Computing Echelon Forms by Polynomial Methods

  • Víctor Gómez
Part of the Statistics and Computing book series (SCO)


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.


  1. Gómez, V. (2016). Multivariate time series models with linear state space structure. New York: Springer.zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Víctor Gómez
    • 1
  1. 1.General Directorate of BudgetsMinistry of Finance and Public AdministrationsMadridSpain

Personalised recommendations