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Given data that arrives at a daily frequency, I aggregated it to a weekly frequency, and estimated an OLS regression on it. Given that there are roughly 5 trading days per week, I can construct 5 different OLS models using 5 different starting points. For example - one model uses returns from Monday-Monday, the next Tuesday-Tuesday, and so on.

Assuming I believe there are no seasonal effects (e.g. models trained using Monday-Monday returns should be no different than Tuesday-Tuesday), is there a correct way to combine the predictions/coefficients of these 5 (or in the general case, N) models? I am inclined to think quick and simple averaging of coefficients would work. In that case, is there a proper way to combine the standard errors and residual standard errors across models? I ask because I am interested in constructing confidence/predictive intervals for forecasts. I hesitate to estimate the model using the full dataset, because this will cause overlaps in my endogenous variable, and I am not well equipped/don't know how to deal with that.

Of course this question could be asked more generally for any (non-linear) kind of model, but it seems like OLS/linear models would have the most hope for a theoretically sound procedure/heuristic.

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  • $\begingroup$ Cross Validated has some related threads: stats.stackexchange.com/questions/tagged/overlapping-data, e.g. this. $\endgroup$ Oct 31, 2022 at 20:32
  • $\begingroup$ Thanks @RichardHardy - I'll be sure to read through them and the references you posted in your answer. $\endgroup$ Oct 31, 2022 at 21:31
  • $\begingroup$ I think it is enough to read the relevant sections of Hayashi's textbook. $\endgroup$ Nov 1, 2022 at 5:55
  • $\begingroup$ I was going through my old answers and noticed this one was not accepted. Do you perhaps need further clarification? $\endgroup$ Apr 17, 2023 at 10:47

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The efficient point estimator would be OLS on all 5-day periods, even though there will be a lot of overlapping. You would need to adjust the standard errors for autocorrelation by using robust standard errors. No model averaging is needed. Here are some references:

  1. Hayashi, Fumio. Econometrics. Princeton University Press (2011). See sections 6.6-6.8.
  2. Britten‐Jones, Mark, Anthony Neuberger, and Ingmar Nolte. "Improved inference in regression with overlapping observations." Journal of Business Finance & Accounting 38.5‐6 (2011): 657-683.
  3. Harri, Ardian, and B. Wade Brorsen. "The overlapping data problem." Available at SSRN 76460 (1998).
  4. Hansen, Lars Peter, and Robert J. Hodrick. "Forward exchange rates as optimal predictors of future spot rates: An econometric analysis." The Journal of Political Economy (1980): 829-853.
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