kpss.test {aTSA} | R Documentation |

## Kwiatkowski-Phillips-Schmidt-Shin Test

### Description

Performs Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the null
hypothesis that `x`

is a stationary univariate time series.

### Usage

```
kpss.test(x, lag.short = TRUE, output = TRUE)
```

### Arguments

`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 |

### Details

The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test tends to decompose the time series into the sum of a deterministic trend, a random walk, and a stationary error:

`x[t] = \alpha*t + u[t] + e[t],`

where `u[t]`

satisfies `u[t] = u[t-1] + a[t]`

, and `a[t]`

are i.i.d
`(0,\sigma^2)`

. The null hypothesis is that `\sigma^2 = 0`

, which implies
`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`

).

### Value

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.

### Note

Missing values are removed.

### Author(s)

Debin Qiu

### References

Hobijn B, Franses PH and Ooms M (2004). Generalization of the KPSS-test for stationarity.
*Statistica Neerlandica*, vol. 58, p. 482-502.

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.

### See Also

`adf.test`

, `pp.test`

, `stationary.test`

### Examples

```
# 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)
```

*aTSA*version 3.1.2.1 Index]