Many people around the world, after the subprime crisis more so , equate correlation with charlatanism. May be , but should that stop anyone from understanding data, not really. Knowing whatever metric about the unknown is much better than just having an intuitive feeling of things. Sometimes having a wrong map while exploring is OK, atleast it gives one confidence to venture and try things out.

Taylor effect is one such aspect about correlation. If you look at a series of returns and consider various metrics, like abs(ret), (ret^2), abs(ret)^2.5 and so on, one can think of this question :

What is the autocorrelation for various lags (let’s say the first 6 lags) for these metrics? This question becomes important when you think about volatility measures ? Should one always go with returns^2 as a metric for vol? what’s wrong with abs(ret), or abs(ret)^1.5 . or why not abs(ret)^2.3434 , whatever!.. What makes ret^2 such a wide spread metric for vol ? Actually with the availability of intraday data, one needs to seriously consider what is a good risk metric ? Anyways, these are questions that will take some time and effort to think about and understand, based on what data/market one is working on.

Coming back to the title of the post, Taylor effect says that correlation of absolute value of returns with its kth lag is always going to be greater than correlation of absolute value of some power of returns with its kth lag.

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Some basic data crunching of NIFTY returns validates this effect to some extent.

**6 lags plotted for various values of d
**Image

One thing to note is that the auto correlation of squared returns for lag =1 is more than the autocorrelation of absolute returns for lag = 1 ( the top most curve in the above figure). Usually it is the otherway round , atleast according to academic literature for US markets.

Why to bother looking at powers like squares cubes of abs(returns) ? Becoz after all volatility is an estimate of what you think captures risk.
What metric to use for volatility is a big question!!!