Some asymptotic results for the periodogram of a stationary time series

Abstract

Let x1, x2,…, xn, be n consecutive observations generated by a stationary time series {x}, t = 0, ±1, ±2,…, with E(xt2) < ∈. The periodogram of the set of observations, which may be defined as a function In of angular frequency with range [0, π] that is proportional to , plays an important part in methods of making inferences about the structure of {xt}, particularly its spectral distribution function or spectral density.