IWR Colloquium Summer Semester 2025 A Brief History of the Periodogram and its Application to Time Series Analysis

The origins of time series analysis trace back to the late 19th century, when Arthur Schuster first introduced the periodogram to detect periodicities in time series data. We begin by revisiting Schuster’s early contributions, along with the follow-up work of Udny Yule and Gilbert Walker, which together laid the foundations of modern time series analysis. Central to the analysis is the periodogram and its close cousin, the spectral density function. We next look at parametric and nonparametric models used for estimating the spectral density function, with special attention to the seminal work of Peter Whittle. In the 1950s, while a PhD student, he introduced the "Whittle likelihood"; a computationally efficient method for fitting parametric models to time series data. This approach relies on approximating the inverse of a Toeplitz matrix with a circulant matrix. The final part of this talk turns to more recent developments motivated by high dimensional time series. The past decade has seen active research into the usage of spectral methods in graph estimation, which we will review.