Check stationarity with KPSS using level or trend. Tune lags, view plots, compare critical values. Save your report and reuse inputs for audits later.
Paste numbers separated by spaces, commas, or new lines.
| t | y | Notes |
|---|---|---|
| 1 | 0.20 | Early observation |
| 2 | 0.30 | Small increase |
| 3 | 0.28 | Minor pullback |
| 4 | 0.35 | Continues upward drift |
| 5 | 0.40 | Potential trend behavior |
1) Fit a regression and compute residuals et:
2) Form cumulative sums St = Σi=1..t ei.
3) Estimate long-run variance with Bartlett weights:
s² = γ0 + 2·Σk=1..L(1 − k/(L+1))·γk, γk = (1/n)·Σt=k+1..n etet−k
4) KPSS statistic:
KPSS = (1/n²)·Σt=1..nSt² / s²
In many workflows, unit-root tests set nonstationarity as the default. KPSS reverses that logic by treating stationarity as the null. Using both perspectives reduces false confidence when a series is near a boundary, short, or affected by structural changes. Analysts often pair KPSS with an ADF result to triangulate whether differencing is needed, or whether a deterministic trend is sufficient for modeling.
The calculator reports the KPSS statistic, the long-run variance estimate, and a decision summary across common significance levels. Larger statistics indicate stronger evidence against the stationarity null. For level stationarity, the 5% reference value is commonly 0.463, while for trend stationarity it is commonly 0.146. If the statistic exceeds the chosen threshold, the series is flagged as inconsistent with the assumed stationarity form.
KPSS relies on a Newey–West style long-run variance, built from residual autocovariances and Bartlett weights. Too few lags can understate persistence and inflate rejections; too many can add noise and reduce power. This tool offers automatic lag rules and a manual override so you can stress-test conclusions. A practical check is to rerun the test across several lags and confirm that decisions remain stable.
Small samples, missing values, and outliers can distort residual sums and long-run variance. Before testing, keep units consistent, remove obvious entry errors, and consider winsorizing extreme spikes if they are measurement artifacts. If you select a trend specification, the tool first detrends via regression, then tests the residuals. If the underlying process has breaks, interpret outcomes cautiously and complement with visual inspection.
For documentation, store the regression type, sample size, lag rule, and the final statistic with the decision level. The included exports produce a compact audit trail that can be attached to reports or notebooks. When comparing multiple series, keep the lag method consistent to avoid mixing variance estimators. Finally, cite the exact thresholds used so reviewers can replicate decisions without ambiguity. In production pipelines, re-test monthly and alert when a once-stationary metric begins failing the same specification repeatedly suddenly again.
KPSS evaluates whether a series is consistent with stationarity around a level or a deterministic trend. The null is stationarity, and large statistics suggest the residuals are too persistent to match that null.
Choose Level when the series fluctuates around a stable mean. Choose Trend when the mean changes smoothly over time. If unsure, run both and report how conclusions differ across the two assumptions.
Lags control the long-run variance estimate by capturing residual autocorrelation. Automatic rules provide a starting point, while manual lags let you test sensitivity. Different lags can change the variance estimate and therefore the statistic.
These tests reverse hypotheses. ADF or PP treat a unit root as the null, while KPSS treats stationarity as the null. Near-unit-root behavior, short samples, or breaks can make the tests point in different directions.
Longer samples improve reliability because residual sums and autocovariances stabilize. With very small samples, results can be volatile and sensitive to lag choice. If you have fewer than about 30 observations, interpret decisions cautiously.
Yes. After calculation, use the CSV or PDF buttons to download parameters, intermediate estimates, and the final decision summary. Keep exports with your dataset so colleagues can reproduce the same specification later.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.