Understanding the prerequisites for a VAR analysis

NoobNoob

New Member
Hello everyone,

I am currently working on a research project in which I need to replicate the results of two researchers (Kilian & Park 2009: The Impact of Oil Price Shocks on the US Stock Market). In their research article, the two authors use a VAR model (a Structural VAR to be more precise) with 4 variables:
1. y1: oil production (% change)
2. y2: aggregate demand
3. y3: real price of oil (deviation from the mean)
4. y4: stock market return
I started by doing some preliminary analysis on the data itself and I found some weird results. I hope you guys can help me understand those.

FIRST: I checked whether the data was stationary and found that the real price of oil ("rpoil") was not stationary. Here are the results.
I was a little bit puzzled by this finding, especially since I thought that all variables in a VAR needed to be stationary. I searched the internet and found surprising results on this topic:
If series levels are non-stationary then estimated regressions involving the levels cannot be trusted (Google "spurious regressions" for details). Differencing the series to make them stationary is one solution, but at the cost of ignoring possibly important (so called "long run") relationships between the levels.
A better solution is to test whether the levels regressions are trustworthy (a situation called "cointegration"). The usual approach is to use Johansen's method for testing whether or not cointegration exists. If the answer is "yes" then a vector error correction model (VECM), which combines levels and differences, can be estimated instead of a VAR in levels. If the answer is "no" then you are stuck with a VAR in differences.
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...
My first question is then: Is it a problem if the data is not stationary ? What are the consequences for the subsequent analysis?

SECONDLY: I decided to follow the recommendations explained above and perform a co-integration test using the Johansen Test. Here are the results. The test rejects the null hypothesis that the rank is at most 3, but I am not sure how I should understand this result.

My second question is then: What should I conclude by looking at this table ?

I sincerely hope you can help me!

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noetsi

Fortran must die
I think the key prerequisites to do VAR analysis is a high tolerance for pain and ambiguity. There is disagreement among authors on Stationarity of VAR models. Some feel that you should not make them stationary because you lose useful data in doing so. Slopes are generally not analyzed in VAR models, I am not sure that the tools that are such as IRT require Stationarity.

If variables are cointegrated then VAR models are not appropriate. You are supposed to use vector error correction models instead. Unfortunately I have never run such a model, I just spent a lot of time reading about them. I have yet to have the courage to analyze them.

I do not remember the test you mention for cointegration well enough to comment on it.

NoobNoob

New Member
I think the key prerequisites to do VAR analysis is a high tolerance for pain and ambiguity. There is disagreement among authors on Stationarity of VAR models. Some feel that you should not make them stationary because you lose useful data in doing so. Slopes are generally not analyzed in VAR models, I am not sure that the tools that are such as IRT require Stationarity.

If variables are cointegrated then VAR models are not appropriate. You are supposed to use vector error correction models instead. Unfortunately I have never run such a model, I just spent a lot of time reading about them. I have yet to have the courage to analyze them.

I do not remember the test you mention for cointegration well enough to comment on it.
Thank you so much for your response! That is very insightful. The slopes are not directly studied but they do influence impulse responses don't they?

At the moment, I am still struggling with the Johansen Test to understand the implication of the results I have found

noetsi

Fortran must die
I don't think slopes would influence IRT. I think slopes and IRT would model in a different way an impact. But slopes in VAR are apparently rarely used so they probably are not very useful.

I should warn you that I have never run VAR. Not brave enough to do so They are very complex by my standards. I just spent a good deal of time reading about them. If you like if I can find my notes on them and I can figure how to post them here I will, but they are simply my understanding of what I read and may not be correct.

You really need Vinux, but he is long gone from these boards sadly.

NoobNoob

New Member
I don't think slopes would influence IRT. I think slopes and IRT would model in a different way an impact. But slopes in VAR are apparently rarely used so they probably are not very useful.

I should warn you that I have never run VAR. Not brave enough to do so They are very complex by my standards. I just spent a good deal of time reading about them. If you like if I can find my notes on them and I can figure how to post them here I will, but they are simply my understanding of what I read and may not be correct.

You really need Vinux, but he is long gone from these boards sadly.
Don't worry I'll just read as much as I can about how to understand the results of the Johansen Test. I think you answered all the questions I had about stationary in VAR models . Thanks again!!

noetsi

Fortran must die
remember there is disagreement. Some feel they do need to have Stationarity (without cointegration) and some feel there is no such requirement. I do not know who is right.

I think starting with the cointegration test is the best move. With cointegration Stationarity is besides the point and VAR models are not appropriate.