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Introduction to Time Series and Forecasting / von Peter J. Brockwell, Richard A. Davis

This book teaches time series and forecasting methods with an emphasis on the fundamentals of data set analysis. It is designed for use in a full-year introduction to univariate and multivariate time series course. This book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The logic and tools of model-building for stationary and nonstationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introductions are also given to cointegration and to nonlinear, continuous-time and long-memory models. The free time series package that accompanies this book is ITSM2000, though the methods can be easily applied to time series packages in other programs, including R. The programs in ITSM are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.