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.


1 Answer 1


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?

  • $\begingroup$ As is said I'm not sure if GLS is appropriate but I found this paper which finds that GLS is superior to other methods that also account for the moving average effect in overlapping samples. However I have not looked deeper into the matter and don't know yet how to apply it in my case. $\endgroup$ Jan 30, 2014 at 15:45
  • $\begingroup$ Also, I don't think there is any other option than to use overlapping samples, since I would be left with to few datapoints considering the long term horizons (20 yrs) I am aiming for. Non-overlapping data would only give me three 20yr returns since 1969... $\endgroup$ Jan 30, 2014 at 15:53
  • $\begingroup$ The paper that you refer to is certainly interesting, but I would not advise you to use the method if you are not familiar enough with time series analysis. For the second comment: you want to calculate asset return correlations for 20 years ... remember 1989 (opening of Eastern Europe), introduction of the Euro in Europe around the year 2000, dot.com bubble, 2008 crash. What do you want to model/predict/estimate based in 20 year periods? You have a bit more than 2 such periods from the end of WW2 1945 until 1989 ... $\endgroup$
    – Richi Wa
    Jan 30, 2014 at 16:33
  • $\begingroup$ I want to explore the time varying covariance structure of asset returns. Traditional mean variance analysis implicitly assumes a linear structure of the asset return correlations, meaning the covariance matrix of a 5 year sample is alos used for estimating a a 20 yr period. However there is substantial evidence that correlations change with increasing investment horizon. A myopic portfolio investor could therefore have a much riskier portfolio in the long run that he might be aware of. Thats what I want to show with histrocial returns. $\endgroup$ Jan 30, 2014 at 17:37
  • $\begingroup$ However the limiting factor is of course the available data. If i want to use international stocks as one of the asset classes, the MSCI World Total Return index only provides monthly returns since 1969... And even if I would use US. Stocks since 1900, I would still only have 5 data points (for the 20 yr return), that can't be enough?!... So let's say I want to use overlapping data (I believe I can aquire the necessary knowledge) what correction method should i use? $\endgroup$ Jan 30, 2014 at 17:44

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