@ERSTEST performs Elliott, Rothenberg and Stock(1996) unit root tests. These are two-step testing procedures, where the data are first de-meaned or de-trended using GLS, then a unit root test is applied to the result. A separate procedure for doing just the detrending is available as @GLSDETREND. It also does the related tests with a different treatment of the initial observation from Elliott(1999).

@ERSTEST( options )   series  start end

Wizards

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

Parameters

Options

DET=NONE/[CONSTANT]/TREND

Deterministic part (TREND uses (1,t))

CBAR=(positive) value of c-bar to use [based upon choice for DET]

The GLS filter is \((1 - \bar cL)\). Although this is provided as an option (for possible experimentation), you shouldn't really use it, as the critical values for the test statistic change with different values.

 

LAGS=number of additional lags [0]

MAXLAGS=maximum number of additional lags to consider [number of observations^.25]

You can use either of these to select the (maximum) number of additional lags. If you don't use either option, the LAGS default of 0 will be used for METHOD=INPUT and the MAXLAGS default will be used for the others.

 

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

METHOD=INPUT uses the input number of LAGS only. METHOD=AIC/BIC (or SBC)/HQ/MAIC test the D-F regressions for everything from 0 to LAGS/MAXLAGS and chooses the minimizer for the chosen criterion. MAIC is the version of AIC modified for unit root testing from Ng and Perron(2001). METHOD=TTEST/GTOS starts with the full set of lags and deletes lags as long as the final one has a marginal significance level less than the cutoff given by the SIGNIF option. (GTOS is short for General-TO-Specific).

 

Note that there are two sets of tests: one for each assumption regarding the initial observation, and those can choose different lag lengths if you use one of the automatic lag length choice methods.

 

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

 

PRINT/[NOPRINT]

TITLE="title of report" ["DF-GLS Tests, Series xxxx"]

Variables Defined

The first two of these are from the original ERS paper; the third and fourth are from Elliott(1999).

 

Example

This does a test allowing for a trend in the data, choosing lags from up to 12 using AIC.

 

@erstest(det=trend,maxlags=12,method=aic) lgnp

 

Sample Output

The first two tests in the output are from Elliott, Rothenberg and Stock(1996) which assume a zero pre-sample residual and the last two are from Elliott(1999) which assumes the pre-sample residual is drawn from its unconditional distribution. As you can see, the values can be quite different even with 169 (quarterly) observations (as seen in the critical values, the U statistics tend to be more smaller numerically), though part of that is due to the lag length choice being different (3 for the first set, 2 for the second). If you fix a certain number of lags (either 2 or 3), (same instruction with LAGS=2 or LAGS=3 option without the METHOD option) the results are qualitatively similar.

 

DF-GLS Tests, Dependent Variable LGNP

From 1947:01 to 1989:01

Lag Length Chosen from 12 by AIC

Detrend = constant and linear time trend, z(t)=(1,t)

Tests for a unit root null. All tests reject null in lower tail

                       Critical values (asymptotic)

Elliott et al (1996 Econometrica)

          Stat    Lags  1%(**)    2.5%    5%(*)     10%

PT          9.839          3.96     4.78     5.62     6.89

DFGLS      -2.014    3    -3.48    -3.15    -2.89    -2.57

Elliott (IER 1999)

QT          3.179          2.05     2.44     3.15     3.44

DFGLSu     -2.957    2    -3.71    -3.41    -3.17    -2.91

 

Copyright © 2025 Thomas A. Doan