Time Series Analysis and Its Applications, second edition, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using non-trivial data illustrate solutions to problems such as evaluating pain perception experiments using magnetic resonance imaging, monitoring a nuclear test ban treaty, evaluating the volatility of an asset, or finding a gene in a DNA sequence. The book is designed to be useful as a text for graduate level students in the physical, biological and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Material from the first edition of the text has been updated by adding examples and associated code based on the freeware R statistical package. As in the first edition, modern developments involving categorical time series analysis and the spectral envelope, multivariate spectral methods, long memory series, nonlinear models, longitudinal data analysis, resampling techniques, GARCH models, stochastic volatility models, wavelets, and Monte Carlo Markov chain integration methods are incorporated in the text. In this edition, the material has been divided into smaller chapters, and the coverage of financial time series, including GARCH and stochastic volatility models, has been expanded. These topics add to a classical coverage of time series regression, univariate and multivariate ARIMA models, spectral analysis and state-space models.