Testing Lead-Lag Relationships Between Returns and Volatility

Summary

The document discusses ways to investigate whether returns lead volatility or volatility leads returns. One suggested exploratory approach is to compare correlations between time-shifted returns and volatility with correlations between time-shifted volatility and returns. A larger correlation in one direction may suggest a lead-lag pattern, but the answer points to Granger causality as the more established framework for assessing whether one series helps predict another.

It also mentions wavelet methods as an area of academic research on lead-lag detection. The exchange provides no worked example, statistical tests, or guidance on choosing lags and handling nonstationary data. The correlation comparison should therefore be treated as an initial heuristic, not proof of causality or a ready-made trading signal; the answer itself recommends further research before applying it.

Key ideas

• Compare lagged returns with volatility and lagged volatility with returns as an exploratory check.
• A stronger correlation in one direction may suggest which series leads, but does not establish causality.
• Granger causality is identified as a more common method for testing predictive relationships.
• Wavelets are noted as another research approach for detecting lead-lag structure.
• Lag selection and suitability for a particular dataset require further investigation.

Tags

# Finding Lead-Lag Relationship


# Finding Lead-Lag Relationship












Given two series of data, volatility and returns, is there a way (Excel) of finding which one is the leading factor and lagging factor?

Thank you for your help.

## Answer by user38805 (score 2)

https://quant.stackexchange.com/a/44434

Recently there's been a lot of academic work involving wavelets to detect lead-lag relationship. I'm afraid it is still not nearly as common as the ubiquitous Granger Causality mentioned above.

Also, if someone wants to take the discussion more complicated/technical, please go ahead. Who doesn't love arbitrage?

## Answer by Varun (score 1)

https://quant.stackexchange.com/a/44277

You can take the time-lagged values of Returns and check the correlation between these values and the volatility. If the correlation coeff of TL-Returns and the Volatility is more than the correlation coeff of TL-Volatility and Returns, then you can say that Returns is the leading factor and volatility is the lagging factor. But as mentioned in the comments by Nick already, what you are looking for is a Granger Causality. Please do more research on this before using it for your case.

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