## Gaussian estimation of parametric spectral density with unknown pole.(English)Zbl 1012.62098

Summary: We consider a parametric spectral density with power-law behavior about a fractional pole at the unknown frequency $$\omega$$. The case of known $$\omega$$, especially $$\omega =0$$, is standard in the long memory literature. When $$\omega$$ 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 $$\omega$$, and discuss its (non-standard) limiting distributional behavior. For the remaining parameter estimates, we establish $$\sqrt{n}$$-consistency and asymptotic normality.

### MSC:

 62M15 Inference from stochastic processes and spectral analysis 62F12 Asymptotic properties of parametric estimators 62E20 Asymptotic distribution theory in statistics
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### References:

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