Intended for students and researchers, this text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals. It provides a broad collection of theorems, placing the techniques on firm theoretical ground. The techniques, which are illustrated by data analyses, are discussed in both a heuristic and a formal manner, making the book useful for both the applied and the theoretical worker. An extensive set of original exercises is included. Time Series: Data Analysis and Theory takes the Fourier transform of a stretch of time series data as the basic quantity to work with and shows the power of that approach. It considers second- and higher-order parameters and estimates them equally, thereby handling non-Gaussian series and nonlinear systems directly. The included proofs, which are generally short, are based on cumulants.