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 `TRUE`.

### 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] = α*t + u[t] + e[t],

where u[t] satisfies u[t] = u[t-1] + a[t], and a[t] are i.i.d (0,σ^2). The null hypothesis is that σ^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] = μ + u[t] + e[t].

The third type (`type3`) is the one with both drift and trend:

x[t] = μ + α*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.

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)
```

[Package aTSA version 3.1.2 Index]