Exponentially Weighted Correlations for Emphasizing Recent Returns
Summary
The document describes ways to estimate correlations that give more weight to recent observations. One method applies exponential weighting directly to the products of paired returns to estimate covariance, then normalizes by the corresponding standard deviations. Another calculates exponentially weighted means and variances, centers each return on its weighted mean, and averages the products of these centered returns before normalizing. The covariance expression shown assumes zero average returns; the answer notes that more general versions are possible.
A further suggestion first calculates rolling correlations over shorter subperiods and then applies an exponential average to those estimates, indirectly emphasizing recent relationships. These approaches resemble exponentially weighted moving averages and allow responsiveness to be adjusted through the decay or window choices. The document offers formulas and procedural descriptions but no empirical comparison of their accuracy, stability, or usefulness. Estimates can differ depending on whether weighting is applied to covariances or to rolling correlation values.
Key ideas
- Exponential weighting can be applied to return cross-products to estimate covariance with greater emphasis on recent data.
- Normalize exponentially weighted covariance by weighted standard deviations to obtain correlation.
- Center returns on exponentially weighted means when estimating covariance with nonzero average returns.
- An alternative is to smooth rolling correlation estimates with an exponential average.
Tags
Full text
# age-sensitive correlation measurements in finances
# age-sensitive correlation measurements in finances
When it comes to comparing returns or prices of instruments like stocks/ETFs, are there any well-established formulas, or ones in common use, that place stronger emphasis on recent correlations more than on historical correlations farther in the past?
An analogy could be the relationship between a simple moving average and an exponential moving average, which weighs more recent prices more heavily.
Comments on relative usefulness also welcome. Fresh in mind is some wisdom I read elsewhere on this site.
If possible try to point out which correlation recipe it may be based off of (some examples).
## Answer by Nemis (score 4, accepted)
https://quant.stackexchange.com/a/3062
You can use the Exponentially Weighted Average directly aswell, finding the covariances and then normalizing back to the correlations:
$ \sigma_{t+1,jk} = (1-\lambda) \sum_{n=0}^\infty \lambda^{n} r_{j,t-n} r_{k,t-n} $
(this assumes average returns 0 etc etc. More general versions can be derived)
## Answer by Joshua Chance (score 3)
https://quant.stackexchange.com/a/3074
1) Calculate exponential averages (EMA) for time series A & B.
2) Calculate exponential standard deviations for A & B. My little hack for this is to calculate an EMA of squared returns, then subtract the squared EMA of simple returns, then take the square root of this.
sqrt( ema(return^2) - ema(return)^2 )
3) Apply the same concept to calculating an exponentially weighted correlation. Instead of summing the products of the two time series' comovements and dividing by the product of their standard deviations you would take A's current return minus its EMA & multiply this with B's return minus EMA. Now take an EMA of this product and divide by (A's exponential stdev times B's exponential stdev).
Sorry but I don't know LaTex, if someone would like to turn my wordy explanation into a much more elegant equation then please feel free to edit this.
## Answer by Kyle Balkissoon (score 1)
https://quant.stackexchange.com/a/3060
Try this:
Given some time horizon of K, which can be divided into subperiods of N, you will calculate a rolling correlation coefficient of length N, then you can use the EMA to weight the more recent correlation coefficient heavier (indirectly weighting the recent relationship more, vs the medium term part).
Never came up with this problem in my work so far however it inspired me to try some stuff out :)Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.