Mike West, a towering figure in the field of statistics, coauthored this book. The targeted readers are graduate students in science and engineering and researchers working on time series modeling. The contents presented in the book cover advanced topics in stochastic processes--particularly the Bayesian approach to time series modeling. Therefore, readers must already be familiar with probability and statistics and some very basic concepts in stochastic processes in order to fully digest the book.
The authors systematically develop a state-of-the-art analysis and modeling of time series. There are ten chapters, each of which presents a modeling topic, along with real-world examples such as biomedical signal analysis.
Chapters 1 through 3 provide fundamental information about stochastic processes. Chapter 1 reviews likelihood, estimation, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. Chapter 2 presents modeling methods in the time domain. As its name suggests, time series are data points recorded over time. Popular methods--for example, autocorrelation--analyze the changes of data points in the time domain. This chapter emphasizes autoregressive models, autoregressive moving average models, and Bayesian inference for these models. In contrast to chapter 2, chapter 3 looks at time series in the frequency domain. Time series usually contain cyclic patterns. Decomposing a time series into waves with distinct frequencies is another way to investigate time series. The book addresses harmonic regression models, the periodogram, and Bayesian spectral analysis.
Chapter 4 discusses dynamic linear models. To achieve data tracking and forecasting, dynamic models are a popular choice. This chapter begins reviewing dynamic linear models and their extensions. The authors also present Gaussian and non-Gaussian dynamic models, MCMC for filtering, parameter learning, and smoothing.
Chapters 5 and 6 address state-space models. Chapter 5 focuses on time-varying autoregressive models. Time series in real-world problems--for example, finance--usually do not have static parameter values. Therefore, we need a way to update parameters over time; chapter 5 provides us with the solutions. Chapter 6 raises more advanced techniques, presenting the sequential Monte Carlo approach to state-space models. The topics include data resampling, Storvik’s algorithm, particle filtering, and parameter learning.
Chapter 7 discusses mixture models. In most cases, a single model is not able to appropriately describe a time series over time. For example, a patient’s electroencephalography (EEG) may behave differently before and after treatment, and the price of a stock has unique patterns in distinct economic cycles. The topics covered include multiprocess models and stochastic volatility models.
Chapter 8 considers modeling time series that result from mixtures of time series. For example, the S&P 500 Index is a weighted average of 500 stocks. Another example is the weather forecast, which is based on recordings of sensors distributed over multiple towns. The authors provide several models handling multiple time series with the same underlying structure.
Extensions of chapter 8, chapters 9 and 10 close the book by discussing advanced topics regarding multivariate models. A time series generated by multiple sources can be considered a multivariate time series--that is, a combined recording of various random variables over time. Chapter 9 discusses multivariate autoregressive models and how we can represent their mathematical manipulation in matrix format. Chapter 10 presents multivariate dynamic models and multivariate graphical models.
In summary, this book is well organized and well written. The authors present various statistical models for engineers to use to solve problems in time series analysis. Readers no doubt will learn state-of-the-art techniques from this book.
