## Nearly cointegrated systems

Even when a vector of time series is I(1), the size of the unit root in each of the series could be very different. For example, in terms of the common trend representation of a bivariate system discussed above, it could well be the case that y1t = ф1 yC + +1t and y2t = ф2yC + +2t are such that ф1 is close to zero and that ф2 is large. Then y1t will not be different from +1t which is an I(0) series while y2t will be clearly I(1). The two series are cointegrated, since they share a common trend. However, if we regress y1t on y2t, i. e. we normalize the cointegrating vector on the coefficient of y1t, the regression will be nearly unbalanced, namely, the regressand is almost I(0) whilst the regressor is I(1)...

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