@LPUNIT implements the Lumsdaine-Papell(1997) unit root test, allowing for two breaks in the intercept, the trend or both at unknown locations. The procedure actually allows for any number of breaks from 0 up. 1 break is the Zivot-Andrews test; the default of 2 is the LP test. The base model is

 

\(\Delta {y_t} = a + bt + \rho {y_{t - 1}} + \sum\limits_i {{a_i}\Delta {y_{t - i}}} \)

 

The break variables are \(c{\rm{ }}I\left( {t > TB} \right)\) or \(d\max (0,t - TB)\) or both, where the break point(s) \(TB\) are unknown and determined by finding the minimum value for the t-statistic for \(\rho  = 0\), which is the value least favorable to the null hypothesis of a unit root. The number of lags of \(\Delta y\) included can either be input, or can be selected automatically using AIC, BIC or general-to-specific pruning by t-tests. All of the automatic lag selections are applied to the base model.

 

This point of this (and similar) tests is widely misunderstood. See Unit Roots and Breaks.

 

The @LSUNIT procedure offers an alternative multiple-break test for unit roots using a slightly different set of hypotheses.

 

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.

 

@LPUNIT and other similar procedures are used in the UNITROOTBREAK.RPF example to test for unit roots.

 

@LPUNIT( options )   series start end

Wizards

This is included as one of the tests in the Time Series>Unit Root Test Wizard.

Parameters

Options

BREAK=[INTERCEPT]/TREND/BOTH

Selects which variables are allowed to have a break

 

NBREAKS=0/1/[2](actually can be any positive integer)

 

METHOD=[INPUT]/AIC/BIC/HQ/TTEST/GTOS

Selects the method for deciding the number of additional lags. If INPUT, the number of lags given by the MAXLAGS option is used. If AIC, the AIC-minimizing value between 0 and MAXLAGS is used; if BIC, it's the BIC-minimizing value, and if TTEST or GTOS (they are identical) the number of lags for which the last included lag has a marginal significance level less than the cutoff given by the SIGNIF option.

 

LAGS=number of additional lags (METHOD=INPUT)

MAXLAGS=number of additional lags (METHOD=INPUT) or the maximum number of lags to consider (other METHOD's) [number of observations^.25]

SIGNIF=cutoff significance level for METHOD=TTEST or GTOS[.10]
 

SMPL=standard SMPL option [unused]

 

PI=fraction of entries on each end of data to exclude as break points, and minimum gap between breakpoints [.10]

 

[PRINT]/NOPRINT

TITLE=title for report ["Lumsdaine-Papell Unit Root Test, Series ..."]

Variables Defined

Example

This does a test for unit roots allowing for two breaks (the default) in the trend rate. (That is, the trend changes the rate of growth, but doesn't have a sudden change in the level at the break points). It allows for up to six augmenting lags, selected by minimum AIC. That's selected separately for each combination of two break points, so this will run quite a few regressions.

 

@lpunit(break=trend,maxlags=6,method=aic) lgdp

Sample Output

The test statistic is the t-Stat on Y{1}. This shows the location of the pair of breaks which generates the most negative t-statistic (at 1968:01 and 2003:02). Note that the critical values are quite large (negative) relative to a non-breaking test so despite a -4.6 t-statistic, the unit root is not rejected.

 

Lumsdaine-Papell Unit Root Test, Series LGDP

Regression Run From 1948:02 to 2012:04

Observations         260

Breaks in Trend Only

Breaks at 1968:01 2003:02

With 3 lags chosen from 6

Selected by AIC

Sig Level    Crit Value

1%(**)           -7.1900

5%(*)            -6.6200

10%              -6.3700

 

Variable     Coefficient T-Stat

Y{1}             -0.0976 -4.5843

DT(1968:01)      -0.0002 -3.2389

DT(2003:02)      -0.0005 -3.8849

Constant          0.7322  4.6273

Trend             0.0009  4.4866

 

Copyright © 2026 Thomas A. Doan