arch.unitroot.KPSS¶

class arch.unitroot.KPSS(y: ndarray | DataFrame | Series, lags: int | None = None, trend: 'c' | 'ct' = 'c')[source]¶

Kwiatkowski, Phillips, Schmidt and Shin (KPSS) stationarity test.

Parameters:¶

y: ndarray | DataFrame | Series¶

The data to test for stationarity.

lags: int | None = None¶

The number of lags to use in the Newey-West estimator of the long-run covariance. If omitted or None, the number of lags is calculated with the data-dependent method of Hobijn et al. (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). Set lags=-1 to use the old method that only depends on the sample size, 12 * (nobs/100) ** (1/4).

trend: 'c' | 'ct' = 'c'¶

The trend component to include in the test. Not case sensitive.

• ”c” - Include a constant

• ”ct” - Include a constant and linear time trend

Raises:¶

• TypeError – If y cannot be converted to numbers, lags is not an integer or None, or trend is not a str.

• ValueError – If y is not 1-d or contains NaN or inf, lags is less than -1, or trend is not one of the options.

• InfeasibleTestException – If y has too few observations for trend, or lags (the number from the rule 12 * (nobs/100) ** (1/4) if it is -1) is larger than the number of observations in y. This is also a ValueError.

Notes

The null hypothesis of the KPSS test is that the series is weakly stationary and the alternative is that it is non-stationary. If the p-value is above a critical size, then the null cannot be rejected and the series appears stationary.

The p-values and critical values were computed using an extensive simulation based on 100,000,000 replications using series with 2,000 observations. See [3] for the initial description of the KPSS test. Further details are available in [2] and [5]. Details about the long-run covariance estimation can be found in [1] and [4].

References

Examples

>>> from arch.unitroot import KPSS
>>> import numpy as np
>>> import statsmodels.api as sm
>>> data = sm.datasets.macrodata.load().data
>>> inflation = np.diff(np.log(data["cpi"]))
>>> kpss = KPSS(inflation)
>>> print(f"{kpss.stat:0.4f}")
0.3916
>>> print(f"{kpss.pvalue:0.4f}")
0.0761
>>> kpss = KPSS(inflation, trend="ct")
>>> print(f"{kpss.stat:0.4f}")
0.2802
>>> print(f"{kpss.pvalue:0.4f}")
0.0026

Methods

summary()

Summary of test, containing statistic, p-value and critical values.

Properties

alternative_hypothesis	The alternative hypothesis.
critical_values	The critical values of the test.
lags	The number of lags used in the model.
nobs	The number of observations used when computing the test statistic.
null_hypothesis	The null hypothesis.
pvalue	The p-value for the test statistic.
stat	The test statistic for a unit root.
trend	The deterministic trend term used in the test.
valid_trends	List of valid trend terms.
y	The data used in the test statistic.