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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
Kit Baum | Boston College Economics & DIW Berlin | http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata | http://www.stata-press.com/books/imeus.html
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