Computing Echelon Forms by Polynomial Methods

Abstract

Given a VARMA, VARMAX, or time invariant state space model, we will show in this chapter how to compute the echelon form by polynomial methods. More specifically, we will use the stable algorithm described in Gómez (Multivariate time series models with linear state space structure. Springer, New York, 2016, Appendix to Chapter 5) to pass from a right matrix fraction description (MFD) to a left coprime MFD in echelon form. In SSMMATLAB, function pecheform.m applies this algorithm to compute the echelon form of a VARMA or VARMAX model. The previous function can also be used with time invariant state space models once they are put into VARMA form. We will show how to do this later in Sect. 6.2. All the MATLAB instructions that appear in this chapter can be found in the script file varmax2echelon_d.m of SSMMATLAB.