Direct Estimation of the Spectrum of Stationary Stochastic Processes

The spectrum of real-valued stationary stochastic processes is estimated directly from observations. The estimators are shown to be unbiased and consistent. A method is proposed for estimating the spectra of the additive components of the observed process $X(t)$ of the form $X(t)=X_r(t)+X_s(t)+V(t)$, where $X_r(t)$ is a regular stochastic process, $X_s(t)$ is a singular stochastic process, and $V(t)$ is white noise.