Hi Guys,

I have a bunch of I(1) and I(0) variables for which I want to use levels VAR. I mean, I skip the usual cointegration / VAR vs. VECM stuff. I get a stable VAR with serially independent residuals, although not normal.

My questions:

1. I want to know what is the worst possible fail of not applying the usual guidelines for VAR vs. VECM (choice of specification depending on order of integration and presence of cointegrating relationships)? I only found examples with two variables, pointing to the problem of spurious regression: falsely attributing a relationship when there is none.

2. I would like to back my choice by some econometric reference. This piece of work of Prof. Lutkepohl http://cadmus.eui.eu/bitstream/handle/1 ... sequence=1 is the only chapter I found to consider levels VARs for nonstationary processes, without looking at the cointegrating relations. Do you agree with my understanding of the exposition?

Thanks so much for your opinions.

## Is using levels VAR for nonstationary series a problem?

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### Re: Is using levels VAR for nonstationary series a problem?

VAR models are usually guided by theory and are dynamic in nature, so you do not have to worry about the nonstationarity. And Prof. Lutkepohl's studies are always good references.

### Re: Is using levels VAR for nonstationary series a problem?

Thanks for reply, trubador.

For me personally your view is just fine. I do not blind look on econometric tests to see if variables have a meaningful relationship or not. My concern is because I seem to encounter everywhere the dictate to test for cointegration and consequently go to a VAR in level or difference, or VECM. It is so widespread that I almost get an impression of a "must" about it. I am almost sure, when I am going to give a seminar on my paper, there will be questions on this. Saying "You know, this choice is guided by theory and look at what Prof. Lutkepohl wrote", would sound just arrogant.

Instead, I want to back myself up by good arguments. What can I say about that? Can someone please translate in layman words what the VAR vs. VECM testing procedure is about? What possible fails do we face? I mean e.g. with Granger causality, the point is that the other's variable history improves the prediction of our variable compared to just its own history. Based on that we infer judgements about causality. The only concrete point I came up with this topic is the hint to spurious regression and type I and type II error acc. to Chiarella-Gao. Which comes back to attributing a meaningful relationship between variables.

Hope to see more of your views, or references that could help. Thanks so much.

For me personally your view is just fine. I do not blind look on econometric tests to see if variables have a meaningful relationship or not. My concern is because I seem to encounter everywhere the dictate to test for cointegration and consequently go to a VAR in level or difference, or VECM. It is so widespread that I almost get an impression of a "must" about it. I am almost sure, when I am going to give a seminar on my paper, there will be questions on this. Saying "You know, this choice is guided by theory and look at what Prof. Lutkepohl wrote", would sound just arrogant.

Instead, I want to back myself up by good arguments. What can I say about that? Can someone please translate in layman words what the VAR vs. VECM testing procedure is about? What possible fails do we face? I mean e.g. with Granger causality, the point is that the other's variable history improves the prediction of our variable compared to just its own history. Based on that we infer judgements about causality. The only concrete point I came up with this topic is the hint to spurious regression and type I and type II error acc. to Chiarella-Gao. Which comes back to attributing a meaningful relationship between variables.

Hope to see more of your views, or references that could help. Thanks so much.

### Re: Is using levels VAR for nonstationary series a problem?

I understand the confusion here. Unfortunately, this false perception is quite common as in the case of multicollinearity and non-normality issues. Please refer to page 303 of Walter Enders's book: "Applied Econometric Time Series, 3rd ed." Below is the verbatim quote as it might be helpful for future discussions in the forum:

There is an issue of whether the variables in a VAR need to be stationary. Sims (1980) and Sims, Stock and Watson (1990) recommend against differencing even if the variables contain a unit root. They argued that the goal of a VAR analysis is to determine the interrelationships among the variables, not to determine the parameter estimates. The main argument against differencing is that it “throws away” information concerning the comovements in the data (such as the possibility of cointegrating relationships). Similary, it is argued that the data need not be detrended. In a VAR, a trending variable will be well approximated by a unit root plus drift. However, majority view is that the form of variables in the VAR should mimic the true data-generating process. This is particularly true if the aim is to estimate a structural model.

### Re: Is using levels VAR for nonstationary series a problem?

Thank you a lot for the quote, trubador!

Maybe I was thinking a wrong direction with the spurious regression and falsely attributing a relationship between variables.

Maybe a better direction to think about this is to look at the purpose of the VAR vs. VECM procedure, and eventual differencing or inclusion of cointegrating relations. What does it help or improve? Is it because we need to get a stationary model process (or, avoid a non-stationary one)? Is it because of the properties of the estimated coefficients etc? In the end, does it come to the point whether the model is a good representation of the underlying DGP...?

Guys, I hope to see more opinions on this. And I am enormously grateful to QMS / IHS for maintaining this forum. Thanks!!

Maybe I was thinking a wrong direction with the spurious regression and falsely attributing a relationship between variables.

Maybe a better direction to think about this is to look at the purpose of the VAR vs. VECM procedure, and eventual differencing or inclusion of cointegrating relations. What does it help or improve? Is it because we need to get a stationary model process (or, avoid a non-stationary one)? Is it because of the properties of the estimated coefficients etc? In the end, does it come to the point whether the model is a good representation of the underlying DGP...?

Guys, I hope to see more opinions on this. And I am enormously grateful to QMS / IHS for maintaining this forum. Thanks!!

### Re: Is using levels VAR for nonstationary series a problem?

Hi there guys,

I too have estimated an unrestricted VAR in levels as best explained by Sims et al (1990). As estimating in VAR in levels correctly estimates the dynamics of the system taking into account whatever cointegration and integration which may exist in the data I wondered if we could extend this line of reasoning across to Granger Causality and Variance Error Decomposition? Or will my results be spurious?

Thanks,

James

I too have estimated an unrestricted VAR in levels as best explained by Sims et al (1990). As estimating in VAR in levels correctly estimates the dynamics of the system taking into account whatever cointegration and integration which may exist in the data I wondered if we could extend this line of reasoning across to Granger Causality and Variance Error Decomposition? Or will my results be spurious?

Thanks,

James

### Re: Is using levels VAR for nonstationary series a problem?

From Bayesian perspective, nonstationarity is not problem.

### Re: Is using levels VAR for nonstationary series a problem?

Dakila is correct. Unless variables in question are not cointegrated, nonstationarity is not a problem with VAR as well. That is because you need to know which variables are cointegrated in order to put long term restrictions on the shocks.

You certainly cannot apply standard Granger causality analysis to nonstationary series, since it does not have an asymptotic F distribution. As for the variance decomposition, you need to be careful with the interpretation. Since error variance will not converge, it may not make much sense for long horizons (e.g. 10 years).

You certainly cannot apply standard Granger causality analysis to nonstationary series, since it does not have an asymptotic F distribution. As for the variance decomposition, you need to be careful with the interpretation. Since error variance will not converge, it may not make much sense for long horizons (e.g. 10 years).

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