Journal of Applied Mathematics and Decision Sciences
Volume 7 (2003), Issue 1, Pages 29-48

A case study of the residual-based cointegration procedure

Riccardo Biondini,1 Yan-Xia Lin,2 and Michael Mccrae1

1Department of Accounting & Finance, the University of Wollongong, Sydney, Australia
2School of Mathematics & Applied Statistics, the University of Wollongong, Sydney, Australia

Copyright © 2003 Riccardo Biondini et al. 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.


The study of long-run equilibrium processes is a significant component of economic and finance theory. The Johansen technique for identifying the existence of such long-run stationary equilibrium conditions among financial time series allows the identification of all potential linearly independent cointegrating vectors within a given system of eligible financial time series. The practical application of the technique may be restricted, however, by the pre-condition that the underlying data generating process fits a finite-order vector autoregression (VAR) model with white noise. This paper studies an alternative method for determining cointegrating relationships without such a pre-condition. The method is simple to implement through commonly available statistical packages. This ‘residual-based cointegration’ (RBC) technique uses the relationship between cointegration and univariate Box-Jenkins ARIMA models to identify cointegrating vectors through the rank of the covariance matrix of the residual processes which result from the fitting of univariate ARIMA models. The RBC approach for identifying multivariate cointegrating vectors is explained and then demonstrated through simulated examples. The RBC and Johansen techniques are then both implemented using several real-life financial time series.