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)
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