Granger Causality Tests

Validate Predictive Relationships in Your Model

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