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Econometrics Paper
Gaussian Estimation of Parametric Spectral Density with Unknown Pole
Liudas Giraitis, Javier Hidalgo and Peter M Robinson
August 2001
Paper No' EM/2001/424:
Full Paper (pdf)

Tags: long-range dependence; unknown pole.

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w 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 establsih n-consistency of the estimate of w, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish Vn-consistency and asymptotic normality.