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Introductory Time Series with R (Use R!)
This is good book to get one started on time series. A nice aspect of this book is that it has examples in R and some of the data is part of standard R packages which makes good introductory material for learning the R language too. That said this is not exactly a graduate level book, and some of the data links in the book may not be valid.
A great book if you are in an economics stream or want to get into it. The nice thing in the book is it tries to bring out a oneness in all the methods used. Econ majors need to be up-to speed on the grounding mathematics for time series analysis to use this book. Outside of those prerequisites, this is one of the best books on econometrics and time series analysis.
Pattern Recognition and Machine Learning (Information Science and Statistics)
This is excellent book to own for scientists and engineers wanting to use time series methods in machine learning, forecasting and regression. Great charts and fairly readable text.
Time Series: Theory and Methods (Springer Series in Statistics)
A good book which covers a lot of theoretical aspects but with little practical applications covered. It comes with software so it doesn't really support open source alternatives like R/Python. This is all about a rigorous treatment to Time series analysis (as is the case with most Springer Series). Good for graduate students and academics.
Time Series Analysis
An ideal book for graduate students and it is fairly comprehensive. Lots of essential approaches are covered in this text. Typical ones include Bayesian approaches, Spectral Analysis and the newer vector auto regression. Strongly recommended for graduate students. The book does not cover real world data sets and applications in enough detail.
Time Series Analysis and Forecasting by Example (Wiley Series in Probability and Statistics)
A good book to get an introduction to time series analysis. It stresses more on the signal processing aspects too like auto regressive models. A drawback is the book requires software and does not use open source, likewise there aren't answers to the questions posted. All said a good book to own but do not forget the caveats.