UNITROOT.RPF

UNITROOT.RPF has examples of unit root testing, including Dickey-Fuller (@DFUNIT), Phillips-Perron (@PPUNIT), Schmidt-Phillips (@SPUNIT), KPSS (@KPSS) and ERS (@ERSTEST). In practice, one would pick at most two of these tests, but for illustration, we include all of them.

If you're looking for unit root tests allowing for breaks, see UNITROOTBREAK.RPF.

This is adapted from Hamilton(1994), examples from Chapter 17.

Full Program

cal(q) 1947
open data gnptbill.txt
data(format=prn,org=obs) 1947:1 1989:1
*
set lgnp = 100.0*log(gnp)
*
* Dickey-Fuller tests (T-bills)
*
@dfunit(det=constant) tbill
@dfunit(det=constant,maxlags=6,method=gtos) tbill
@dfunit(det=constant,maxlags=6,method=aic) tbill
*
* Dickey-Fuller tests (log GNP)
*
@dfunit(det=trend) lgnp
@dfunit(det=trend,maxlags=6,method=gtos) lgnp
@dfunit(det=trend,maxlags=6,method=aic) lgnp
*
* Phillips-Perron tests
*
@ppunit(det=constant,lags=12,table) tbill
@ppunit(det=trend,lags=12,table) lgnp
*
* Schmidt-Phillips tests
*
@spunit(p=1,lags=12) tbill
@spunit(p=1,lags=12) lgnp
*
* ERS tests
*
@erstest(det=trend,lags=12) lgnp
*
* KPSS tests
*
@kpss(det=constant,lmax=12) tbill
@kpss(det=trend,lmax=12) lgnp

Output

All of the tests point to acceptance of a unit root in both series tested. (KPSS has a null of stationarity, so it rejecting stationarity is compatible with the other results). The only test which has a somewhat ambiguous result is the Schmidt-Phillips on the T-Bill series, which is around the 5% level.

Dickey-Fuller Unit Root Test, Series TBILL

Regression Run From 1947:02 to 1989:01

Observations 169

With intercept

Using fixed lags 0

Null is unit root. Reject in left tail.

Sig Level Crit Value

1%(**) -3.47002

5%(*) -2.87859

10% -2.57577

T-Statistic -1.72945

Dickey-Fuller Unit Root Test, Series TBILL

Regression Run From 1948:04 to 1989:01

Observations 163

With intercept

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

Null is unit root. Reject in left tail.

Sig Level Crit Value

1%(**) -3.47140

5%(*) -2.87921

10% -2.57609

T-Statistic -1.70800

Dickey-Fuller Unit Root Test, Series TBILL

Regression Run From 1948:04 to 1989:01

Observations 163

With intercept

With 6 lags chosen from 6 by AIC

Null is unit root. Reject in left tail.

Sig Level Crit Value

1%(**) -3.47140

5%(*) -2.87921

10% -2.57609

T-Statistic -1.70800

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

Phillips-Perron Test for a Unit Root for TBILL

Regression Run From 1947:02 to 1989:01

Observations 168

With intercept

Null is unit root. Reject in left tail.

Sig Level Crit Value

1%(**) -3.47002

5%(*) -2.87859

10% -2.57577

Lags Statistic

0 -1.73984

1 -1.86648

2 -1.78961

3 -1.78634

4 -1.80563

5 -1.83592

6 -1.85085

7 -1.80795

8 -1.77327

9 -1.76985

10 -1.75947

11 -1.73244

12 -1.70691

Phillips-Perron Test for a Unit Root for LGNP

Regression Run From 1947:02 to 1989:01

Observations 168

With intercept and trend

Null is unit root. Reject in left tail.

Sig Level Crit Value

1%(**) -4.01489

5%(*) -3.43712

10% -3.14247

Lags Statistic

0 -1.95898

1 -2.18369

2 -2.34662

3 -2.42578

4 -2.45203

5 -2.44927

6 -2.43843

7 -2.42781

8 -2.40975

9 -2.38650

10 -2.36745

11 -2.34807

12 -2.32257

Schmidt-Phillips Test (TAU) for a Unit Root in TBILL

Regression Run From 1947:02 to 1989:01

Observations 168

Null of unit root. Reject in left tail.

Signif. Level Critical Value

1%(**) -3.610

2.5% -3.300

5%(*) -3.040

10% -2.760

LM Test Auxiliary Regression

Variable Coefficient T-Stat

SBAR{1} -0.09399 -2.861

Constant 0.09187 1.469

Semiparametric Corrections for TAU

Bartlett Window Estimates of sigma^2

Schwert value of L4 =4, L12=13

Lags Sigma^2 tau

0 0.611220 -2.861

1 0.736752 -3.141*

2 0.688609 -3.037

3 0.701993 -3.066*

4 0.732948 -3.133*

5 0.771827 -3.215*

6 0.795973 -3.265*

7 0.768943 -3.209*

8 0.748042 -3.165*

9 0.751997 -3.174*

10 0.748943 -3.167*

11 0.731061 -3.129*

12 0.713412 -3.091*

Schmidt-Phillips Test (TAU) for a Unit Root in LGNP

Regression Run From 1947:02 to 1989:01

Observations 168

Null of unit root. Reject in left tail.

Signif. Level Critical Value

1%(**) -3.610

2.5% -3.300

5%(*) -3.040

10% -2.760

LM Test Auxiliary Regression

Variable Coefficient T-Stat

SBAR{1} -0.02927 -1.570

Constant 0.93251 8.112

Semiparametric Corrections for TAU

Bartlett Window Estimates of sigma^2

Schwert value of L4 =4, L12=13

Lags Sigma^2 tau

0 1.152130 -1.570

1 1.587814 -1.843

2 1.931105 -2.033

3 2.110782 -2.125

4 2.178638 -2.159

5 2.183142 -2.161

6 2.170572 -2.155

7 2.159320 -2.150

8 2.133469 -2.137

9 2.098492 -2.119

10 2.074358 -2.107

11 2.051445 -2.095

12 2.016410 -2.077

DF-GLS Tests, Dependent Variable LGNP

From 1947:01 to 1989:01

Lag Length Chosen from 12 by User Input

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 12.800 3.96 4.78 5.62 6.89

DFGLS -1.447 12 -3.48 -3.15 -2.89 -2.57

Elliott (IER 1999)

QT 4.157 2.05 2.44 3.15 3.44

DFGLSu -2.135 12 -3.71 -3.41 -3.17 -2.91

KPSS Test for Stationarity, Series TBILL

From 1947:01 to 1989:01

Observations 169

Null is Stationary about Level. Reject for large values.

Sig Level Crit Value

1%(**) 0.739

2.5% 0.574

5%(*) 0.463

10% 0.347

Lags TestStat

0 12.347**

1 6.301**

2 4.278**

3 3.258**

4 2.644**

5 2.234**

6 1.942**

7 1.724**

8 1.554**

9 1.417**

10 1.305**

11 1.211**

12 1.132**

KPSS Test for Stationarity, Series LGNP

From 1947:01 to 1989:01

Observations 169

Null is Stationary about Trend. Reject for large values.

Sig Level Crit Value

1%(**) 0.216

2.5% 0.176

5%(*) 0.146

10% 0.119

Lags TestStat

0 2.002**

1 1.021**

2 0.695**

3 0.534**

4 0.438**

5 0.375**

6 0.331**

7 0.297**

8 0.272**

9 0.251**

10 0.235**

11 0.222**

12 0.211*