topic Interpret Covariance of Innovation in Proc Varmax in SAS Forecasting and Econometrics

Interpret Covariance of Innovation in Proc Varmax

eemrun — Tue, 24 Oct 2017 02:34:30 GMT

I am trying to run a var model in sas using Proc Varmax and am struggling to interpret the covariance of innovation matrix. The following is the output for the matrix

Covariances of Innovations Variable CPI UMP GDP HPI

CPI	0.26246	-0.00878	0.00407	-0.00069
UMP	-0.00878	0.06139	-0.01408	0.00033
GDP	0.00407	-0.01408	0.09407	0.00089
HPI	-0.00069	0.00033	0.00089	0.00018

Any help or guide towards any material would be much appreciated!

Re: Interpret Covariance of Innovation in Proc Varmax

ChristianMac — Wed, 25 Oct 2017 17:20:42 GMT

From what I understood, you have 4 dependent variables that you are modeling jointly: CPI, UMP, GDP, HPI.

Presumably the model is characterized by an autoregressive/moving average part (for example the lags of CPI, UMP, GDP, HPI) and by an innovation term.

The innovation term is a 4x1 vector which is assumed to follow a normal distribution with mean (0,0,0,0)' and a variance/covariance matrix of dimensions 4x4. I believe that the covariance that you are referring to is the estimate of the variance/covariance matrix of the innovation term. For example:

0.26246 is the variance of the innovation term associated with the equation whose dependent variable is CPI.

-0.00878 is the covariance between the innovation term associated with the CPI dependent variable equation and the innovation term associated with the UMP dependent variable equation.

Hopefully this is what you were looking for.

Re: Interpret Covariance of Innovation in Proc Varmax

eemrun — Wed, 25 Oct 2017 20:55:56 GMT

Thanks for that explanation! I should have been clearer so apologies. I am fitting a VAR model with those variables.