I have a question about VAR estimation. With no unit root, no problem. Unit root found, we check the cointegration. If cointegrated, we use VEC. If not, we difference the time series (and consume a little degree of freedom). Am I correct or is there any other way to go?
As far as I know, many macro time series should result in VEC. But people seem to prefer first-differencing. I often see the impulse response function with 95% confidence interval, which is not available if VEC is used.
Generally the strategy you described is correct. Of course you should make additional tests: for normality, lag specification, heteroscedasticity, autocorrelation, etc. The problem with impulse response function, simply depends on the software you are using. you can always calculate band of confidence.
Dear Prof. Beck,
Many thanks for your detailed reply. I'll try to get the confidence band even when I use VEC (I use Eviews).
Can I ask you an additional question? Some people use Hodrick-Prescott (HP) Filter for time series data (to distinguish "trend" component and "cyclical" component). If I use HP filter to begin with, what would happen to the strategy I described above (or nothing changes)?
Warm Regards,
Mizuki Tsuboi
Frequency filters like Hodrick-Prescott filter allow separation of components of a give times series characterized by a given frequency. So if you use results of HP filtered data, you can create a VAR – using the cyclical component. Of course, you’ll have to change the interpretations to cyclical components, accordingly. Just remember that, as shown in http://people.bu.edu/mbaxter/papers/mbc.pdf, observations at the beginning and at the end of the series are behaving strange, so you should eliminate them or use for example Baxter-King filter (described in the link). This filter removes them automatically, and as it is symmetric, it removes trend and gives stationary cyclical component (other option is Cristiano-Fitzgerald filter: http://www.nber.org/papers/w7257.pdf ).
That being said, I must say it is rather unconventional practice, and I would strongly recommend using the procedure, you described in the first place. Frequency filters are very useful in other applications, and you can take different kind of conclusions from your data.
Dear Prof. Beck,
Again, thank you very much for your detailed explanation! It is really helpful.
I'm writing the paper in which I have to use VARs to support my macro theory. I am grateful to you. I'll post the paper when it is done.
All the best,
Mizuki Tsuboi
Hi,
no problem - if you want i can take a look at it. just tell me one thing - what software are you using for calculations?
best regards
Krzysztof Beck
Hi, I use Eviews. But it is a student version and thus some functions are limited.
I'm attaching two pictures of IRFs (using hypothetical numbers for illustration). As you can see, with unrestricted VARs, I can get the confidence band. However, with VEC, I cannot.
hi,
i think you can not make them in Eviews, i just checked it and don't see that option. Here is how you can make them in Jmulti:
http://davegiles.blogspot.com/2011/11/impulse-response-functions-from-vecms.html
Wow! Thank you so much. This is really helpful.
Is it okay to include your name in the acknowledgement, when the paper is done?
Many thanks from the bottom of my heart,
Mizuki Tsuboi
My pleasure. Please do so if you want to, although i don't think i deserve it.
Best regards
Krzysztof Beck
It is not what people says, it is what test says. Please check Johansen method. If cointegration is not rejected then you can use for a prediction in the short-run a first-difference and the cointegration vector together (Johansen's method). If you only need a long-run forecast use the cointegrated vector.
Dear Prof. Rojas,
Thank you for your another recommendation. It is worth trying.
I am sorry but it turns out that the main point of my question is whether we can do that in the statistical software, not to look for the econometric theory. I use Eviews, and I am not sure whether I can do what you have described in Eviews.
Best,
Mizuki Tsuboi