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Gaussian estimation of parametric spectral density with unknown pole

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We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency !. The case of known !, especially ! = 0, is standard in the long memory literature. When ! is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establish n ¡ consistency of the estimate of !, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish P--n- consistency and asymptotic normality.

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en

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application/pdf

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http://eprints.lse.ac.uk/297/1/Ann_Stat_29-4.pdf

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