GAUSSIAN SEMIPARAMETRIC ESTIMATION FOR RANDOM FIELDS
WITH SINGULAR SPECTRUM
Abstract: We analyze the asymptotic behaviour of the tapered discrete Fourier transforms for
random fields with singular spectrum. The results are used to establish consistency and
asymptotic normality for semiparametric estimates of the singularity parameter under broad
conditions.
2000 AMS Mathematics Subject Classification: 60G60, 62M15, 62G20.
Key words and phrases: Discrete Fourier transforms, random fields, singular spectrum,
Whittle semiparametric estimates.