Solution for a time-series AR model based on robust TLS estimation

Abstract

We discuss an algorithm for the autoregression (AR) model as a typical time-series model. By analyzing the structure of the AR model, we highlight the shortcomings of traditional algorithms for model parameter estimation and propose an approach to overcome the shortcomings of traditional solutions for the AR model. The errors-in-variables (EIV) model is used to solve an existing problem. There is an obvious difference between the AR model and a traditional model. For the AR model, one observation datum appears repeatedly; hence, the residual of one observation datum is not unique. Furthermore, in theory, the optimal estimation of model parameters cannot be obtained by current solutions. Based on an analysis of the AR model, we focus on how to obtain the optimal estimation when the observation data of the AR model are contaminated by outliers. The median function is used to establish a modified solution for the AR model based on the institute of geodesy & geophysics, Chinese academy of sciences (IGG) weight function by comparison with current algorithms for the robust estimation of the EIV model. We propose an iterative algorithm based on median function. Finally, we apply two numerical instances to compare the proposed algorithm with traditional algorithms and draw conclusions from results of the instances.