> For the complete documentation index, see [llms.txt](https://mixmodeler.gitbook.io/mixmodeler-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mixmodeler.gitbook.io/mixmodeler-docs/model-building/variable-testing/granger-causality-tests.md).

# Granger Causality Tests

### What is Granger Causality?

Granger Causality tests whether one time series can predict another. It doesn't prove true causation, but shows if past values of X help forecast Y.

**Key question:** Does knowing X's history improve predictions of Y beyond Y's own history?

**Marketing application:** Does marketing activity predict sales changes, or do they just happen to move together?

### Why Test Granger Causality?

#### Validate Marketing Effectiveness

**Without test:**

* Correlation might be coincidence
* Can't confirm marketing drives sales
* Stakeholder skepticism

**With test:**

* Statistical evidence of predictive relationship
* Confidence marketing influences outcomes
* Stronger business case

#### Detect Reverse Causality

**Possible scenarios:**

* Marketing causes sales ✓
* Sales cause marketing (budget follows performance)
* Both influence each other
* Neither causes the other (coincidence)

**Granger test reveals:** Direction of predictive relationship

#### Improve Variable Selection

**Use to:**

* Validate variable relevance before adding
* Confirm marketing variables predict KPI
* Identify spurious correlations
* Build more credible models

### How Granger Causality Works

#### The Test Logic

**Question:** Does X Granger-cause Y?

**Process:**

1. Predict Y using only Y's past values
2. Predict Y using Y's past + X's past values
3. Compare prediction accuracy
4. If adding X improves predictions significantly → X Granger-causes Y

**Statistical test:** F-test comparing models

**Result:** P-value indicating significance

### Using Granger Causality in MixModeler

#### Location

Variable Testing page → Granger Causality tab

#### Configuration Options

**Test Target:**

* **KPI Testing:** Test if variables predict KPI (recommended for MMM)
* **Between Variables:** Test causality between variables

**Max Lags:**

* Number of past periods to include
* **4 lags (default):** Good for weekly MMM
* **1-52 lags:** Adjustable based on data frequency

**Significance Level:**

* **95% (0.05):** Standard (recommended)
* 90%, 99%, 99.9% also available

**Stationarity Test:**

* **Include:** Run ADF test first (recommended)
* Ensures data suitable for Granger test

#### Step-by-Step Process

**Step 1: Select Model**

Choose existing model with KPI defined

**Step 2: Select Variables**

Check variables to test:

* Marketing channels
* Control variables
* External factors

**Step 3: Configure Settings**

* Target: KPI Testing
* Max Lags: 4 (weekly data)
* Significance: 95%
* Include stationarity: Yes

**Step 4: Run Test**

Click "Test Granger Causality"

**Step 5: Review Results**

Results table shows:

* Variable name
* Optimal lags
* F-statistic
* P-value
* Significance status

### Interpreting Results

#### Results Table

**Columns:**

**Variable:**\
Tested variable name

**Cause → Effect:**\
Shows relationship direction (Variable → KPI)

**Optimal Lags:**\
Best number of past periods (automatically selected)

**F-Statistic:**\
Test statistic value (higher = stronger)

**P-Value:**\
Significance level

* < 0.05: Significant Granger causality
* < 0.01: Strong Granger causality
* > 0.05: No significant causality

**Is Significant:**\
Yes/No indicator

#### What Results Mean

**Significant (p < 0.05):**

✅ Past values of marketing variable help predict KPI\
✅ Evidence of predictive relationship\
✅ Good candidate for model inclusion\
✅ Can defend variable choice statistically

**Not Significant (p > 0.05):**

❌ Marketing doesn't predict KPI changes\
❌ Relationship may be coincidental\
❌ Weaker case for inclusion\
❌ Consider alternative variables

#### Example Results

| Variable       | Optimal Lags | F-Stat | P-Value | Significant |
| -------------- | ------------ | ------ | ------- | ----------- |
| TV\_Spend      | 2            | 8.45   | 0.001   | **Yes**     |
| Digital\_Spend | 1            | 5.21   | 0.008   | **Yes**     |
| Radio\_Spend   | 3            | 2.10   | 0.087   | No          |
| Weather        | 4            | 1.45   | 0.234   | No          |

**Interpretation:**

* TV and Digital show strong Granger causality
* Radio borderline (may still include if theoretically important)
* Weather doesn't predict sales in this case

### Stationarity Testing

#### What is Stationarity?

**Stationary series:**

* Constant mean over time
* Constant variance
* No trends

**Non-stationary series:**

* Trending up or down
* Changing variance
* Violates Granger test assumptions

#### ADF (Augmented Dickey-Fuller) Test

**Tests for stationarity**

**Results:**

* **P-value < 0.05:** Stationary ✓
* **P-value > 0.05:** Non-stationary (trend present)

**If non-stationary:**

* Consider differencing (week-over-week change)
* Add trend variable
* Detrend before testing

#### Why It Matters

**Non-stationary data:**

* Can show spurious Granger causality
* Trends create false relationships
* Must address before relying on results

**Stationary data:**

* More reliable Granger tests
* True relationships detected
* Safer interpretation

### Common Testing Scenarios

#### Scenario 1: Validate Marketing Variables

**Question:** Do our marketing channels predict sales?

**Test:**

* All marketing variables vs KPI
* Look for p < 0.05

**Decision:**

* Include variables with significant causality
* Question variables without causality

#### Scenario 2: New Channel Evaluation

**Question:** Should we model new Radio campaign?

**Test:**

* Radio\_Spend → Sales

**If significant:** Strong case for inclusion\
**If not:** May need more data or channel doesn't drive sales

#### Scenario 3: Resolve Multicollinearity

**Question:** TV\_Spend and TV\_GRPs both predict sales, which to keep?

**Test:**

* Both separately
* Compare F-statistics

**Decision:** Keep variable with stronger Granger causality

#### Scenario 4: Detect Reverse Causality

**Question:** Does marketing drive sales or vice versa?

**Test:**

* Marketing → Sales
* Sales → Marketing

**If only Marketing → Sales:** Marketing drives sales ✓\
**If only Sales → Marketing:** Budget follows performance\
**If both:** Complex bidirectional relationship

### Best Practices

#### When to Use

✅ **Before adding variables:** Validate predictive power\
✅ **Stakeholder skepticism:** Provide statistical evidence\
✅ **Variable selection:** Choose among alternatives\
✅ **Model validation:** Confirm model makes sense

#### When NOT to Use

❌ **Small sample:** Need 30+ observations minimum\
❌ **Obvious relationships:** Don't need test for core channels\
❌ **Real-time decisions:** Test takes time, use judgment\
❌ **Non-time-series:** Data must be time-ordered

#### Configuration Guidelines

**Max Lags:**

* Weekly data: 4-8 lags
* Monthly data: 2-4 lags
* Too many lags: Reduces power
* Too few: Misses relationships

**Significance Level:**

* Use 95% (p < 0.05) as standard
* 99% for stronger evidence
* 90% if exploratory

### Limitations

#### What Granger Causality IS NOT

❌ **Not true causation:** Only predictive relationship\
❌ **Not immediate effect:** Tests lagged relationships\
❌ **Not comprehensive:** Just one piece of evidence\
❌ **Not sufficient alone:** Combine with other tests

#### Considerations

**Can miss:**

* Contemporaneous effects (same period)
* Non-linear relationships
* Complex interactions

**Sensitive to:**

* Lag selection
* Non-stationarity
* Missing data

**Use as:** Supporting evidence, not sole justification

### Troubleshooting

#### All variables show no causality

**Possible causes:**

* Too few lags tested
* Non-stationary data
* Contemporaneous effects (no lag)

**Solutions:**

* Increase max lags
* Check stationarity
* Still include theoretically important variables

#### Stationarity test fails

**All variables non-stationary**

**Solutions:**

* Add trend variable to model
* Use first differences
* Acknowledge limitation in interpretation

#### Test takes very long

**Many variables, many lags**

**Solutions:**

* Test fewer variables
* Reduce max lags
* Test in batches

### Key Takeaways

* Granger Causality tests if past marketing predicts future sales
* P-value < 0.05 indicates significant predictive relationship
* Use to validate variable selection and support business case
* Include stationarity test (ADF) for reliable results
* Not proof of true causation, but strong supporting evidence
* Configure 4 lags for weekly MMM data
* Test marketing variables against KPI (recommended)
* Combine with other validation methods for robust models


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