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.


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