Adding dummy variables to vector autoregression (VAR) results in covariance matrix being not positive-definite.

When adding dummy variables to a VAR, I get an error when using VAR estimate command (https://se.mathworks.com/help/econ/varm.estimate.html). Specifically i get the following error message:

Error using statecmobj (line 43)
Covariance matrix SIGMA is not positive-definite.

How does one add dummy variables to a VAR in such a way as to not get this error message?

Answer 1

[Sarthak]

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.

• https://www.mathworks.com/help/econ/introduction-to-vector-autoregressive-var-models.html
• https://www.mathworks.com/help/econ/model-specification-structures.html