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:

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:

I sincerely hope you can help me!

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:

- y1: oil production (% change)
- y2: aggregate demand
- y3: real price of oil (deviation from the mean)
- y4: stock market return

**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:

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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.*
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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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