Cointegration by MCA and modular MCA

A new approach for investigating the cointegration relationship between time series is proposed based on the so called minor component analysis (MCA) and its extension, modular MCA. With no need to place one variable on the left-hand side and use the others as regressors on the estimation of the long-run equilibrium regression, and also no need to build up a vector autoregression model for rank based analysis, this approach conducts cointegration analysis directly based on the linear combination of the instantaneous values of nonstationary variables via an eigen-analysis corresponding to the smallest eigenvalue, which can be implemented either in a batch way or by a Hebbian learning adaptive algorithm. A method for estimating the order of the cointegration has been also developed. Experiments are made in comparison with the least square regression based cointegration approach and have demonstrated the advantages of the approach