arch.unitroot.KPSS¶

class arch.unitroot.KPSS(y, lags=None, trend='c')[source]¶

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

Parameters

y ({ndarray, Series}) -- The data to test for stationarity
lags (int, optional) -- 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'}, optional) --

The trend component to include in the ADF test
'c' - Include a constant (Default) 'ct' - Include a constant and linear time trend

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 that there 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.

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('{0:0.4f}'.format(kpss.stat))
0.2870
>>> print('{0:0.4f}'.format(kpss.pvalue))
0.1473
>>> kpss.trend = 'ct'
>>> print('{0:0.4f}'.format(kpss.stat))
0.2075
>>> print('{0:0.4f}'.format(kpss.pvalue))
0.0128

References

*: Andrews, D.W.K. (1991). "Heteroskedasticity and autocorrelation consistent covariance matrix estimation". Econometrica, 59: 817-858.
†: Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502.
‡: 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
§: Newey, W.K., & West, K.D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies, 61: 631-653.
¶: Schwert, G. W. (1989). "Tests for unit roots: A Monte Carlo investigation". Journal of Business and Economic Statistics, 7 (2): 147-159.

Methods

summary()

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

Properties

`alternative_hypothesis`	The alternative hypothesis
`critical_values`	Dictionary containing critical values specific to the test, number of observations and included deterministic trend terms.
`lags`	Sets or gets 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`	Returns the p-value for the test statistic
`stat`	The test statistic for a unit root
`trend`	Sets or gets the deterministic trend term used in the test.
`valid_trends`	List of valid trend terms.
`y`	Returns the data used in the test statistic