Spectral estimation

Abstract

Wereview spectral analysis and its application in inference for stationary processes. As can be seen from the list of references, the practice of spectral analysis is widespread in diverse scientific and engineering fields, particularly in signal processing and communications. One of the most striking characteristics of time series is their oscillatory behavior. This behavior is manifested, for example, in electroencephalogram (EEG) records, weekly sales, monthly environmental data, hourly financial indices, and in numerous economic data observed periodically in time. When observing such data the intuitive notion of periodicity is inescapable, and this led to the statistical problem of estimation of 'hidden periodicities' in time series. Schuster [47] was among the first who studied the problem seriously, and is credited with the invention of the so-called periodogram, a tool for discovering periodicities in oscillatory data. Consequently, spectral analysis and its ramification was further advanced by the pioneering works of Slutsky, Yule, Khintchine, Wiener, Cramer, Kolmogorov, Bartlett, Tukey, Parzen,Rosenblatt, Grenander, Koopmans, Brillinger, and Hannan. The goal of this communication is to introduce the reader to the topic of spectral analysis, and to review some state-of-the-art developments. It is of course not possible to give a full account of the literature on spectral analysis within this limited space. The selection of the references has been influenced by my own personal research interests . © 2010 John Wiley & Sons, Inc.