ASYMPTOTIC PROPERTIES OF CUMULANT SPECTRAL DENSITY ESTIMATORS

Abstract

This paper examines the limiting distribution of estimates of cumulant spectral densities. The proposed estimator of the cumulant spectral density is constructed by replacing product moments with estimates of product moments according to the definition of the cumulant, followed by taking a weighted Fourier transform of these estimated cumulants. Kim (1989) showed this estimator to be consistent. Under stationarity and ρ-mixing, asymptotic normality is shown to obtain.