PPUNIT Procedure

@PPUNIT computes one of the Phillips-Perron(1988) modifications to the Dickey-Fuller unit root tests. This estimates the following (or the same without the intercept and trend, depending upon the choice of the deterministics)

\(\Delta {y_t} = \alpha + \beta t + \left( {\rho - 1} \right){y_{t - 1}} + {v_t}\)

and tests for \(\left( {\rho - 1} \right) = 0 \) with a semi-parametric correction for possible serial correlation in the residuals \({v_t}\). This correction requires an estimate of the long-run variance of \(v\), which is done using a Bartlett (Newey-West) estimator. The number of lags used in that is governed by the LAGS option, or you can do a sensitivity table which shows how the test statistic varies with the number of lags.

An example of the use of @PPUNIT and several other unit root tests is unitroot.rpf.

@PPUNIT( options ) series start end

Wizards

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

Parameters

series	series to analyze
start end	range of series to use (not range over which test is run). By default, the defined range of series.

Options

DET=[CONSTANT]/TREND

Choose what deterministic components to include.

[TTEST]/NOTTEST

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

LAGS=number of lags in long-run variance estimation [4]

TABLE/[NOTABLE]

If TABLE, shows a sensitivity table (for all lags 0 to LAGS)

[PRINT]/NOPRINT

TITLE=Title for output ["Phillips-Perron Test for a Unit Root for xxxx"]

Variables Defined

%NOBS	number of regression observations + 1 (tables are based upon this) (INTEGER)
%RHO	the lag coefficient (REAL)
%CDSTAT	test statistic (for the full number of lags) (REAL)

Example

This is an example of the use of the procedure out of UNITROOT.RPF. It does a Phillips-Perron test allowing for trend, doing a sensitivity table with up to 12 lags.

@ppunit(det=trend,lags=12,table) lgnp

Sample Output

This is the output from the example. The test statistics generally stabilize once an adequate number of lags has been reached; here in the range of around -2.4, which is well short of the critical values. So you would not, on this evidence, reject the unit root.

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