ZIVOT Procedure

@ZIVOT implements the Zivot-Andrews(1992) unit root test, allowing for a single break in the intercept, the trend or both.

The @LPUNIT procedure generalizes this to more than one break. The @LSUnit procedure offers an alternative LM testing procedure with one or more breaks.

@Zivot( 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. By default, the defined range of series.

Options

BREAK=[INTERCEPT]/TREND/BOTH

Selects which variables are allowed to have a break

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

Selects the method for deciding the number of additional lags. (You can also use the older CRIT=... with the same choices). 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 GTOS (general-to-specific) or TTEST (they're equivalent), the number of lags for which the last included lag has a marginal significance level less than the cutoff given by the SIGNIF option.

PI=fraction of data range to skip at either end when examining possible break points [.15]

LAGS=number of additional lags (METHOD=INPUT)

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

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

SMPL=standard SMPL option [not used]

GRAPH/[NOGRAPH]

GRAPH requests a graph of the unit-root statistics with the different break points.

[PRINT]/NOPRINT

TITLE=title for report ["Zivot-Andrews Unit Root Test, Series ..."]

Variables Defined

%CDSTAT	unit root test statistic (REAL)
%%BREAKPOINT	entry at which %CDSTAT is achieved (REAL)
%%AUTOP	number of augmenting lags used (INTEGER)

Example

This test for a unit root allowing for one simultaneous break in both the level and trend rate, with a maximum of eight augmenting lags with the number used chosen by general-to-specific pruning.

@zivot(break=both,maxlags=8,method=gtos) logwage

Sample Output

This is from the example above. The first part of this is the test information. The range of possible breaks is 1912:1 to 1960:1 (from the full range of 1902:1 to 1970:1)—the distance from either end that is excluded from the search is controlled by the PI option. GTOS picks 1 lag (on the difference) when we allowed for up to 8. The null is for a unit root, so at the .05 level we would reject that in favor of a process stationary around a broken trend. Note well that this does not mean that the process is best described as a stationary process around a broken trend (that confuses the null and the alternative), nor does it mean that if it has a broken trend, that 1940:1 is the best estimate of the break location—1940:1 is chosen to be least favorable to the null hypothesis, not to be the best description of the data. All that this shows is that the data do not appear to have a unit root.

Zivot-Andrews Unit Root Test, Series LOGWAGE

Allowing for Break in both Intercept and Trend

Breaks Tested for 1912:01 to 1960:01

With 1 lags chosen from 8

Selected by GTOS/t-tests(0.10)

Sig Level Crit Value

1%(**) -5.57000

5%(*) -5.08000

Breakpoint TestStat

1940:01 -5.12833*

Linear Regression - Estimation by Zivot-Andrews---Selected Regression

Dependent Variable DY

Annual Data From 1902:01 To 1970:01

Usable Observations 69

Degrees of Freedom 63

Centered R^2 0.3506687

R-Bar^2 0.2991345

Uncentered R^2 0.4747088

Mean of Dependent Variable 0.0178571548

Std Error of Dependent Variable 0.0370170270

Standard Error of Estimate 0.0309898071

Sum of Squared Residuals 0.0605031932

Regression F(5,63) 6.8046

Significance Level of F 0.0000394

Log Likelihood 144.9445

Durbin-Watson Statistic 2.0902

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. LOGWAGE{1} -0.454974141 0.088717722 -5.12833 0.00000301

2. Constant 1.146973940 0.225925326 5.07678 0.00000365

3. TREND 0.006433816 0.001269354 5.06857 0.00000376

4. DY{1} 0.338999737 0.111067388 3.05220 0.00332416

5. D(1940:01) 0.075369271 0.018973313 3.97238 0.00018549

6. DT(1940:01) 0.002995382 0.001161852 2.57811 0.01228433