With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explores the connections among stochastic dynamic models. Emphasizing the time domain description, the author presents theorems to highlight the most important results, proofs to clarify some results, and problems to illustrate the use of the results for modeling real-life phenomena.
The book first provides the formulas and methods needed to adapt a second-order approach for characterizing random variables as well as introduces regression methods and models, including the general linear model. It subsequently covers linear dynamic deterministic systems, stochastic processes, time domain methods where the autocorrelation function is key to identification, spectral analysis, transfer-function models, and the multivariate linear process. The text also describes state space models and recursive and adaptivemethods. The final chapter examines a host of practical problems, including the predictions of wind power production and the consumption of medicine, a scheduling system for oil delivery, and the adaptive modeling of interest rates.
Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems. It will help you understand the relationship between linear dynamic systems and linear stochastic processes.
Introduction
Examples of time series
A first crash course
Contents and scope of the book
Multivariate random variables
Joint and marginal densities
Conditional distributions
Expectations and moments
Moments of multivariate random variables
Conditional expectation
The multivariate normal distribution
Distributions derived from the normal distribution
Linear projections
Problems
Regression-based methods
The regression model
The general linear model (GLM)
Prediction
Regression and exponential smoothing
Time series with seasonal variations
Global and local trend model—an example
Problems
Linear dynamic systems
Linear systems in the time domain
Linear systems in the frequency domain
Sampling
The z transform
Frequently used operators
The Laplace transform
A comparison between transformations
Problems
Stochastic processes
Introduction
Stochastic processes and their moments
Linear processes
Stationary processes in the frequency domain
Commonly used linear processes
Non-stationary models
Optimal prediction of stochastic processes
Problems
Identification, estimation, and model checking
Introduction
Estimation of covariance and correlation functions
Identification
Estimation of parameters in standard models
Selection of the model order
Model checking
Case study: Electricity consumption
Problems
Spectral analysis
The periodogram
Consistent estimates of the spectrum
The cross-spectrum
Estimation of the cross-spectrum
Problems
Linear systems and stochastic processes
Relationship between input and output processes
Systems with measurement noise
Input-output models
Identification of transfer-function models
Multiple-input models
Estimation
Model checking
Prediction in transfer-function models
Intervention models
Problems
Multivariate time series
Stationary stochastic processes and their moments
Linear processes
The multivariate ARMA process
Non-stationary models
Prediction
Identification of multivariate models
Estimation of parameters
Model checking
Problems
State space models of dynamic systems
The linear stochastic state space model
Transfer function and state space formulations
Interpolation, reconstruction, and prediction
Some common models in state space form
Time series with missing observations
ML estimates of state space models
Problems
Recursive estimation
Recursive LS
Recursive pseudo-linear regression (RPLR)
Recursive prediction error methods (RPEM)
Model-based adaptive estimation
Models with time varying parameters
Real life inspired problems
Prediction of wind power production
Prediction of the consumption of medicine
Effect of chewing gum
Prediction of stock prices
Wastewater treatment: Using root zone plants
Scheduling system for oil delivery
Warning system for slippery roads
Statistical quality control
Modeling and control
Sales numbers
Modeling and prediction of stock prices
Adaptive modeling of interest rates
appendix A: The solution to difference equations
appendix B: Partial autocorrelations
appendix C: Some results from trigonometry
appendix D: List of Acronyms
appendix E: List of symbols
Bibliography
Index
Biography
Henrik Madsen
"In this book the author gives a detailed account of estimation, identification methodologies for univariate and multivariate stationary time-series models. The interesting aspect of this introductory book is that it contains several real data sets and the author made an effort to explain and motivate the methodology with real data. … this introductory book will be interesting and useful not only to undergraduate students in the UK universities but also to statisticians who are keen to learn time-series techniques and keen to apply them. I have no hesitation in recommending the book."
—Journal of Time Series Analysis, December 2009"The book material is invaluable and presented with clarity … it is strongly recommended to libraries and all who are interested in time series analysis."
—Hassan S. Bakouch, Tanta University, Journal of the Royal Statistical Society"Although the book is simply called Time Series Analysis, it is really a time series text for engineers—and that is a good thing … I see this text as a marble cake, mixing time series analysis and engineering in harmony, frosted with applications, and ready for students to gobble up."
—Joshua D. Kerr, California State University–East Bay, Journal of the American Statistical Association, June 2009, Vol. 104, No. 486"It is a very important and useful book which can be seen as a text for graduates in engineering or science departments, but also for statisticians who want to understand the link between models and methods for linear dynamical systems and linear stochastic processes."
—T. Postelnicu, Zentralblatt MATH, 2009
