Spectral density estimation for linear processes with dependent innovations

This paper considers the problem of estimating the spectral density of a linear process whose innovations are uncorrelated and strongly mixed. We prove that the Periodogram ordinates In([lambda]i) at any set of frequencies [lambda]1,...,[lambda]m,0<[lambda]1<...<[lambda]m<[pi], are asymptotically independent exponential random variables with means 2[pi]f([lambda]i). Consequently the periodogram In is not a consistent estimator of 2[pi]f. Consistent estimators can, however, be constructed by applying linear smoothing filters to the periodogram.