Asymptotic properties of the periodogram of a discrete stationary process

Suppose x 1 , …, x N are indefinitely many observations on a stochastic process which is weakly stationary with spectral density f(λ), – π ≦ λ ≦ π. An asymptotically unbiased, and to that extent plausible, estimate of 4r f ( λ )is the periodogram Yet the periodograms of processes which possess spectral densities are notoriously subject to erratic behavior.