Obsidian | Level 7

## Interpret Covariance of Innovation in Proc Varmax

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!

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SAS Employee

## Re: Interpret Covariance of Innovation in Proc Varmax

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.

2 REPLIES 2
SAS Employee

## Re: Interpret Covariance of Innovation in Proc Varmax

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.

Obsidian | Level 7

## Re: Interpret Covariance of Innovation in Proc Varmax

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