Questions about components' stationarity in VAR model.

[Zachary Jiang]

I am very confused about the stationarity of variables in VAR. It seems that different econometrics researchers give different opinions of this issue. Some say all variables in VAR should be stationary (traditional time series analysis), some say all varibles in VAR should be I(1) process (a youtuber called Crunch Econometrix who teaches econometrics), while others say it is ok even variables in VAR are integrated of different orders if we don't care the point estimation! (i.e. regardless of stationarity and order of integrated) They even dont require variables are of the same integrated order! (Sims, Stock and Watson 1990 and Walter Enders in his textbook)

What on earth is the answer? In general (I mean, the most common case), should we take stationary tests for all variables before constructing a VAR model? Or we can just directly input var x y z.... in Stata without any consideration of stationarity? Or should we at least make sure all variables are integrated of the same order?

[Justin Niakamal]

What are you using a VAR for? If it's for impulse response analysis, work with all stationary variables I~(0). If you have all I~(1) variables and they're cointegrated you can look at VECM.
If you're looking to do Granger Causality testing, follow the Toda and Yamamoto (1995) procedure -- there's an excellent overview of this by Dave Giles here.

https://davegiles.blogspot.com/2011/...r-granger.html


Also consider taking a look at

https://pdfs.semanticscholar.org/776...8d032ee2eb.pdf


Ashley, Richard A., and Randal J. Verbrugge. "To difference or not to difference: a Monte Carlo investigation of inference in vector autoregression models." International Journal of Data Analysis Techniques and Strategies 1, no. 3 (2009): 242-274.

Toda, Hiro Y., and Taku Yamamoto. "Statistical inference in vector autoregressions with possibly integrated processes." Journal of econometrics 66, no. 1-2 (1995): 225-250.

Hope this helps.

[Zachary Jiang]

What are you using a VAR for? If it's for impulse response analysis, work with all stationary variables I~(0). If you have all I~(1) variables and they're cointegrated you can look at VECM.
If you're looking to do Granger Causality testing, follow the Toda and Yamamoto (1995) procedure -- there's an excellent overview of this by Dave Giles here.

https://davegiles.blogspot.com/2011/...r-granger.html


Also consider taking a look at

https://pdfs.semanticscholar.org/776...8d032ee2eb.pdf


Ashley, Richard A., and Randal J. Verbrugge. "To difference or not to difference: a Monte Carlo investigation of inference in vector autoregression models." International Journal of Data Analysis Techniques and Strategies 1, no. 3 (2009): 242-274.

Toda, Hiro Y., and Taku Yamamoto. "Statistical inference in vector autoregressions with possibly integrated processes." Journal of econometrics 66, no. 1-2 (1995): 225-250.

Hope this helps.

Hi Justin,
Thanks for your kind reply.
My goal is to forecast the value of this two variables in short run, so point estimation is important for me.
Actually, I read in Chapter 5, page 308, Applied Econometric Time Series by Walter Enders(4th edition) that even a VAR composed of a I(1) and a I(0) series can apply t-test. I think this is interesting.

Anyway, there are so many different opinions about series stationarity in VAR and they are even contradictory to some extents.

Regard

[Eric de Souza]

Actually, I read in Chapter 5, page 308, Applied Econometric Time Series by Walter Enders(4th edition) that even a VAR composed of a I(1) and a I(0) series can apply t-test. I think this is interesting.

I don't have the book but I doubt very much he said that. This is from his slides which are in the public domain:
"• Recall a key finding of Sims, Stock, and Watson (1990):
If the coefficient of interest can be written as a coefficient on a
stationary variable, then a t-test is appropriate.
• You can use t-tests or F-tests on the stationary variables.
• You can perform a lag length test on any variable or any set of
variables
• Generally, you cannot use Granger causality tests concerning
the effects of a nonstationary variable
• The issue of differencing is important.
– If the VAR can be written entirely in first differences,
hypothesis tests can be performed on any equation or any
set of equations using t-tests or F-tests.
– It is possible to write the VAR in first differences if the
variables are I(1) and are not cointegrated. If the variables
in question are cointegrated, the VAR cannot be written in
first differences
"
Not the same.

[Zachary Jiang]

I don't have the book but I doubt very much he said that. This is from his slides which are in the public domain:
"• Recall a key finding of Sims, Stock, and Watson (1990):
If the coefficient of interest can be written as a coefficient on a
stationary variable, then a t-test is appropriate.
• You can use t-tests or F-tests on the stationary variables.
• You can perform a lag length test on any variable or any set of
variables
• Generally, you cannot use Granger causality tests concerning
the effects of a nonstationary variable
• The issue of differencing is important.
– If the VAR can be written entirely in first differences,
hypothesis tests can be performed on any equation or any
set of equations using t-tests or F-tests.
– It is possible to write the VAR in first differences if the
variables are I(1) and are not cointegrated. If the variables
in question are cointegrated, the VAR cannot be written in
first differences
"
Not the same.

Yeah... but the part of his book I mentioned does think a VAR composed of a I(1) and a I(0) series can apply t-test and it has detailed mathematical procedures. You can check it if possible.