Abstract.In Geweke and Porter‐Hudak's estimator ωd(GPH)of the memory parameter of a long‐memory process, a critical choice the user must make is the number of frequencies,M, to be used in the regression of the log periodogram on log frequency. This choice is critical in practice because by simply varyingMfor a given data set it is often possible to obtain a very wide range of values of the estimator. Although Geweke and Porter‐Hudak have found that choosingMto be the square root of the sample size gave good results in simulation, they gave no theoretical justification for this choice. Here, we propose automatic criteria for selectingM, and another tuning constant used in related estimates of the memory parameter, based on frequency domain cross‐validation. We provide some theoretical and heuristic justification for the proposed criteria. In a simulation study, we compare some of the resulting automatic methods of estimating the memory parameter with existing non‐auto
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