Need help: Correlation of aggregated data

giangle · 11-19-2007, 01:48 PM

Please help me to answer/get reference for this question: Is it possible to derive cross correlation of two monthly (price) series aggregated from two daily series with known distributions. Thanks.

ngtridung · 11-20-2007, 07:25 AM

Let $X_t$ and $Y_t$ be the two time series. The answer depends on your assumptions The popular assumptions are: $X_t$ are IID, $Y_t$ are IID, $corr(X_t, Y_s) = 0, for~ t \neq s$ . With these assumptions, you can show:
$Corr(\bar{X}, \bar{Y}) = \frac{cov(\bar{X}, \bar{Y}) }{\sqrt{Var(\bar{X})*Var(\bar{Y})} } = \frac{1/n*cov(X_t, Y_t) }{1/n*\sqrt{Var(X_t)*Var(Y_t)} } = corr(X_t,Y_t)$

neomikeo · 11-20-2007, 05:43 PM

This might not work because monthly and daily data might have different distributions. Because it is aggregated from 22 trading days, the Central Limit Theorem tells that monthly data tends to be normally distributed. Daily data is not normal as it is subject to things like microstructure effects, nonsynchronous trading and conditional variance and covariance.
What ngtridung writes is more unconditional correlation, while conditional correlation might time vary a lot. This is the same like you have daily data and think that tick data would behave the same.
The best way if you could is still getting the raw data for monthly and daily data and work on these separately.

giangle · 11-21-2007, 08:37 AM

I just did some quick simulations and the evidence seems to support neomikeo line. It looks like the answer to my question is NO and I have to treat daily and monthly series with two independent distributions.

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Need help: Correlation of aggregated data

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