# Pearson correlation coefficient based on OHLC data

Pearson correlation coefficient based on OHLC data

I've found only this article "Estimating correlation from high, low, opening and closing prices" by L. C. G. Rogers and Fanyin Zhou (2007) http://www.skokholm.co.uk/wp-content/uploads/2013/02/RZdraft.pdf about the topic of question, so I would like to ask if there is standard approach of using OHLC data which incorporates high and low prices into estimation process ?

Given only OHLC information, with no timing information as when H and L occured in relation to one another, the covariance between any two assets is only defined for O and C since you know when these occurred in relation to one another. If you use H and L in a co-movement estimator, it must be assumed that H and L of any two assets occured simultaneously. This is a very weak assumption. Therefore, it seems inappropriate to estimate correlation using OHLC. However, it is possible to estimate variance more efficiently using OHLC data than the standard $C_{t}$ to $C_{t-1}$ method.

In order to estimate variance using OHLC data, I highly recommend Yhang Zhang's (YZ) estimator for intraday variance. Please see: Understanding Yang-Zhang Volatility Estimator.

In numerous tests on simulated data, the YZ estimator converges to the actual variance process more efficiently than any other estimator.

Given that:

${\displaystyle \rho _{XY}= \frac{\sigma_{X,Y}}{(\sigma _{X}\sigma _{Y})}}$

you could use YZ to estimate $\sigma_X$ and $\sigma_Y$. However, the correlation may no longer be bounded between $-1$ and $1$. Still, since we know that the realized variances are more likely to estimate the true variance, we can constrain the covariance such that an estimator is bounded appropriately.

Moreover, if its possible to determine when H and L happened in relation to one another, you could use the YZ framework to develop a co-movement estimator than should also converge more efficiently than close-to-close estimators.

• If you have time series then HL must have a lot of info on covariance, and shouldn't be ignored. You don't know exactly the intraday time of HL, but you know the day. There must be MLE of covariance that takes into account HL and OC – Aksakal Apr 30 '17 at 14:20