Calculator
Overall page sections stay in a single vertical flow, while the calculator controls use a responsive 3/2/1 column grid.
Example Data Table
This sample can be pasted directly into the calculator.
| Period | Value |
|---|---|
| 1 | 104.0 |
| 2 | 102.7 |
| 3 | 101.9 |
| 4 | 101.2 |
| 5 | 100.8 |
| 6 | 100.1 |
| 7 | 99.7 |
| 8 | 99.3 |
| 9 | 99.0 |
| 10 | 98.7 |
| 11 | 98.4 |
| 12 | 98.2 |
Formula Used
Δyt = α + βt + γyt-1 + Σ φiΔyt-i + εt
H0: γ = 0 → the series has a unit root.
τ = γ̂ / SE(γ̂)
AIC = n ln(RSS / n) + 2kBIC = n ln(RSS / n) + k ln(n)
The calculator estimates the regression with ordinary least squares, reports the tau statistic for the lagged level term, and compares it with conventional reference critical values for the selected deterministic specification.
How to Use This Calculator
- Paste your time series values into the data box.
- Choose how the values are separated or leave auto detection on.
- Select the deterministic term: none, constant, or constant with trend.
- Pick automatic lag search or enter a manual lag order.
- Choose the decision level and preferred decimal precision.
- Click Run ADF Test to view results above the form.
- Review the tau statistic, decision, coefficients, and Plotly graph.
- Use the CSV and PDF buttons to export the summary.
FAQs
1. What does the Augmented Dickey-Fuller test measure?
It tests whether a time series contains a unit root. The null hypothesis is non-stationarity. A sufficiently negative tau statistic supports rejecting that null and treating the series as stationary under the chosen specification.
2. Why are lagged differences included?
Lagged differences absorb serial correlation in the residuals. Without them, the basic Dickey-Fuller setup can misstate the test statistic and weaken the reliability of the stationarity decision.
3. When should I choose a constant or trend?
Use a constant when the series fluctuates around a nonzero mean. Add a trend when the series shows a deterministic upward or downward path. Avoid unnecessary terms because they change the critical values and test power.
4. What is the null hypothesis in this calculator?
The null hypothesis is that the series has a unit root. If the tau statistic is more negative than the selected critical value, you reject that null at the chosen significance level.
5. Is the reported p-value exact?
No. This page reports an approximate significance band from standard critical values. Exact MacKinnon response-surface p-values require specialized tables or dedicated statistical libraries.
6. What does automatic lag selection do?
It estimates several candidate models from lag 0 up to your chosen maximum lag. The calculator keeps the model with the lowest AIC or BIC, depending on your selected criterion.
7. Can I test very short series?
You can try, but very short samples reduce power and may not leave enough usable observations after adding lags and deterministic terms. Longer series usually produce more stable inference.
8. What should I do if the series is non-stationary?
Common next steps include differencing the series, removing a deterministic trend, applying a transformation, or checking for structural breaks. Then rerun the test on the adjusted series.