Mathematical Problems in Engineering
Volume 7 (2001), Issue 1, Pages 97-112

Identification of an unstable ARMA equation

Yulia R. Gel1,2 and Vladimir N. Fomin2

1Malardalen University, PO Box 883, Vasteras S-721 23, Sweden
2St. Petersburg State University, Bibliotechnaya pl., Petersburg 2 198904 St., Russia

Received 23 May 2000

Copyright © 2001 Yulia R. Gel and Vladimir N. Fomin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.

Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.