Granger CausalityGC
Granger causality is a test of whether past values of one series help forecast another. Despite the name it shows predictive usefulness, not true cause and effect.
Granger causality asks a narrow question: do past values of one series help forecast another series better than its own past alone? It measures predictive usefulness, not true cause and effect.
- Category
- Indicators and Tools
- Reading time
- 3 min
- Also called
- Granger causality test, Predictive causality
- Updated
Granger causality in plain words
Clive Granger's 1969 testable definition of causality sparked a huge body of research.1
In common software implementations, the null hypothesis is that past values of the second series add nothing — their coefficients are zero.2
If those past values add forecasting power, we say the first series “Granger-causes” the second — which means it predicts, not that it truly causes.
How a Granger causality test works
Make series stationary
Make the series stationary first, by differencing or transforming them; standard tests break down on trending data.1
Pick the lag length
Choose the number of lags on purpose — some tools default to just one.3
Fit restricted model
Forecast the target using only its own past.
Fit unrestricted model
Add lagged values of the candidate predictor.
Compare with a test
Reject “no Granger causality” only if the p-value falls below your chosen significance level.2
Check other variables
Try a conditional test too: a link that seems real can vanish once you control for a third variable.3
Worked examples
Example 1 — Predictor helps
Granger-causesA hypothetical test of oil returns on airline returns gives p-value 0.01 with 2 lags.
| p-value | 0.01 |
| Lags | 2 |
Below a 0.05 test size, the null is rejected, so oil returns add forecasting power in this sample.2
Example 2 — No help
No evidenceA hypothetical test of sentiment scores on index returns gives p-value 0.42.
| p-value | 0.42 |
The null that past sentiment coefficients are zero is not rejected, so no predictive link is shown.2
Example 3 — Hidden third factor
Spurious linkA hypothetical link from series A to B disappears once series C is added, p-value rising from 0.02 to 0.31.
| p-value without C | 0.02 |
| p-value with C | 0.31 |
Conditioning matters, as MathWorks’ conditional test example shows; the first result was likely driven by C.3
Granger causality vs correlation
| Aspect | Granger causality | Correlation |
|---|---|---|
| Uses time order | Yes, lagged values | No |
| Direction | Tested each way | Symmetric |
| Answers | Does X help forecast Y? | Do X and Y move together? |
| Proves causation | No | No |
Where Granger tests are used
Lead–lag research
Check whether one market leads another, alongside Correlation.
Indicator vetting
Test if an Economic Indicator predicts returns.
Signal research
Pre-screen ideas before Backtesting.
Classifying tools
Separate Leading and Lagging Indicators statistically.
Advantages and disadvantages
Advantages
- Simple, widely available test.
- Uses time ordering explicitly.
- Can be run in both directions.
- Extends to many variables.
Disadvantages
- Does not prove real causation.
- Sensitive to lag choice.
- Needs stationary data.
- Missing variables can create false links.
Going deeper
Read as far as you need. Each level builds on the one before it.
Prediction, not cause
Beginner
The Nobel committee calls it a testable definition of causality, but it is defined purely through forecasting improvement.1
Lag sensitivity
Intermediate
Because gctest assumes an underlying VAR(1) model by default, results can change when more lags are allowed.3
Nonstationarity
Advanced
Trending prices break the usual statistics, so analysts work with returns or use cointegration methods instead.1
Common mistakes
Calling it true causation
It only shows predictive help.
Testing raw prices
Use stationary data such as returns.
Trying many lags until significant
That is data mining.
Ignoring third variables
Condition on likely drivers.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- Granger causality is about forecasting, not true cause.
- It compares models with and without lagged predictors.
- Low p-values reject the no-predictive-power null.
- Lag choice and stationarity matter.
- Omitted variables can create false links.
Frequently asked questions
Does Granger causality prove cause?
Can both directions be significant?
What data should I use?
Further learning
- Correlation
The simpler co-movement measure.
- Leading and Lagging Indicators
What lead–lag means for tools.
- Backtesting
Testing a predictive idea.
- Economic Indicator
Common series tested.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- The Royal Swedish Academy of Sciences (Nobel Prize). Time-series Econometrics: Cointegration and ARCH (2003 advanced information) (opens in a new tab) Checked .
- statsmodels. statsmodels.tsa.stattools.grangercausalitytests (opens in a new tab) Checked .
- MathWorks. gctest – Granger causality and block exogeneity tests (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.