PERRONBREAKS—Unit Roots with Structural Breaks

[TomDoan]

@PERRONBREAKS is a procedure for a very general approach to handling unit root tests allowing for structural breaks. It is based upon the set of models in Perron(2006), "Dealing with Structural Breaks," in Palgrave Handbook of Econometrics, Vol. 1, pp 278-352, but with extension to allow more than one break. An example of its use with one and two breaks is provided at http://www.estima.com/forum/viewtopic.php?f=8&t=1215.

Detailed description

[caromax]

When @Perronbreaks gives the optimal breaks, do I have to add to that number(suppose my data goes from 1 to 800 and break is found on 38) the number from which the program start the regressions, let's day it regress from observation 13 to 800) so I need to add 13+38 for the final break ,or the break date the procedure gives is the final one?
Thanks

[TomDoan]

When @Perronbreaks gives the optimal breaks, do I have to add to that number(suppose my data goes from 1 to 800 and break is found on 38) the number from which the program start the regressions, let's day it regress from observation 13 to 800) so I need to add 13+38 for the final break ,or the break date the procedure gives is the final one?
Thanks

The break points are relative to the start of the data set, not to the start of the regression. So 38 means 38.

[caromax]

Can you explain me which regression the prog runs when its doing AO=Mean?
I use the porgram to test for 3 breaks and 13 lags.The program finds 3 optimal lags but when I run the regression as...
delta.y= mean l1.y delta.y (1 to optimal lag in perronbreaks) d1 d2 d3 (where d1,2,3 are the breaks) I can not find the same coeffcient or t-stastic that the programs gives.
Moreover, in my series that goes form 1 to 161, the program runs the regression from 15 to 161 but the number of observations used is 157, when I test for 13 lags and 2 breaks regression is still 15 to 161 but observations go down to 151..what does this means?

[TomDoan]

You'll have to read Perron's paper. Additive outliers produce very complicated dynamic models because they don't simplify easily when you difference or filter them.

[unitroot]

I have the following output from the @PERRONBREAKS procedure:
#############################################################
Unit Root Test, Series LFP
Regression Run From 1987:02 to 2013:02
Observations 323
IO Model: Crash with 1 breaks
With 2 lags chosen from 12
Selection by AIC

Variable Coefficient T-Stat
Y{1} -0.049432 -4.882039

Break point(s)
2010:05
#############################################################
How to get the critical values or p-values for inference on the null hypothesis of unit root?
Thanks

[TomDoan]

Per the Perron and Vogelsang program, for that test, the 1% cv is -5.151115, 5% is -4.643519 and 10% is -4.376293. (Not sure why those are shown to six decimal places---I be surprised if they are accurate even to three). So you're somewhere in the .03 significance level range.

[BinhPham]

Hi Tom,

Sorry for the silly question. Where I can find critical values of @PERRONBREAKS output? Could you please point out the paper which shows them?

Thank you very much!

[TomDoan]

For the one break model, they are in Perron and Vogelsang(1992), "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity", JBES, vol 10, no 3. This is probably more interesting for the observation that different ways of handling level shifts may be appropriate for different situations, rather than being a useful tool in empirical work.

[jhusein]

For the one break model, they are in Perron and Vogelsang(1992), "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity", JBES, vol 10, no 3. This is probably more interesting for the observation that different ways of handling level shifts may be appropriate for different situations, rather than being a useful tool in empirical work.

I know it is an old thread but how about what critical values to use for more than one break, i.e., two breaks! Thanks.

[TomDoan]

I don't believe they (Perron and Vogelsang) analyzed the two-break case. Given the complexity of the critical values for one break, a two break table would probably be 50 pages. To repeat the final sentence from the previous post: "This is probably more interesting for the observation that different ways of handling level shifts may be appropriate for different situations, rather than being a useful tool in empirical work."

[jhusein]

Thanks Tom.
For those interested:
The paper "Testing for a unit root in variables with a double change in the mean, Jesus Clemente, Antonio Montanes, Marcelo Reyes, Economics Letters, 1998" extended the analysis of Perron/Vogelsang to a double structural change in the mean.

The above paper is implemented in STATA (I did not find any other program implementing it and I am curious if anyone knows otherwise). Thanks.