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re: st: Correction for overlapping return series

From   Kit Baum <>
Subject   re: st: Correction for overlapping return series
Date   Wed, 10 Feb 2010 20:21:27 -0500

Malcolm said

I have a series of annual returns on one-year futures contracts for every month they expire.  Essentially I have a monthly time series of annual returns.  I'm regressing these on a similarly calculated annual return series.  Assuming for a moment that the series is i.i.d from year to year, how do I correct for the fact that I have 12 quasi-overlapping observations in each year?  I feel like the answer to this question should be easy, but I'm not sure I'm doing it right.

Hansen and Hodrick solved this problem some time ago. I believe the correct cite is
Hansen, L.P., Hodrick, R.J.. "Forward Exchange-Rates As Optimal Predictors of Future Spot Rates - An Econometric-Analysis." Journal of Political Economy 88: 829-853, 1980.

Essentially if you overlap by 12, you are creating a MA(11) in the errors. (The more common issue, three-month T-bill rates observed monthly, gives rise to MA(2)). So applying a HAC estimator (e.g. Newey-West) with lag length = 11 should do it. Yes, this models the errors as AR(11) rather than MA(11), but it works. You can do this with -newey-.


Kit Baum   |   Boston College Economics & DIW Berlin   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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