Direct Answer
The KPSS statistic, from Kwiatkowski, Phillips, Schmidt and Shin, tests the null hypothesis that a series is stationary, in contrast with unit-root tests whose null is non-stationarity. It sums squared partial sums of regression residuals relative to a long-run variance. Larger values are evidence against stationarity.
KPSS Statistic: Formula, Meaning, Signals, Examples and How to Use It
How Is KPSS Statistic Calculated?
The KPSS statistic, from Kwiatkowski, Phillips, Schmidt and Shin, tests the null hypothesis that a series is stationary, in contrast with unit-root tests whose null is non-stationarity. It sums squared partial sums of regression residuals relative to a long-run variance.
Formula: KPSS = (1 / T^2) * sum of S_t^2 / s^2(l), where S_t are cumulative sums of residuals from a regression on a constant (or constant and trend) and s^2(l) is a long-run variance estimate
Inputs:
- Series values
- Deterministic terms (constant, or constant and trend)
- Bandwidth l for the long-run variance
Worked example. A sum of squared partial sums of 24, 10 observations and a long-run variance of 0.6 give a statistic of 0.400. The inputs are illustrative numbers, not market data.
Reading it. Larger values are evidence against stationarity. For the level-stationarity case, the commonly published critical values are 0.347 at 10 percent, 0.463 at 5 percent and 0.739 at 1 percent, and a statistic above them rejects stationarity.
Limits. Results are sensitive to the bandwidth choice and the test has low power in small samples. It is often used together with a unit-root test, since the two can disagree.
What is KPSS Statistic?
The KPSS statistic, from Kwiatkowski, Phillips, Schmidt and Shin, tests the null hypothesis that a series is stationary, in contrast with unit-root tests whose null is non-stationarity. It sums squared partial sums of regression residuals relative to a long-run variance.
How to use KPSS Statistic
Larger values are evidence against stationarity. For the level-stationarity case, the commonly published critical values are 0.347 at 10 percent, 0.463 at 5 percent and 0.739 at 1 percent, and a statistic above them rejects stationarity. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Making stationarity the null reverses the logic of unit-root tests, so the two can be run together as a cross-check.
- Including a trend term in the regression lets the same statistic test stationarity around a trend, not only around a constant.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- Rejecting the null says the series is not stationary but not whether the cause is a unit root, a trend or a structural break.
- Because the null is stationarity, persistent but stationary series can be rejected too often, so the test over-rejects in them.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is KPSS Statistic a buy or sell signal?
No. Larger values are evidence against stationarity. Results are sensitive to the bandwidth choice and the test has low power in small samples. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for KPSS Statistic?
KPSS Statistic is computed from series values; deterministic terms (constant, or constant and trend); bandwidth l for the long-run variance, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner.
Can KPSS Statistic be used by itself?
Results are sensitive to the bandwidth choice and the test has low power in small samples. It is often used together with a unit-root test, since the two can disagree. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does KPSS Statistic work on every timeframe?
The calculation (KPSS = (1 / T^2) * sum of S_t^2 / s^2(l), where S_t are cumulative sums of residuals from a regression on a constant (or constant and trend) and s^2(l) is a long-run variance estimate) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does KPSS Statistic give false signals?
Rejecting the null says the series is not stationary but not whether the cause is a unit root, a trend or a structural break. Because the null is stationarity, persistent but stationary series can be rejected too often, so the test over-rejects in them. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should KPSS Statistic be backtested?
Rebuild KPSS Statistic from series values using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.