Overlapping Returns and Correlation Estimation
Summary
The question concerns estimating covariance and correlation across investment horizons using overlapping historical returns. Rolling windows create serial dependence, which affects estimated volatility and correlation; the author asks whether generalized least squares can correct this when the target is correlation rather than regression coefficients.
The response cautions that overlapping-return patterns can be misleading and difficult to interpret, and advises against applying unfamiliar econometric corrections as black boxes. It questions whether GLS addresses the issue in this setting but does not provide a correction procedure or quantitative evidence. The discussion is therefore a warning about interpretation and econometric understanding, rather than a worked method. It leaves unresolved how to estimate uncertainty or adjust correlation estimates under overlapping observations.
Key ideas
- Overlapping return windows induce autocorrelation that can affect volatility and correlation estimates.
- The question distinguishes correlation estimation from regression settings where generalized least squares may be used.
- The response warns that patterns in overlapping returns can invite misleading interpretations.
- Econometric corrections should be understood before being applied to overlapping data.
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Full text
# Need overlapping sample autocorrelation correction for calculating asset return correlations # Need overlapping sample autocorrelation correction for calculating asset return correlations I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, yield spread,..) to describe asset returns with an AR(1) process. They find US stock and US gov bond correlations between close to 0 and up to 0.6 , depending on the lenght of the investment period. However I want to analyse ex post return data (ranging from 1 month to at least 20 years), starting at 1969. Overlapping data will be used to get a (hopefully) sufficient amount of data points. Now to my question: I am aware that rolling returns induce autocorrelation, this will effect the asset return volatility as well as the correlation coefficients. So I'm looking for correction methods to get rid of the auto correlation probelm. So far I have found something called Generalised Least Square (GLS) which seems to work for overlapping data in case of regression analysis. However I am not sure if this is really applicable in my case since I am measuring correlation coefficients. Are there any corrections for overlapping sample autocorrelation when calculating asset return correlation coefficients? As you might have noticed I am fairly new to the world of econometrics. I have only used excel so far, but am eager to learn R. ## Answer by Richi Wa (score 2) https://quant.stackexchange.com/a/10112 I would advice you not to do any overlapping analysis. The results will be hard to interpret and misleading. I have seen many "practioners" looking at histograms of overlapping returns. They saw interesting patterns and found funny explanations - which were simply wrong. If you are new to econometrics then correction methods (do there exist helpful techniques ?) will be black boxes to you. Then you should not apply them. Finally Generalised Least Square (GLS) - I assume you mean this. How should this help you to correct overlapping samples?
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