The Maximum of the Periodogram of a Non-Gaussian Sequence

摘要: It is a well-known fact that the periodogram ordinates of an lid mean-zero Gaussian sequence at Fourier frequencies constitute exponential vector, hence maximum these has limiting Gumbel distribution. We show for non-Gaussian mean-zero, finite variance this statement remains valid. also prove point process constructed from converges to Poisson process. This implies joint weak convergence upper order statistics ordinates. These results are in agreement with empirically observed phenomenon various functionals have very much same asymptotic behavior as applied sample.