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Time series analysis: Introductions
The
Analysis of Time Series: An Introduction
by Chris Chatfield (6th ed, 2003). A readable presentation of time
series theory and practice. Covers autoregressive ARMA/ARIMA models,
Fourier spectral analysis, linear systems, likelihood-based state-space
models, and the Kalman filter, nonlinear models, multivariate time
series, and long-memory models.
An
Introduction to Time Series and Forecasting
by Peter J. Brockwell, Richard A. Davis & P. J. Rockwell (2nd ed,
2002). Undergraduate-level monograph on time series with Windows-based
software. Includes regression with stationary autoregressive ARMA/ARIMA
models, nonstationary ARCH/GARCH models, multivariate time series,
maximum likelihood state space modeling, time series errors, Poisson
data. Methods include Burg, Hannan-Rissanen, EM, Holt-Winters, Kalman,
and other algorithms.
A
First Course in Statistics for Signal Analysis
by Wojbor A. Woyczunski (2006). Text for engineering students on random signal processing. Covers Fourier transforms and power spectra, stationarity and autocorrelation, bandpass and other filters, Gaussian signals, and discrete signals.
Time series analysis: More advanced
A
Wavelet Tour of Signal Processing
by Chibli G. Mallat & Stephane Mallat (2nd ed, 1999). Comprehensive
graduate textbook of wavelet theory and engineering applications with
Matlab-based software. Topics include Fourier methods, wavelet &
related transforms, analog & digital methods, noise removal,
deconvolution, signal and image compression, singularity and edge
detection, multifractal analysis, and time-frequency problems.
Wavelet
Methods for Time Series Analysis
by Donald B. Percival & Andrew T. Walden (2000). Graduate-level
text with emphasis on applications in the physical sciences. Includes
introductions to wavelets and Fourier theory, development of the
discrete wavelet transform, stochastic processes, wavelet variance,
long memory processes, and signal estimation (thresholding, scaling,
shrinkage).
Time
Series Analysis by State Space Methods
by Durbin & S. J. Koopman (2002). Monograph on parametric maximum
likelihood modeling of time series using state space methods, with
applications in econometrics. Topics include linear Gaussian models,
filtering & smoothing, maximum likelihood estimation, Kalman
filtering, Bayesian analysis & Gibbs sampling, nonlinear &
nonGaussian models.
Smoothness
Priors Analysis of Time Series
by Genshiro Kitagawa & Will Gersch (1996). Monographs on Bayesian
approaches to modeling of complex time series in the context of state
space modeling, including applications in the physical sciences. Covers
linear Gaussian state space modeling, nonstationary models and
variance, multivariate time series, inhomogeneous Poisson processes,
quasi-periodic processes, and non-linear smoothing.
Stochastic processes
Introduction to Probability Models
by Sheldon M. Ross (9th ed, 2006). Popular undergraduate-level textbook on stochastic processes. Topics include introduction to probability theory and random variables, conditional probability, Markov chains, Poisson processes, renewal theory, queueing theory, reliability theory, Brownian motion & stationary processes, and simulation techniques.
Stochastic Processes & Models
by David Stirzaker (2005). Well-written undergraduate-level text from Oxford introducing stochastic processes. Covers random variables; martingales and Poisson processes, Markov chains, Monte Carlo simulation, birth processes and queues, and diffusion processes.
Statistical Analysis of Stochastic Processes in Time
by James K. Lindsey (2004). Moderately advanced text on stochastic processes with R code available. Topics include state space modeling, survival processes, Markov chains, dynamic models (hidden Markov models & Kalman filtering), doubly stochastic processes, change points, autoregression, spectral analysis, growth curves, and repeated measurements.
Poisson Processes
by J. F. C. Kingman (1993). Slim, insightful volume arguing for the importance of Poisson processes in the theory of random processes. Discusses Poisson processes, various theorems, Poisson processes on a line, marked Poisson processes, Cox processes, stochastic geometry, and the Poisson-Direchlet distribution.
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