GREGORYHANSEN—cointegration test with breaks

[TomDoan]

@GregoryHansen performs a cointegration test with structural breaks. It includes the model with a breaking trend in the cointegrating vector from Gregory and Hansen(1996), "Tests for Cointegration in Models with Regime and Trend Shifts," Oxford Bulletin of Economics and Statistics, vol. 58, no 3, pp 555-560 as well as the original models from Gregory and Hansen(1996), "Residual-based Tests for Cointegration in Models with Regime Shifts", Journal of Econometrics, vol 70, 99-126.

The cointegrating regression is allowed to have a trend or not, and can have either a break in the intercept only or a break in all coefficients. The break point t0 is unknown and determined by finding the minimum value for the ADF statistic on the residuals from the broken cointegration regression. The number of lags of the change in the residual used in computing the ADF statistic can either be input, or can be selected automatically using AIC, BIC or general-to-specific pruning by t-tests.

gregoryhansen.src

Detailed description


Example

Code: Select all

*
* Replication file for Gregory, Allan W. & Hansen, Bruce E., 1996.
* "Residual-based tests for cointegration in models with regime shifts,"
* Journal of Econometrics, vol. 70, no 1, 99-126.
*
* Example from Bruce Hansen's web site.
*
open data gregoryhansen.rat
calendar(q) 1959:1
*
* M1 and TBILLS are monthly data. M1 is compacted by quarterly averages,
* while TBILLS select the 3rd month of the quarter.
*
data(format=rats,compact=average) 1959:01 1990:04 nomnnp realnnp m1
data(format=rats,select=3)        1959:01 1990:04 tbills
*
set deflator = nomnnp/realnnp
set realm1   = m1/deflator
*
set logm1    = log(realm1)
set loginc   = log(realnnp)
*
@GregoryHansen(lag=6,method=ttest,det=constant,break=all,graph)
# logm1 loginc tbills

gregoryhansen.rat

Data file for example

(12 KiB) Downloaded 1774 times

[chiade]

Hi Tom,

Is there any inclusion using modified PP tests as the paper indicated? How do you incorporate it? Thanks again.

Des

[TomDoan]

Hi Tom,

Is there any inclusion using modified PP tests as the paper indicated? How do you incorporate it? Thanks again.

Des

It would require a completely different design from the main part of the loop. Instead of searching for a lag length for an ADF regression, you would do a PP test. However, PP tests are rarely used in applications like this (generally for very good reason).

[atarca]

Hi Tom,
Can you please explain what other co-integration procedures are supported by the options of the @GregoryHansen procedure and how can I obtain this new design?
Best Regards.

[TomDoan]

Hi Tom,
Can you please explain what other co-integration procedures are supported by the options of the @GregoryHansen procedure and how can I obtain this new design?
Best Regards.

There aren't any. It's basically Engle-Granger tests with various breaks. The previous poster asked about the variant from the paper that's based upon Phillips-Perron rather than ADF statistics, but this doesn't do that, and I wouldn't recommend it anyway.

[abi]

Code: Select all

Gregory-Hansen Cointegration Test
Variables
LOGM1
LOGINC
TBILLS
Full Structural Break. No Trend
With 6 lags chosen from 6 by GTOS/t-tests(0.100)
Minimum T-Statistic  -4.592
Achieved At         1976:02
1% Critical Value    -5.970
5% Critical Value    -5.500

Dear Tom,
I have two question
does H0 rejected in this example?
Gregory-Hansen Cointegration Test propose a suit of statics (ADF*, Zt* and Za*) could you tell me this example containing which one of them? and what should i do to include all of them?
Thanks,

[TomDoan]

H0 is accepted, that is, you do not reject the unit root, so you do reject cointegration. This is ADF*. The other tests are Phillips-Perron-based rather than ADF, and those are discussed above. We don't include them and I don't recommend them.

[Zankawa]

Dear Tom Doan,
I have a question regarding the Gregory-Hansen cointegration test. I tested a group of series for cointegration with structural break using the Gregory-Hansen method in RATS and I only obtained results for the ADF statistic. However, I also need the results for the z-scores, i.e. the two z-statistics which are also reported in the Gregory-Hansen's (1996) paper. I would be very glad if you could kindly assist me on how to obtain these results either in RATS or any econometrics software.
Thank you

[TomDoan]

Dear Tom Doan,
I have a question regarding the Gregory-Hansen cointegration test. I tested a group of series for cointegration with structural break using the Gregory-Hansen method in RATS and I only obtained results for the ADF statistic. However, I also need the results for the z-scores, i.e. the two z-statistics which are also reported in the Gregory-Hansen's (1996) paper. I would be very glad if you could kindly assist me on how to obtain these results either in RATS or any econometrics software.
Thank you

That's discussed above. The "Z" tests are based upon the Phillips-Perron tests which are almost never done any longer. Stick with the ADF-based tests.

[Zankawa]

Dear Tom Doan,
I am using the Gregory-Hansen cointegration test allowing for regime shifts to test for cointegration with structural breaks. In this test, there are three possible models which are model C, C/T, and C/S. I want to know how to set out the options in the RATS software in order to obtain the results for each of these models. There are two options to choose under the deterministic components which are (constant and linear trend). There are also two options to choose under type of break and these are (intercept only and full break). I am not sure how to choose the deterministic component and type of break options to obtain results for the three models (i.e. model C, C/T, and C/S) and I would be very grateful if you could assist me to do so.
Thank you

[TomDoan]

If you combine the two papers, there are four possibilities, not three, which is why the MODEL option has four choices. The one that wasn't in the original JOE paper is the combination of DET=TREND,BREAK=ALL or equivalently MODEL=FULLBREAK, which has a trending cointegrating vector and a break in all the coefficients (intercept, trend and cointegrating vector slope coefficients). You either use a combination of DET and BREAK options or the MODEL option, both of which will cover all four possibilities.

[fgamboes]

Dear Rats users

I am using the gregory and hansen cointegration test. When I use the following command I cannot get the critical values. Why is that? And how to get 10% critical values?

@gregoryhansen(MODEL=TREND, method=BIC, LAGS=6, PI=0.20, BREAK = ALL, NOGRAPH) 1 186
# RERCOP DIFRIRCOP DIFIPICOP DIFBSACOP LCDSCOP LRWTI

this is the output that I am getting

Gregory-Hansen Cointegration Test
Variables
RERCOP
DIFRIRCOP
DIFIPICOP
DIFBSACOP
LCDSCOP
LRWTI
Break in Intercept. Trend Included
With 0 lags chosen from 6 by BIC/SBC
Minimum T-Statistic -5.783
Achieved At 2006:02
1% Critical Value NA
5% Critical Value NA

[TomDoan]

The Gregory-Hansen papers don't include critical values for more than five endogenous variables (one left-side and four right).

[fgamboes]

Thanks a lot Tom

Is there any way to get 10% critical values for the ghansen procedure?

Thanks

[TomDoan]

I added the .10 critical values and rewrote much of the description. Go back to the top of the thread and download the new version from the link provided.

I asked Bruce Hansen about the m=4 limit. He is not aware of anyone who has extended that, and feels (as do I) that it probably makes little sense to try to isolate a single cointegrating vector on such a large set of variables---if there's cointegration, there's likely to be more than one cointegrating vector.