I am reading Pfaff "Analysis of Integrated and Cointegrated Time Series with R" (2008). On page 130, section 8.1.2 "Determining the Cointegration Rank" they start by determining cointegration rank. Because inferences on cointegration space spanned by its vectors are dependent on whether or not linear trends exist in the data, they argue by ocular econometrics and logical reasoning that the price series have a linear trend that is consistent with the steady-state assumption of constant nominal price growth as implied by economic theory, and therefore the vector $\mu$ can be estimated without imposing any restrictions.
What is the relation between "cointegration space spanned by the eigenvectors" and "the existence of linear trend in the data"?
The cases are:
- no linear trend in the data;
- linear trend in the data.
What is the result of these two cases on "cointegration space spanned by the eigenvectors"?