statsmodels.tsa.stattools.kpss(x, regression='c', nlags=None, store=False)[source]

Kwiatkowski-Phillips-Schmidt-Shin test for stationarity.

Computes the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the null hypothesis that x is level or trend stationary.

xarray_like, 1d

The data series to test.

regressionstr{“c”, “ct”}

The null hypothesis for the KPSS test.

  • “c” : The data is stationary around a constant (default).

  • “ct” : The data is stationary around a trend.

nlags{None, str, int}, optional

Indicates the number of lags to be used. If None (default), lags is calculated using the legacy method. If “auto”, lags is calculated using the data-dependent method of Hobijn et al. (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). If set to “legacy”, uses int(12 * (n / 100)**(1 / 4)) , as outlined in Schwert (1989).


If True, then a result instance is returned additionally to the KPSS statistic (default is False).


The KPSS test statistic.


The p-value of the test. The p-value is interpolated from Table 1 in Kwiatkowski et al. (1992), and a boundary point is returned if the test statistic is outside the table of critical values, that is, if the p-value is outside the interval (0.01, 0.1).


The truncation lag parameter.


The critical values at 10%, 5%, 2.5% and 1%. Based on Kwiatkowski et al. (1992).

resstore(optional) instance of ResultStore

An instance of a dummy class with results attached as attributes.


To estimate sigma^2 the Newey-West estimator is used. If lags is None, the truncation lag parameter is set to int(12 * (n / 100) ** (1 / 4)), as outlined in Schwert (1989). The p-values are interpolated from Table 1 of Kwiatkowski et al. (1992). If the computed statistic is outside the table of critical values, then a warning message is generated.

Missing values are not handled.



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: 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.