x is a stationary univariate time series.kpss.test(x, lag.short = TRUE, output = TRUE)TRUE.lag, kpss,
p.value) and three rows (type1, type2, type3).
Each row is the test results (including lag parameter, test statistic and p.value) for
each type of linear regression models.x is a stationary time series. In order to calculate the test statistic,
we consider three types of linear regression models.
The first type (type1) is the one with no drift and deterministic trend,
defined as $$x[t] = u[t] + e[t].$$
The second type (type2) is the one with drift but no trend:
$$x[t] = \mu + u[t] + e[t].$$
The third type (type3) is the one with both drift and trend:
$$x[t] = \mu + \alpha*t + u[t] + e[t].$$
The details of calculation of test statistic (kpss) can be seen in the references
below. The default parameter of lag to calculate the test statistic is
$max(1,floor(3*sqrt(n)/13)$ for short term effect, otherwise,
$max(1,floor(10*sqrt(n)/13)$ for long term effect.
The p.value is calculated by the interpolation of test statistic from tables of
critical values (Table 5, Hobijn B., Franses PH. and Ooms M (2004)) for a given
sample size $n$ = length(x).Kwiatkowski, D.; Phillips, P. C. B.; Schmidt, P.; Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54 (1-3): 159-178.
adf.test, pp.test, stationary.test# KPSS test for AR(1) process
x <- arima.sim(list(order = c(1,0,0),ar = 0.2),n = 100)
kpss.test(x)
# KPSS test for co2 data
kpss.test(co2)Run the code above in your browser using DataCamp Workspace