Kwiatkowski-Phillips-Schmidt-Shin Test for Assessing Level or Trend Stationarity

A test for stationarity in time series, complementary to unit root tests such as the ADF test: it tests the null hypothesis of stationarity against the alternative of a unit root.

Usage

kpssTest(
  y,
  type = c("mu", "tau"),
  lags = c("short", "long", "nil"),
  useLag = NULL
)

Arguments

y: numeric vector or univariate time series to be tested for stationarity.
type: the deterministic part of the model, one of "mu" (default, constant) or "tau" (constant plus linear trend).
lags: the rule for the number of lags used for the error term correction, one of "short" (default), "long" or "nil". See the Details. Ignored if useLag is given.
useLag: an optional integer explicitly specifying the number of lags, overriding lags.

Value

An object of class "htest" containing the following components:

statistic: the value of the KPSS test statistic.
parameter: the number of lags used for the error term correction.
p.value: the interpolated p-value of the test.
critical.values: the asymptotic critical values at the 10%, 5%, 2.5% and 1% significance levels (not shown on screen).
alternative: a character string describing the alternative hypothesis.
method: a character string indicating the test performed.
data.name: a character string giving the name of the data.

Details

Performs the KPSS test (Kwiatkowski et al., 1992), where the null hypothesis is stationarity. The test types specify as deterministic component either a constant ("mu", null hypothesis of level stationarity) or a constant with linear trend ("tau", null hypothesis of trend stationarity).

lags = "short" sets the number of lags used for the long-run variance estimation to \(4 (n/100)^{1/4}\), whereas lags = "long" sets it to \(12 (n/100)^{1/4}\) (each truncated to an integer). With lags = "nil" no error correction is made. Alternatively, an explicit number of lags can be given via useLag, which then takes precedence.

The p-value is obtained by linear interpolation in the asymptotic critical values of Kwiatkowski et al. (1992, Table 1), following the approach of tseries::kpss.test(). If the statistic falls outside the range of the table, the p-value is reported as the respective boundary (0.01 or 0.10) and a warning is issued.

Missing values are silently removed.

Note

Based on code by Bernhard Pfaff previously published in the urca package, adapted to conform to package standards.

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.

Examples

# trend-stationary series: null hypothesis is not rejected
set.seed(1)
x <- 0.2 * seq_len(200) + rnorm(200)
kpssTest(x, type = "tau")
#> Warning: p-value greater than reported p-value
#> 
#> 	KPSS test for trend stationarity
#> 
#> data:  x
#> KPSS = 0.065919, lags = 4, p-value = 0.1
#> alternative hypothesis: not trend stationary (unit root)
#> 

# random walk: null hypothesis of level stationarity is rejected
set.seed(2)
rw <- cumsum(rnorm(200))
kpssTest(rw, type = "mu")
#> 
#> 	KPSS test for level stationarity
#> 
#> data:  rw
#> KPSS = 0.51701, lags = 4, p-value = 0.03784
#> alternative hypothesis: not level stationary (unit root)
#> 

kpssTest(AirPassengers, type = "tau", lags = "short")
#> Warning: p-value greater than reported p-value
#> 
#> 	KPSS test for trend stationarity
#> 
#> data:  AirPassengers
#> KPSS = 0.09615, lags = 4, p-value = 0.1
#> alternative hypothesis: not trend stationary (unit root)
#>