Sample Splitting and Threshold Estimation

[EViewsbrah]

Hi all,

I have estimated a cointegrating relationship between two crude oil benchmarks (Brent and WTI) using a VECM model. I am now trying to use threshold estimation to see if the cointegrating relationship changes over time. Although I understand the theory behind threshold regressions, I am unsure of how to implement what I am trying to do in EViews 9.

1) What should I use as the dependent variable?
2) What should I use as threshold and non-threshold regressors?
3) What should I use as the threshold variable?

I am thinking of storing the cointegrating relation as a series and then running a SETAR-type model. I would have the dependent variable and threshold variable be the cointegrating relation series. The threshold regressors would be lags of the cointergrating relation. I am not sure if this is the correct way of going about it, however.

Any advice whatsoever would be appreciated!

Many thanks for your help.

[trubador]

I would assume a stable/known long run equilibrium as it makes more sense to me than a time varying cointegrating relationship. Of course, adjustment towards this equilibrium (i.e. error correction) may not be fixed over time. As a reference, I would cite Balke and Fomby (1997) and Enders and Siklos (2001). And for the latter, there is already an EViews add-in available at: http://forums.eviews.com/viewtopic.php?f=23&t=5604

[EViewsbrah]

I would assume a stable/known long run equilibrium as it makes more sense to me than a time varying cointegrating relationship. Of course, adjustment towards this equilibrium (i.e. error correction) may not be fixed over time. As a reference, I would cite Balke and Fomby (1997) and Enders and Siklos (2001). And for the latter, there is already an EViews add-in available at: http://forums.eviews.com/viewtopic.php?f=23&t=5604

Trubador,

Many thanks for your reply.

As you can see from the below image, it would be interesting to see if there has been a change in the cointegrating relationship in the second half of the series!



Although it's not my main goal to investigating asymmetry in the adjustment toward equilibrium, I found your recommended reading on the topic very interesting, and so generated an output using the add-in you kindly linked me to. Forgive me if I am wrong, but there did not appear to be a read me file in the download - would this be the correct way of interpreting the output? Above the threshold, 15.61% of the disequilibrium is corrected per period. Below the threshold, 17.96% of the disequilibrium is corrected per period. In other words, there is a tendency for disequilibrium in the cointegrating relation to be corrected more quickly when it is below the threshold rather than above it. The high value of phi suggests that this asymmetry is statistically significant.



In addition to the asymmetric correction, I would also like to find out if the cointegrating relation in the first image has deteriorated post-1999.
The output of the SETAR model which I was trying to use for this purpose is as follows:



Is this the appropriate way of going about seeing if the cointegrating relationship has changed?

Note that the year 2000 is (roughly) the midpoint of my data.

70 observations lie below the -0.0472 threshold. Of these 70 observations, 63 (90%) occur on or after January 2000!
31 observations lie above the 0.07987028 threshold. Of these 31 observations, 23 (75%) on or occur after January 2000.
302 observations lie between the two thresholds. Of these 302 observations, 107 (35%) occur on or after January 2000.

Thank you for your time, it is very much appreciated!

[trubador]

As you can see from the below image, it would be interesting to see if there has been a change in the cointegrating relationship in the second half of the series!

That requires a breakpoint not a threshold analysis, though. You can try Gregory-Hansen Cointegration Test.

Although it's not my main goal to investigating asymmetry in the adjustment toward equilibrium, I found your recommended reading on the topic very interesting, and so generated an output using the add-in you kindly linked me to. Forgive me if I am wrong, but there did not appear to be a read me file in the download - would this be the correct way of interpreting the output? Above the threshold, 15.61% of the disequilibrium is corrected per period. Below the threshold, 17.96% of the disequilibrium is corrected per period. In other words, there is a tendency for disequilibrium in the cointegrating relation to be corrected more quickly when it is below the threshold rather than above it. The high value of phi suggests that this asymmetry is statistically significant

Your interpretation about the adjustment parameters are correct. However, you cannot comment on their significance unless you simulate for critical values. F-equal is the test statistic of null hypothesis of Above=Below, whereas F-joint is the test statistic of Above=Below=0. And T-max is used to test the null of no cointegration.

[EViewsbrah]

That requires a breakpoint not a threshold analysis, though. You can try Gregory-Hansen Cointegration Test.

Trubador,

Thank you once again for pointing me in the right direction!

My last few questions are as follows:

1) If I am interested in testing for a regime shift in the cointegration relation between Brent and WTI, am I correct in thinking that I should specify the dependent variable as Brent and the independent as WTI in the Gregory-Hansen Cointegration Test code? In other words, I do not store the cointegrating relation that I am trying to test as a series, and then use that as the dependent.

2) Since the estimated Za-stat (-126.99) is in excess of the 1% significance regime shift scenario critical value in Gregory and Hansen (1996) (-57.17), I can reject the null of no cointegration in favour of the alternative; that there is a regime shifting cointegrating relation with a breakpoint at 2010M10.

3) Is the insignificance of "@TREND>347-2" and "(@TREND>347-2)*LOG_WTI" a cause for concern? When I run the Gregory-Hansen Cointegration Test for the other scenarios (level shift and level shift with trend) all of the coefficients are highly significant (P=0.00 for all). Note that the breakpoint remains 2010M10 for every scenario.

Please see the image below for further details.

Thank you very much for your time.

[trubador]

Your implementation of the model and reading of the output are correct. Insignificance of those results are quite probably due to high correlation among them (as expected), so you do not have to worry. Just use the first part of the test results (i.e. ADF Procedure) when deciding the breakpoint as Phillips Procedure is not that much recommended in practice.

You may also be interested in the way of handling the breakpoints in this example: http://davegiles.blogspot.com.tr/2015/0 ... ews-9.html

[EViewsbrah]

Your interpretation about the adjustment parameters are correct. However, you cannot comment on their significance unless you simulate for critical values. F-equal is the test statistic of null hypothesis of Above=Below, whereas F-joint is the test statistic of Above=Below=0. And T-max is used to test the null of no cointegration.

Trubador,

Many thanks for your help! I am now 7,000 words into my 10,000 word report.

Before I write up the last section could you please clarify how to interpret the results of ρ1=ρ2=0 and ρ1=ρ2 in the Enders and Siklos (2001) threshold cointegration method? For my data, I can reject null hypothesis ρ1=ρ2=0 at the 1% level of significance based on the simulated critical values. I cannot however, reject the null of ρ1=ρ2.

To me, the fact that I can reject that ρ1=ρ2=0 but not reject that ρ1=ρ2 is slightly counter intuitive in terms of commenting on the asymmetry of adjustment. Which of these two tests should I listen to? Presumably, the fact that I cannot reject ρ1=ρ2 means that I must conclude that there is no evidence of asymmetric adjustment. If this is the case, then all the test of ρ1=ρ2=0 must tell me is that my adjustment parameters are both non-zero? For further details, I have attached an image of the test output below.

Many thanks for your time.

[trubador]

It is perfectly normal to have a cointegrating relationship with a symmetric adjustment. Since you have tested for asymmetry and concluded otherwise, now you can continue your analysis with good old cointegration models if you like.