is derived. Furthermore, it is applied to the variance component estimation of the AR model. Through the real example, the effectiveness of proposed algorithm is verified. Meanwhile, the results are consistent with those of modified existing variance component estimation methods, but the construction of observation weight matrix is simple, it can also applied to the estimation of covariance factors.