KPSS Test

KPSS test is a stationarity test whose null hypothesis is that a time series is stationary around a constant level, rejected when cumulative deviations from the mean grow too large.

KPSS 검정은 시계열이 일정한 수준 주위에서 정상적이라는 귀무가설을 두고, 평균으로부터의 누적 편차가 지나치게 커지면 이를 기각하는 정상성 검정이다.

How do I confirm that my time series is stationary rather than only failing to find a unit root?

단위근을 찾지 못한 것에 그치지 않고 시계열이 정상적이라는 것을 어떻게 확인하나요?

The KPSS test reverses the logic of unit root tests: its null hypothesis is stationarity, so a significant result indicates a unit root or another form of non-stationarity. Using it together with the augmented Dickey-Fuller test helps separate clearly stationary series, clearly non-stationary series and inconclusive cases.

When to use KPSS Test

• Confirming stationarity alongside an augmented Dickey-Fuller test
• Checking whether a series is level-stationary before modelling
• A single, regularly spaced time series

When to use something else

• Series that fluctuate around a linear trend, which this level-stationarity version treats as non-stationary: use a trend-stationarity KPSS test or an ADF test with trend
• Many short series observed in parallel: use a panel unit root test

Assumptions and requirements

• Regularly spaced observations ordered by time
• Null hypothesis of stationarity around a constant level
• Long-run variance estimated with an automatically chosen lag window

What the analysis reports

• KPSS statistic
• p-value interpolated from tabulated critical values, so it is bounded between 0.01 and 0.10
• Lag truncation used
• 5% critical value

How to report it

The KPSS test did not reject the null hypothesis of level stationarity for [series], KPSS = [value], p > [value].

Related methods

• Augmented Dickey-Fuller Test
• ARIMA Model
• Seasonal Decomposition

Run KPSS Test on Quorant