Why Correlation Does Not Identify a Lead-Lag Relationship

Summary

This discussion asks how to determine which of two highly correlated stocks drives the other. One response suggests testing for Granger causality as a starting point, while warning that the results must be interpreted carefully and that the test has assumptions about possible influences. A predictive relationship in past data should not automatically be treated as proof of economic causation.

Another response argues that shared exposure to a common risk factor can explain high correlation without either stock driving the other. It recommends considering the underlying factors and using principal component analysis to identify factors that may account for the joint movements. No data, test results, or worked example are supplied, so the discussion offers methods to investigate rather than a conclusion about any particular pair. The distinction between predictive timing and causal influence remains central, and factor analysis alone does not establish causation.

Key ideas

• High correlation between two stocks does not by itself show that one causes or leads the other.
• Granger causality can be used to investigate whether one series helps predict another, subject to the test's assumptions.
• A common underlying risk factor may explain the stocks' co-movement.
• Principal component analysis can help identify shared factors in a group of related assets.
• Statistical lead-lag evidence requires careful interpretation and does not automatically establish economic causation.

Tags

# Two correlated time series - driver and follower


# Two correlated time series - driver and follower












Say that there are two time series of highly correlated stocks one of which is the driver and the second one follows the first one.

What mathematical measure or formula would you use to identify which one is the driver and the follower?

## Answer by Rusan Kax (score 3, accepted)

https://quant.stackexchange.com/a/15950

What techniques have you tried?

If none, you could start with looking into Granger Causality @wiki by, perhaps, using this Bivariate Granger Causality R tool

You have to be quite careful in how you interpret the results, as there are constraints on what the possible factors of influence can be (when testing for Granger Causality).

## Answer by QuantK (score 1)

https://quant.stackexchange.com/a/16038

The anwser is clear cut, there isn't one. The high correlation between the 2 stocks is explained by a common underlying risk factor, for example both 2 gold mining companies. This common factor explains the high correlation. The correlation doesn't mean that one 1 stock drives the other, meaning actual causation.

The best you can do is think about risk factors that could explain the high correlation and then use principle component analysis to select those which fit best.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.