8.5 Unit-Root Nonstationarity and Cointegration
When modeling several unit-root nonstationary time series jointly, one may encounter the case of cointegration. Consider the bivariate ARMA(1,1) model
where the covariance matrix of the shock is positive definite. This is not a weakly stationary model because the two eigenvalues of the AR coefficient matrix are 0 and 1. Figure 8.10 shows the time plots of a simulated series of the model with 200 data points and = , whereas Figure 8.11 shows the sample autocorrelations of the two component series xit. It is easy to see that the two series have high autocorrelations and exhibit features of unit-root nonstationarity. The two marginal models of are indeed unit-root nonstationary. Rewrite the model as
Premultiplying the above equation by ...