Periodograms and the Method of Averaged Periodograms [Lecture Notes]

Abstract

In this “Lecture Notes” column, we show that it is possible to use deterministic arguments to gain some intuition into why using periodograms without averaging does not work well and why they “fail” in the way they do. We then explain how the probabilistic case can be seen as an extension of the deterministic case. Next, we give a brief description of the method of averaged periodograms and explain how the deterministic perspective points to additional cases where the method of averaged periodograms should prove effective. Finally, we provide several numerical examples to demonstrate the theoretical material, and “A Probabilistic Argument” provides a fairly detailed probabilistic justification that is an extension of the deterministic one.