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I am running regressions of long-horizon gross financial returns $$R_{t+k} = \prod_{i=1}^{k} R_{t+i}$$ where $R_t=1+r_t$, on current dividend-price ratios $DP_t=\frac{D}{P}_t$: $$R_{t+k}=\alpha +\beta DP_t+\epsilon_t.$$ The way in which the dependent variable is defined generates some sort of autocorrelation in the error terms obtained by OLS. Does this mean that the standard errors for $\beta$ and $\alpha$ are inefficient? Does this methodology also give rise to heteroscedasticity?

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The estimators of standard errors are downward biased and inconsistent (as they are also asymptotically biased) since they neglect positive autocorrelation.

There need not be heteroskedasticity if there is no heteroskedasticity in single-period returns. But if there is, there will also be heteroskedasticity in your multiple-period returns.

How to deal with overlapping observations is discussed in sections 6.6-6.8 of Hayashi "Econometrics". Basically, the optimal point estimate is the OLS estimate (as simple as that!), but the standard errors need to be adjusted for autocorrelation (e.g. as in Newey-West).

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  • $\begingroup$ Does GLS help in this case? $\endgroup$
    – Mr Frog
    Nov 27, 2021 at 18:20
  • $\begingroup$ @MrFrog, not really, as the optimal point estimate is OLS, though the standard errors need to be adjusted. $\endgroup$ Nov 27, 2021 at 19:45

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