LSUnit—Lee-Strazicich unit root test with multiple breaks

[TomDoan]

@LSUNIT implements a variety of LM unit root tests allowing for 0, 1, 2 or even more structural breaks of one of two varieties, as described in Lee and Strazicich(2003), "Minimum LM Unit Root Test with Two Structural Breaks," Review of Economics and Statistics, vol 85, no. 4, pp 1082-1089. This has been updated to include critical values (for 0, 1 and 2 breaks) interpolated out of greatly expanded lookup tables.

Note that this can take a very long time for two or more breaks if the data set is large (>500 observations). The calculation time goes up with T^(# of breaks+1), so with 1000 data points, you're looking at roughly 1000 times as long to do two breaks as one. We've added a THIN option to reduce the number of break points examined---for a two break model, for instance, THIN=5 will reduce the length of time by a factor of roughly 25.

Detailed Description

[prakash]

Hello all, can any one let me know that is it possible to test more than two structural break in the series, using LM test, if yes than what are the critical values for it at 1, 5 and 10 % level os significance.

[TomDoan]

Hello all, can any one let me know that is it possible to test more than two structural break in the series, using LM test, if yes than what are the critical values for it at 1, 5 and 10 % level os significance.

I allowed for more than two breaks in programming the LS test since there was no added complexity to doing that. To my knowledge, no one has ever actually looked at the behavior of the test with three or more breaks, and I'm not sure it would be particularly interesting. Once the trend is so broken up, it's not likely to show the level of persistence that would give a false signal of unit-root-ness.

[trangan_20142011]

Hi Tom Doan,
Thank you for your reply.
In the results for model C, there are two calculated values for D(11) and DT(11). What t-statistics (for D(11) or DT(11)) should I use to compare with the the critical value? I ask this because Model C for both intercept and trend stationary. In my study, there is little statistically significant breaks, is there any problem for this?
Many thanks.

[TomDoan]

Hi Tom Doan,
Thank you for your reply.
In the results for model C, there are two calculated values for D(11) and DT(11). What t-statistics (for D(11) or DT(11)) should I use to compare with the the critical value?

Neither. The test statistic is the t-stat on S{1}.

I ask this because Model C for both intercept and trend stationary. In my study, there is little statistically significant breaks, is there any problem for this?

No. Read carefully section 11.6 of the User's Guide, particularly the second paragraph.

[trangan_20142011]

Dear Tom Doan,

I read the citation that Doan (2000) recommends against differencing even if the variable contains a unit root because it throws away in information concerning the co-movements of variables. Could you explain it for me? If it is right, why do we need to test unit root?

Thank you very much.

[TomDoan]

Dear Tom Doan,

I read the citation that Doan (2000) recommends against differencing even if the variable contains a unit root because it throws away in information concerning the co-movements of variables. Could you explain it for me?

That's specifically in the context of a VAR, and that's not all that controversial---if there is cointegration, then a VAR estimated in differences is misspecified.

If it is right, why do we need to test unit root?

Because referees insist upon it. That's not intended to be flip. That's reality.

[upani]

Hi All,

I have used the following command to test the structural break in my data set. I suspect one structural break as there is a presence of Financial crisis during my sample period. I have run the following command as suggested by Tom Doan in his following post. http://www.estima.com/forum/viewtopic.php?t=126
After i run the command i got the following output as follows;

• @lsunit(breaks=1,pi=.10,lags=2,method=gtos,model=break) LFP
  
  Lee-Strazicich Unit Root Test, Series LFP
  Regression Run From 4 to 2359
  Observations 2356
  Trend Break Model with 1 breaks
  With 0 lags chosen from 2
  
  Variable Coefficient T-Stat
  S{1} -0.0084 -3.1518
  Constant 0.0014 1.9925
  D(840) -0.0479 -3.5107
  DT(840) -0.0005 -0.7756

How to interpret the result. Does it mean that there is a structural break at the 840 data point. Am i making any wrong inference? Why it has not taken any lag although i have mentioned 2 lag. Is there any possibility to include dummy variable to check the change in intercept and slope around the date the test is showing ? How to include the dummies in intercept and dummy in slope on the point of structural break to confirm whether the date it is suggesting is correct or not.

With regards,
Upananda

[TomDoan]

The LS test (and those like it) is a test for a unit root in the presence of a (possible) structural break. It is not a test for a structural break itself. The breakpoint(s) are chosen to make the t-stat on the lagged dependent variable as significant as possible, not to locate the biggest break. Your conclusion is that the series seems to have a unit root even if you allow for a trend break.

You allowed for up to 2 lags and it chose 0. There's always the one lag for the test, so there are no added lags on the difference.

The dummy for a trend break can be done using the DUMMY instruction with

set dt = %max(t-t0,0)

where t0 is the period where you want the trend rate to change. Note, however, that the LS test uses an LM setup, so the "model" can't be estimated by a single linear regression. Instead, it does a de-trending regression followed by a unit root test on the detrended data.

[zw83189]

hello, i have a VAR model with some exogenous variables and using daily data (7days a week).For two of the exogenous variables, I used lee strazicich unit root test with one structural break which allows for both intercept and trend. And the test-statistics are 5% significant. Now I am trying to estimate my VARX model with consideration of dummy variables. But I am not sure how to input my two dummy variables (intercept dummy and slope dummy) into my model on RATS. I just started learning RATS last week. Could you please help me with this? Thanks in advance!

[TomDoan]

First of all, you're making a common error of misinterpreting the tests. See the thread

https://estima.com/forum/viewtopic.php?f=5&t=1766

Second, if the "breaks" (not that you've actually estimated breaks) are in the exogenous variables, you don't need to do anything.

[zw83189]

Thanks for your reply! Just to confirm that, So now I have rejected the null hypothesis, so that i can conclude there is no unit root if i allow for a structural break at 5% significant level?
the series from exogenous variables are then stationary, so i do not need to add any dummy variables into my model and treat these series as stationary series?

[TomDoan]

You don't need dummy variables, and you don't need to treat the series as stationary anyway. There is no compelling reason to even do the unit root test (with or without breaks) before using the series in a VAR. See the question and answer at https://estima.com/forum/viewtopic.php?p=7088#p7088.

[alexecon]

How does the procedure treat NA's? I still get output even though there are missing observations in the series under test. Thank you.

[TomDoan]

It's not designed to handle embedded missing values. It looks like it will cut off the "STILDE" at the first NA so it might give you output, but is only really analyzing part of the sample.