Two series can track each other closely and have nothing to do with one another. Correlation measures co-movement. It has no opinion about why the co-movement exists, and several mechanisms manufacture it out of nothing.
The four common manufacturers
| Mechanism | How it creates the correlation | The usual fix |
|---|---|---|
| Common trend | Both series rise over the sample for unrelated reasons | Correlate changes, not levels |
| Overlapping windows | Consecutive observations share most of their data | Sample at the horizon length |
| Small sample | Few observations, wide sampling distribution | Require a minimum count and report the error bar |
| Selection from many pairs | The strongest pair from a large scan | Apply a multiple-testing penalty |
Common trends are the most frequent cause in Indian macro work. Index of Industrial Production and a capital goods index have both risen since 2010. Correlate the levels and you get something near 0.9, driven entirely by two upward slopes. Correlate month-on-month changes and the number typically collapses toward zero. Levels of trending series correlate almost by default, so the level correlation is not a finding.
Overlapping windows are the quiet one. Rolling 12-month returns sampled monthly reuse eleven months of data at each step. The series looks smooth, the correlation looks stable, and both are artefacts of the overlap rather than evidence of a relationship. The independent sample size is closer to the number of non-overlapping windows.
Small samples do not need a mechanism at all. With 20 observations, two pure noise series produce a correlation above 0.44 about 5% of the time, which is high enough to look like a discovery on a chart.
How to tell the difference
Split the sample in half and compute the correlation separately in each half. A relationship that holds in one half and vanishes in the other is not a relationship. Then check whether the association survives on differences rather than levels, and whether it survives after controlling for the obvious common driver, which in Indian equities is usually the Nifty itself.
A mechanism you can state in a sentence is the strongest filter. If you cannot say who is trading on what information and why the effect persists, treat the correlation as a coincidence until proven otherwise.
Caveats
Rank correlation is more robust to outliers than Pearson, but it is equally vulnerable to shared trends and overlapping windows. Switching to Spearman does not fix a spurious result.
Statistical significance does not rule out spuriousness. A trending pair will produce a large t-statistic precisely because the trend is persistent, which is the thing generating the false signal.
Regime changes create the reverse error too. A real relationship can break down when policy or market structure shifts, so stability across halves is necessary rather than sufficient.