Existence of a time-series spectral density
= Existence of a time-series spectral density
A <weakly stationary process> has a <time-series spectral density> precisely when its <spectral measure of a stationary time series> is <absolutely continuous with respect to> <Lebesgue measure>. Absolute summability of its <autocovariances> is sufficient and yields a continuous Fourier-series density. It is not necessary for existence; for a general integrable density, <Fejér sums> give an $L^1$ recovery formula.