Some asymptotic results for the periodogram of a stationary time series

Let x 1, x 2, …, x n, be n consecutive observations generated by a stationary time series x, t = 0, ±1, ±2, …, with E (x t 2) < ∈. The periodogram of the set of observations, which may be defined as a function I n of angular frequency with range 0, π that is proportional to, plays an important part in methods of making inferences about the structure of x t, particularly its spectral distribution function or spectral density.