Test paired series for stable equilibrium using residuals. Tune lags, confidence, and decimal precision easily. Review statistics, interpretations, and exports in one clean workspace.
| t | Series X | Series Y | Fitted Y | Residual |
|---|---|---|---|---|
| 1 | 100.0000 | 200.0000 | 199.6859 | 0.3141 |
| 2 | 102.0000 | 203.0000 | 203.3451 | -0.3451 |
| 3 | 103.0000 | 205.0000 | 205.1747 | -0.1747 |
| 4 | 105.0000 | 209.0000 | 208.8340 | 0.1660 |
| 5 | 107.0000 | 213.0000 | 212.4932 | 0.5068 |
| 6 | 108.0000 | 214.0000 | 214.3228 | -0.3228 |
| 7 | 110.0000 | 218.0000 | 217.9821 | 0.0179 |
| 8 | 111.0000 | 220.0000 | 219.8117 | 0.1883 |
| 9 | 113.0000 | 223.0000 | 223.4710 | -0.4710 |
| 10 | 114.0000 | 225.0000 | 225.3006 | -0.3006 |
| 11 | 116.0000 | 229.0000 | 228.9598 | 0.0402 |
| 12 | 118.0000 | 233.0000 | 232.6191 | 0.3809 |
Step 1: Cointegrating regression
Estimate a long-run relationship using ordinary least squares:
Yt = β₀ + β₁Xt + et
Residuals et represent deviations from the long-run equilibrium.
Step 2: Residual stationarity (ADF-style)
Δet = α + γet-1 + ΣφiΔet-i + νt
If γ is sufficiently negative (t-statistic below the critical threshold), residuals are treated as stationary and cointegration is likely.
This implementation provides a practical approximation for educational and screening use.
Cointegration testing works best when both series are aligned, complete, and sampled at one frequency. Analysts often use paired prices, yields, or macro indicators with matching dates. Before testing, remove entry errors, confirm ordering, and avoid mixing weekly values with monthly values. Clean alignment matters because timing mismatches can distort residual patterns and produce weak decisions. Consistent scaling is also helpful, especially when users compare multiple test windows during routine validation cycles.
The first stage estimates a long run equation linking Series X and Series Y. The slope shows the average equilibrium response of Y to X, while the intercept captures baseline offset. R-squared and correlation are useful context metrics, but they do not prove cointegration. Residuals from this stage are the key output because they measure deviations from the estimated equilibrium path. Document the chosen sample window and data source so repeated tests can be audited and reproduced later.
The second stage applies an ADF style regression to residuals. The gamma coefficient reflects whether deviations shrink over time. A negative gamma with a sufficiently low t statistic supports residual stationarity, which suggests cointegration. This tool provides an approximate interpretation using selected significance levels, making it useful for screening, education, and exploratory research before deeper econometric validation. Because critical values depend on specification details, treat borderline cases carefully and retest under alternative settings.
Lag selection controls how much short run dependence is absorbed in the residual test. Too few lags may leave autocorrelation in errors, while too many reduce degrees of freedom and weaken power. A practical workflow is testing nearby lag counts and checking whether the conclusion stays stable. If results change easily, review outliers, sample length, and possible structural breaks. Many analysts start with one lag, then increase gradually until residual autocorrelation risk appears reduced.
Cointegration screening is used in spread research, macro tracking, and monitoring workflows. A positive result does not guarantee a tradable signal, but it can justify deeper analysis. Teams usually combine this test with rolling windows, break detection, and risk limits to monitor stability. This calculator supports transparent review with table exports and printable reports, helping analysts compare runs and document assumptions consistently. Internally.
Enter two equal-length numeric series collected at the same frequency. Use aligned observations only. Daily, weekly, or monthly values are all fine if timestamps match.
No. Correlation shows co-movement, but cointegration requires residual stationarity around a long-run equilibrium. Two series can be highly correlated and still fail cointegration.
At least 10 are required here, but practical analysis usually benefits from 60 or more points. More observations improve stability unless structural breaks dominate the sample.
Gamma measures error-correction speed in the residual test. A negative and statistically strong gamma suggests residuals revert toward equilibrium after short-term deviations.
Lag choice affects residual autocorrelation control and degrees of freedom. Testing nearby lag values helps you check whether conclusions remain stable and dependable.
It is best for screening, learning, and rapid analysis. For formal reporting, validate results with specialized econometric software and exact critical values.
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.