KPSStest

KPSStest is commonly used to refer to the KPSS test, a statistical method for assessing whether a time series is stationary. The KPSS test was developed by Kwiatkowski, Phillips, Schmidt, and Shin in 1992 as part of a framework to evaluate stationarity around a deterministic trend or a constant. Although the term KPSStest appears in some discussions, the widely accepted name is KPSS test, and some sources treat KPSStest as a variant spelling.

The test is formulated with a null hypothesis that the time series is stationary around a deterministic component (level or trend), with the alternative hypothesis that the series is non-stationary due to a unit root or other forms of non-stationarity. There are two common specifications: KPSS Level, where the series is tested for stationarity around a constant, and KPSS Trend, where it is tested for stationarity around a deterministic trend. The null of stationarity contrasts with tests like the Augmented Dickey–Fuller test, which use the opposite null hypothesis.

Methodologically, the KPSS test regresses the series on the chosen deterministic component to obtain residuals, computes the partial sums of these residuals, and forms a statistic based on these partial sums scaled by an estimator of the residuals’ long-run variance. Critical values are obtained from simulations because the distribution under the null is non-standard.

Applications of the KPSS test span macroeconomics and finance, where researchers assess whether a series is stationary before modeling or differencing. Limitations include sensitivity to the choice of deterministic specification, bandwidth, and potential distortions from structural breaks; results are often complemented with other unit-root tests and break-sensitive approaches. Implementations are available in major econometrics software packages such as R, Python (statsmodels), Stata, and EViews. See also: unit root tests, ADF test, Phillips–Perron test.