# Interpreting SAS output - Roots of AR Characteristic Polynomial

I urgently need help on interpreting the numbers from a SAS output on Characteristic Roots:

The VARMAX Procedure

The VARMAX Procedure Roots of AR Characteristic Polynomial

Index Real Imaginary Modulus Radian Degree

1 0.77238 0.35899 0.8517 0.4351 24.92842

2 0.77238 -0.35899 0.8517 -0.4351 -24.9284

I understand that by looking at the Modulus of the eigenvalue it's stationary if it's less than one. But what about the other elements in the results, i.e Real, Imaginary, Radian, Degree? What do they mean and how should I interpret them?

• These are just ways of telling you what the eigenvalues are. E.g., the first one is $z=0.77238+0.35899i$ entailing $|z|=\sqrt{0.77238^2+0.35899^2}=0.8517$ and $\arg(z)=\arctan(0.35899,0.77238)=0.4351=24.92842$ degrees. I am not aware of any statistical interpretations of the angle and would be interested to learn of any. – whuber Aug 28 at 14:27