@DFUnit performs an (augmented) Dickey-Fuller unit root test. This estimates the following (or the same without the intercept and trend, depending upon the choice of the deterministics):
 

\(\Delta {y_t} = \alpha  + \beta t + \left( {\rho  - 1} \right){y_{t - 1}} + \sum\limits_{j = 1}^p {{\varphi _j}\Delta {y_{t - j}}}  + {u_t}\)

 

and tests for \(\left( {\rho  - 1} \right) = 0 \). The number of augmenting lags (\(p\)) is to be chosen to make the residuals serially uncorrelated. This can be input directly, or you can allow it to be chosen automatically using one of several methods. The @ADFAutoSelect procedure can be used if you want to look more broadly at the effect of lag lengths on the Dickey-Fuller test statistic.

 

This is used in quite a few examples, but UNITROOT.RPF includes this and quite a few other unit-root testing procedures.

 

@DFUNIT( options )   series  start end

Wizards

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

Parameters

Options for Selecting Lags

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).
 

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

Other Options

DET=NONE/[CONSTANT]/TREND

Choose what deterministic components to include.
 

[TTEST]/NOTTEST

Computes the regression t test, as opposed to the T(rho-1) test.

 

[PRINT]/NOPRINT

TITLE=Title for output ["Dickey-Fuller Unit Root Test, Series xxxx"]

Variables Defined

Example

This is part of unitroot.rpf. LGNP is log GNP, which has an apparent trend (thus the use of DET=TREND). The first of these will do the test using no augmenting lags, the second and third choosing the number of augmenting lags from a maximum of 6, the first by general-to-specific pruning, the second by minimum AIC.
 

@dfunit(det=trend) lgnp

@dfunit(det=trend,maxlags=6,method=gtos) lgnp

@dfunit(det=trend,maxlags=6,method=aic) lgnp

Output

The output from the three is very similar other than the description of how lags are selected. The null is a unit root, which is rejected in the left tail (for large negative values). With the two augmenting lags chosen automatically by both criteria, the test statistic is only slightly above the 10% critical value.

 

Dickey-Fuller Unit Root Test, Series LGNP

Regression Run From 1947:02 to 1989:01

Observations        169

With intercept and trend

Using fixed lags 0

Null is unit root. Reject in left tail.

 

Sig Level    Crit Value

1%(**)         -4.01489

5%(*)          -3.43712

10%            -3.14247

 

T-Statistic    -1.94141

 

Dickey-Fuller Unit Root Test, Series LGNP

Regression Run From 1947:04 to 1989:01

Observations        167

With intercept and trend

With 2 lags chosen from 6 by GTOS/t-tests(0.100)

Null is unit root. Reject in left tail.

 

Sig Level    Crit Value

1%(**)         -4.01552

5%(*)          -3.43742

10%            -3.14265

 

T-Statistic    -3.13012

 

Dickey-Fuller Unit Root Test, Series LGNP

Regression Run From 1947:04 to 1989:01

Observations        167

With intercept and trend

With 2 lags chosen from 6 by AIC

Null is unit root. Reject in left tail.

 

Sig Level    Crit Value

1%(**)         -4.01552

5%(*)          -3.43742

10%            -3.14265

 

T-Statistic    -3.13012

 

Copyright © 2025 Thomas A. Doan