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The subject of time series is of considerable interest, especially among researchers in econometrics, engineering, and the natural sciences. As part of the prestigious Wiley Series in Probability and Statistics, this book provides a lucid introduction to the field and, in this new Second Edition, covers the important advances of recent years, including nonstationary models, nonlinear estimation, multivariate models, state space representations, and empirical model identification. New sections have also been added on the Wold decomposition, partial autocorrelation, long memory processes, and the Kalman filter. Major topics include: Moving average and autoregressive processes Introduction to Fourier analysis Spectral theory and filtering Large sample theory Estimation of the mean and autocorrelations Estimation of the spectrum Parameter estimation Regression, trend, and seasonality Unit root and explosive time series To accommodate a wide variety of readers, review material, especially on elementary results in Fourier analysis, large sample statistics, and difference equations, has been included.