On a recursive method including both CG and Burg’s algorithms

The CG method (conjugate gradient method) is one of the most important and useful algorithms for the numerical solution of linear equations. On the other hand, Burg’s algorithm is an algorithm for estimating the parameters of time series models. Both algorithms are quite popular in the field of numerical calculation and time series analysis, respectively. It is less known, however, that these algorithms have a common mathematical structure. It seems that not so many researchers are familiar with both of these algorithms. Therefore, in this paper, we review these algorithms and see how they are related with each other. This leads to a notion of “anti-stationarity” in time series analysis.