## How does one practically implement a Vector Autoregression (VAR)?

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anni0308
Posts: 3
Joined: Sat Jun 02, 2018 3:04 am

### How does one practically implement a Vector Autoregression (VAR)?

Dear EViews-Forum,

First: Thank you for the time and effort for answering this question. It is much appreciated!

I am currently writing my Master Thesis and analyze the relationship of the return of a specific group of stocks and some macroeconomic variables An example could be: How does the level of short-term interest rates affect the return of stock X ?

In the end, I would like to have a single equation which describes the return of stock X and its dependencies on the macroeconomic variables. If you would use an OLS Analysis, for example, you would get such an equation:

y = 0,5 + 1,8 * x + 0,9 * z + 14 * v

with
x = short-term interest rate
x = inflation rate
v = GDP growth rate

In my opinion, however, a Vector Autoregression is a better fit as it incorporates dependencies among the macroeconomic variables.
When I choose "Estimate VAR" in EViews, I choose the stock as the endogenous variable (in the following example it is the Index MSCI World) and the macroeconomic variables as the exogenous variables (in this case inflation rate and short-term interest rate). The results are as follows:
test.PNG (27.92 KiB) Viewed 1265 times

I did some research about VAR and know that it is usually provided in the format of a matrix. Unfortunately, I have problems to connect the values I receive from EViews and the standard formula:

formula.PNG (5.94 KiB) Viewed 1265 times

How would the above formula look like if I incorporate the results from the first picture? What are the values for a(1,1), a(1,2) or a(2,1) and y(1) etc?

If the current macroeconomic variables are available, in the case of the OLS, I can simply insert the values for x, z and v to receive the value for y.
How does it work with an Vector Autoregression? Which part of the formula contains the macroeconomic variables (x, z and v respectively).Would I even receive one value or is the result a matrix? What would the matrix tell me?

Best regards,
Anni

startz
Non-normality and collinearity are NOT problems!
Posts: 3406
Joined: Wed Sep 17, 2008 2:25 pm

### Re: How does one practically implement a Vector Autoregression (VAR)?

A VAR is simply a set of OLS regressions of each endogenous variable on lags of all the endogenous variables and on the exogenous variables. Just enter in a couple of endogenous variables and you'll see what you get.

anni0308
Posts: 3
Joined: Sat Jun 02, 2018 3:04 am

### Re: How does one practically implement a Vector Autoregression (VAR)?

Dear Startz,

Is it correct that the equation for the Current MSCI World Variable would be as follows?

Y = 0,616156 + 0,088438 * Previous MSCI World (t-1) - 0,048816 * MSCI World (t-2) + 0,762225 * Current Inflation - 0,076586 * Current Short-term Interest

This would imply that the Variable World is dependend on itself, although its previous values. This is not true, though. Only the macroeconomic variables are dependend on the other variables, for example: Short-term Interest is also affected by inflation.

Does this mean, for my purpoe a VAR is not even the best choice?

Thank you again for your time and knowledge!!

startz
Non-normality and collinearity are NOT problems!
Posts: 3406
Joined: Wed Sep 17, 2008 2:25 pm

### Re: How does one practically implement a Vector Autoregression (VAR)?

To know whether a model is a standard VAR, you'll have to show what you want all the equations to look like.