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The effect of estimating the order of an autoregressive process on estimating the peak frequency is examined. For consistent order determining methods it is shown that the asymptotic results are the same as for the case when the order is known. For the order criteria which asymptotically overestimate the order, the peak frequency estimator is shown to be a consistent estimator of the true peak frequency.
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Ensor et al. (1988) studied this question.
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