References
The descriptions above only scratch the surface of stationary time series. There are wide range of stationary time series models, methods for estimation of autocorrelation and the spectrum as well as methods for multivariate stationary series, series with heavy-tailed and forecasting future values. The following references cover much of this for stationary series (and some mention nonstationary concepts also).
A good all-round reference is Chatfield, C. (2003) The Analysis of Time Series: An Introduction, Chapman and Hall/CRC Press, sixth edition.
An excellent reference that makes use of the R programming language to explain and expand is Shumway, R.H. and Stoffer, D.S. (2010) Time Series Analysis and Its Applications: With R Examples, Springer Texts in Statistics.
For time series in economics and related fields the books by Hamilton, J. (1994) Time Series Analysis, Princeton University Press and Tsay, R.S. (2010) Analysis of Financial Time Series, Wiley are excellent.
Other books on my bookshelf are (in alphabetical order):
Brillinger, D.R. (2001) Time Series : Data Analysis and Theory, SIAM.
Brockwell, P.J. and Davis, R.A. (2009) Time Series: Theory and Methods, Springer Series in Statistics.
Hannan, E.J. (1960) Time Series Analysis, Methuen, Wiley.
Percival, D.B. and Walden, A.T. (1993) Spectral Analysis for Physical Applications, Cambridge University Press.
Priestley, M.B. (1982) Spectral Analysis and Time Series, Academic Press.
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