KPSS Test for Stationarity

Computes the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the null hypothesis that x is level or trend stationary.

kpss.test(x, null = c("Level", "Trend"), lshort = TRUE)

Arguments

x

a numeric vector or univariate time series.

null

indicates the null hypothesis and must be one of "Level" (default) or "Trend". You can specify just the initial letter.

lshort

a logical indicating whether the short or long version of the truncation lag parameter is used.

Details

To estimate sigma^2 the Newey-West estimator is used. If lshort is TRUE, then the truncation lag parameter is set to trunc(4*(n/100)^0.25), otherwise trunc(12*(n/100)^0.25) is used. The p-values are interpolated from Table 1 of Kwiatkowski et al. (1992). If the computed statistic is outside the table of critical values, then a warning message is generated.

Missing values are not handled.

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

parameter

the truncation lag parameter.

p.value

the p-value of the test.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name of the data.

References

D. Kwiatkowski, P. C. B. Phillips, P. Schmidt, and Y. Shin (1992): Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometrics 54, 159–178.

Author

A. Trapletti

See also

pp.test

Examples

x <- rnorm(1000)  # is level stationary
kpss.test(x)
#> 
#> 	KPSS Test for Level Stationarity
#> 
#> data:  x
#> KPSS Level = 0.39009, Truncation lag parameter = 7, p-value = 0.08143
#> 

y <- cumsum(x)  # has unit root
kpss.test(y)
#> Warning: p-value smaller than printed p-value
#> 
#> 	KPSS Test for Level Stationarity
#> 
#> data:  y
#> KPSS Level = 7.4202, Truncation lag parameter = 7, p-value = 0.01
#> 

x <- 0.3*(1:1000)+rnorm(1000)  # is trend stationary
kpss.test(x, null = "Trend")
#> Warning: p-value greater than printed p-value
#> 
#> 	KPSS Test for Trend Stationarity
#> 
#> data:  x
#> KPSS Trend = 0.082535, Truncation lag parameter = 7, p-value = 0.1
#>