ZA_1br: Zivot-Andrews unit root test with unknown one structural...

In COINT: Unit Root Tests with Structural Breaks and Fully-Modified Estimators

Zivot-Andrews unit root test with unknown one structural break.

Description

This function implements Zivot-Andrews sequential ADF unit root test with unknown one structural break. Handling two outlier models: "Innovational outlier" and "Additive outlier".

Usage

ZA_1br(y,
      model=c("intercept", "trend", "both"),
      outlier=1,
      pmax=8,
      ic=c("AIC","BIC"),
      fixed=FALSE,
      trim=0.1,
      eq=1,
      season=FALSE)

Arguments

y	Univariate time series data, a preferable format is ts when season=TRUE.
model	Modelling where the unknown structural change occurs. intercept= structural change occurs at the intercept. trend= structural change occurs at the trend. both= structural changes occur at both the intercept and the trend.
outlier	The outlier model. 1=Innovational outlier model. 2=Additive outlier model.
pmax	The maximal lags that are either included in the test regression or lag selection searches its optimal lag via "ic".
ic	Information criteria, "AIC" or "BIC". The default is "AIC".
fixed	Logical. If TURE, pmax is the fixed inputed lags. If FALSE, pmax is the maximal lags where lag selection searches its optimal lag.
trim	The trimming percentage. Default is 10
eq	The type of dependent variable in ADF equation. 1= original y. 2= differenced y.
season	Logical. If TURE,then seasonal dummies will be included in the test regression.

Value

teststat	The Zivot-Andrews test statistic, which is the min(tstats).
cval	The critical values that are tabulated in Zivot and Andrews(1992)
p	The number of lags that are included in the test regression.
bpoint	The breaking point that corresponds to the teststat.
tstats	The sequential ADF test statistic.
testreg	The lm() output that corresponds to teststat.
timeElapse	Time elapsed for sequential search.

Note

This code modifies function ur.za of package urca. We add "season", "eq", "outlier",and "trim". Specifically, "outlier" is crucial, "season" is left to advanced research.

Author(s)

Ho Tsung-wu <[e-mail]>, College of Management, National Taiwan Normal University.

References

Zivot,E. and Andrews, W.K. (1992) Further Evidence on the Great Crasch, the Oil-Price Shock, and the Unit-Root Hypothesis. Journal of Business & Economic Statistics,10(3), 251-270.

Examples

data(macro) #US inflation rate, 1958M1-2025M7
y=macro[1:200,"INF"]
za1=ZA_1br(y,
           ic=c("AIC","BIC")[2],
           outlier=1,
           pmax=8,
           fixed=TRUE,
           model=c("intercept","trend","both")[1],
           trim=0.01,
           eq=1,
           season=TRUE)
za1$timeElapse[3]
za1$teststat
za1$cval
y[za1$bpoint,]
za1$tstats
za1$p

#plotting
plot.ts(za1$tstats,ylim=range(c(za1$tstats,za1$cval)))
abline(h=za1$cval[1],col="red")
abline(h=za1$cval[2],col="blue")
abline(h=za1$cval[3],col="green")
abline(v=za1$bpoint,col="red",lty=2)

COINT documentation built on Sept. 9, 2025, 5:51 p.m.