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This question already has an answer here:

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.

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marked as duplicate by vonjd, skoestlmeier, LocalVolatility, byouness, Lliane Mar 6 at 8:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Isn’t this a question of Granger Causality? I presume you don’t want anything more complicated/subtle (because one can get a whole lot more complicated!) $\endgroup$ – Nick Firoozye Feb 25 at 4:46
  • $\begingroup$ Have a look at VAR models - en.wikipedia.org/wiki/Vector_autoregression. $\endgroup$ – LocalVolatility Feb 25 at 11:08
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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?

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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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