`x`

is a stationary univariate time series.`kpss.test(x, lag.short = TRUE, output = TRUE)`

x

a numeric vector or univariate time series.

lag.short

a logical value indicating whether the parameter of lag to calculate
the test statistic is a short or long term. The default is a short term. See details.

output

a logical value indicating to print out the results in R console.
The default is

`TRUE`

.- A matrix for test results with three columns (
`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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