Engle-Granger Cointegration Test
Test whether non-stationary series share a long-run equilibrium. The Engle-Granger method estimates the long-run regression, then applies an ADF test to its residuals using cointegration critical values.
Updated · By Bibin XavierData 160 × 6
| Quartertext · 160 levels | Log_GDPnumeric | Log_Consumptionnumeric | Inflationnumeric | Interest_Ratenumeric | Money_Growthnumeric |
|---|---|---|---|---|---|
| 2000Q1 | 9.2061 | 8.6572 | 1.17 | 1.32 | 4.05 |
| 2000Q2 | 9.2005 | 8.6695 | 1.97 | 3.2 | 3.9 |
| 2000Q3 | 9.216 | 8.6727 | 2.61 | 3.54 | 4.84 |
| 2000Q4 | 9.2115 | 8.6923 | 2.15 | 2.53 | 3.4 |
| 2001Q1 | 9.224 | 8.6957 | 1.98 | 3.14 | 1.25 |
| 2001Q2 | 9.2286 | 8.6884 | 1.47 | 3.11 | 2.17 |
| 2001Q3 | 9.232 | 8.7052 | 1.55 | 2.65 | 1.8 |
| 2001Q4 | 9.2207 | 8.6907 | 2.18 | 2.43 | 3.5 |
Variables and options
Results
160 rows · example dataPre-test: unit roots (ADF with constant)
| Series | Level τ | p | Difference τ | p | Order |
|---|---|---|---|---|---|
| Log_Consumption | 0.512 | .985 | -12.292 | < .001 | I(1) |
| Log_GDP | 0.907 | .993 | -13.862 | < .001 | I(1) |
Note. Engle-Granger requires all series to be I(1).
Long-run (cointegrating) regression
| Variable | Coefficient |
|---|---|
| Constant | -0.3821 |
| Log_GDP | 0.9834 |
Note. OLS standard errors are not valid for the long-run regression, so they are not reported.
Engle-Granger test
| Statistic | Value |
|---|---|
| ADF τ on residuals | -13.357 |
| MacKinnon p | < .001 |
| Critical value 1% | -3.967 |
| Critical value 5% | -3.375 |
| Critical value 10% | -3.071 |
| Lags (AIC) | 0 |
| Number of variables | 2 |
Note. H₀: no cointegration. Critical values from MacKinnon (2010) for the number of variables in the system.
Residuals of the long-run regression (equilibrium error)
Interpretation
The series are cointegrated (τ = -13.36, p < .001): Log_Consumption and Log_GDP move together in the long run, so an error-correction model is appropriate.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Engle-Granger Cointegration Test [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/engle-granger-cointegration-test/
BibTeX
@software{xavier_cointegrationtest_2026,
author = {Xavier, Bibin},
title = {Engle-Granger Cointegration Test},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/engle-granger-cointegration-test/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Engle-Granger Cointegration Test tool on FreeStatisticalTools.com (Xavier, 2026).”
What is the Engle-Granger cointegration test?
Two or more non-stationary series are cointegrated when a linear combination of them is stationary, which means they share a long-run equilibrium. The Engle-Granger method estimates that combination and tests its residuals for a unit root.
When to use the Engle-Granger cointegration test
Use it after unit root tests show that two or more series are I(1), to decide between an error-correction model (cointegrated) and a model in differences (not cointegrated).
Assumptions
- All series are I(1).
- With more than two variables there may be several cointegrating vectors; Johansen’s test handles that case.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the dependent series and other i(1) series.
- Set the options. Fill in deterministic terms.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report the Engle-Granger cointegration test in APA style
Report the residual ADF statistic, its MacKinnon p-value and critical values, and the long-run coefficients.
Frequently asked questions
What does cointegration mean?
That the series drift together over time, so deviations from their long-run relationship are temporary.
Why can’t I use normal ADF critical values?
The residuals come from an estimated regression, which makes them look more stationary than they are; cointegration critical values (MacKinnon, 2010) correct for this.
What should I do if series are cointegrated?
Estimate an error-correction model, which combines short-run dynamics in differences with the long-run relationship.
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