Detecting Spurious Regressions in Non-Stationary Time Series
Summary
This article explains why regressions between unrelated non-stationary time series can appear convincing. It generates two independent random walks, regresses one on the other, and shows that fit statistics and coefficient significance can falsely suggest a strong relationship. It also describes adding a lagged predictor and discusses high R-squared values alongside low Durbin-Watson statistics as warning signs.
The proposed diagnostic is to test regression residuals for unit roots, with Augmented Dickey-Fuller and KPSS tests given as examples. The article notes that unit-root tests can make both false positive and false negative errors; the warning indicators alone do not establish spuriousness, so further diagnostics and domain knowledge matter. Its synthetic example demonstrates a failure mode rather than establishing how frequently it affects market data. The later trading implementation is only partly visible in the supplied text, so its strategy and validation details cannot be assessed fully.
Key ideas
- Independent non-stationary series can produce apparently significant regressions with misleadingly strong fit statistics.
- A synthetic pair of random walks illustrates how stochastic trends can create false evidence of association.
- Residual unit-root tests, including ADF and KPSS, can help assess whether a regression is spurious.
- High R-squared and low Durbin-Watson values are warning signs, not conclusive proof.
- Unit-root tests have error risks and should be interpreted alongside other diagnostics and domain knowledge.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.