Stable identification of linear autoregressive model with exogenous variables on the basis of the generalized least absolute deviation method

Least Absolute Deviations (LAD) method is a method alternative to the Ordinary Least Squares OLS method. It allows to obtain robust errors in case of violation of OLS assumptions. We present two types of LAD: Weighted LAD method and Generalized LAD method. The established interrelation of methods made it possible to reduce the problem of determining the GLAD estimates to an iterative procedure with WLAD estimates. The latter is calculated by solving the corresponding linear programming problem. The sufficient condition imposed on the loss function is found to ensure the stability of the GLAD estimators of the autoregressive models coefficients under emission conditions. It ensures the stability of GLAD-estimates of autoregressive models in terms of outliers. Special features of the GLAD method application for the construction of the regression equation and autoregressive equation without exogenous variables are considered early. This paper is devoted to extension of the previously discussed methods to the problem of estimating the parameters of autoregressive models with exogenous variables.