Hi Carl,
As per my understanding, covariance matrix SIGMA is not positive-definite when at least one of your variables can be expressed as a linear combination of others.
It is suggested to add variables sequentially and check the covariance matrix at each step. If adding a new variable creates a singularity, please drop it and go on to the next one. Eventually you should have a subset of variables with a positive definite covariance matrix. You can read more about the calibration method for non-positive covariance matrices.
Please go through the following documentations on Vector Autoregressive Models for your reference.
