kpss: KPSS Unit Root Test for the null of stationarity

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

KPSS Unit Root Test for the null of stationarity

Description

Implement the KPSS unit root test for the null of I(0) stationarity. The test type as deterministic component is specified as x, see example below.

Usage

kpss(y, x, lags = c("short", "long", "nil"), use=c("nw","ba"))

Arguments

y	Vector to be tested for a unit root.
x	data matrix for deterministic component. For example a vector of one for intercept, or trend. The default is "x=NULL", which is the same of a vector of one
lags	Lags used for correction of error term.
use	User specified lags for correction of error term. See section details below.The default is the lag determined by Newey-West bandwidth ("nw") with Bartlettkernel ("ba").

Details

lags="short" sets the number of lags to \sqrt[4]{4 \times (n/100)}, whereas lags="long" sets the number of lags to \sqrt[4]{12 \times (n/100)}. If lags="nil" is choosen, no error correction is made.

Furthermore, "lags" and "use" are mutually exclusive: As long as "use" is not NULL, its argument will be chosen first. One can specify a different number of maximum lags by setting "use" accordingly. Users can input number of your souce. This version suports two bandwidth functions: "nw" for Newey-West and "and" for Andrews. The kernel functions are supported: "ba"=Bartlett, "pa"=Parzen, "qs"=Qudratic Spectral

Value

teststat	The KPSS test statistic.
cval	Critical values.
lag	Number of lags used for kernel function.
resid	Regression residuals.

Author(s)

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

References

Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992) Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root? Journal of Econometrics, 54,159-178.
Phillips, P.C.B. and Sainan Jin (2002) The KPSS test with seasonal dummies. Economics Letters, 77, 239-243.

Examples

data(macro)
y=macro[,"INF"]
const=rep(1,nrow(y))
trend=seq(nrow(y))/nrow(y)
D=cbind(const,trend) #seasonal dummies can be specified here
KPSS=kpss(y,x=D,lags = c("short", "long", "nil")[2],
          use=c("nw","ba")) # If argument use isn't NULL, the argument "lags" will be ignored.
KPSS$teststat
KPSS$cval
KPSS$lag

kpss(y,x=D,lags = c("short", "long", "nil")[2],use=15)

kpss(y,x=D,
    lags = c("short", "long", "nil")[2],
    use=NULL) #if "use=NULL", argument "lags"  will be chosen as input.

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