The Distribution of Periodogram Ordinates

Abstract. The empirical distribution function of y i = I (ω j) /2π f (ω j), ω j = 2π j / T, where I (ω) is the periodogram for a set of observations from a stationary time series with spectral density f (ω), is shown to converge, almost surely, to the distribution with density exp (‐ x), under appropriate conditions. The same methods are used to prove the convergence, almost surely, of an estimate of the prediction error variance constructed from the I (ω j) and of the complex empirical distribution function based on the Fourier coefficients.