Part VI · Chapter 17
Spurious Regression
Two independent random walks can produce R² > 0.9 and "significant" t-stats — but the relationship is entirely accidental. Granger–Newbold (1974) made this famous.
Learning objectives
Reproduce a spurious regression from two random walks.
Spot the symptoms: high R², low DW, persistent residuals.
Apply the Granger-Newbold rule R² > DW.
Fix by differencing or testing cointegration.
Fake Regression Generator
Seed:
Regression output
Estimated β: —
R²: —
t-stat (β): —
Durbin-Watson: —
📐 Symptoms of spurious regression
\[ R^2 > DW \;\Rightarrow\; \text{Granger-Newbold spurious-regression flag} \]
High R² could just be shared drift
Low DW (≪ 2) residuals highly autocorrelated
Non-stat residuals ADF fails to reject
Phillips (1986) t-stat diverges as n grows
🔍 What to look for
- Levels regression often shows R² > 0.9 by accident — DW near 0.
- Switch to differences: R² collapses to near zero (correct result for unrelated series).
- Real relationship would survive the differencing — see Ch 20 (cointegration).
⚠️ Pro Tip: What to Avoid
Student says
"R² = 0.94 and t = 18 — the relationship is real."
Why this is wrong
With I(1) variables, standard inference breaks down. High R² can be entirely from coincidental trending; DW near 0 betrays the trap.
Correct interpretation
Check DW, residual stationarity (ADF), apply Granger-Newbold rule. If spurious, difference both series or test for cointegration.
📝 Mini-quiz
📋 Key Takeaways
| Symptom | Spurious indicator |
|---|---|
| R² | > 0.7 with I(1) regressors |
| DW | < 1 (strong positive AC) |
| R² > DW | Granger-Newbold flag |
| Residual ADF | Fails to reject = non-stationary |
| Fix | Difference or test cointegration |