I am currently working through this paper on overlapping observations by Britten-Jones, Neuberger and Nolte 1, which presents an estimation method for correcting standard errors when performing inference on overlapping observations.

In order to evaluate different estimators (White, Newey-West, Hansen-Hodrick), they perform Monte Carlo simulations of AR processes with different configurations described at the bottom of page 12 and the top of page 13. In Table 1 on page 15 they give the numerical results of the simulations for one configuration (with Obs being the total number of observations in a single simulated path and $k$ being the number of overlapping periods). The column Bias gives the bias of the standard errors for the different estimators based off the simulations.

It is clear to me how to calculate the values for the different estimation methods, but the Bias column shows their difference to the true standard error. Is my understanding of the Bias column correct?

If it is, how can the true standard error be calculated for the various processes? Do analytical solutions exist for the various AR configurations listed in the article?

1 Britten-Jones, Mark, Neuberger, Anthony and Nolte, Ingmar (2011) Improved inference and estimation in regression with overlapping observations. Journal of Business Finance & Accounting, Vol.38 (No.5-6). pp. 657-683.



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