Time Series Analysis: 1st Edition (Hardback) book cover

Time Series Analysis

1st Edition

By Henrik Madsen

Chapman and Hall/CRC

400 pages | 69 B/W Illus.

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pub: 2007-11-28
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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.


"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

Table of Contents



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


Regression-based methods

The regression model

The general linear model (GLM)


Regression and exponential smoothing

Time series with seasonal variations

Global and local trend model—an example


Linear dynamic systems

Linear systems in the time domain

Linear systems in the frequency domain


The z transform

Frequently used operators

The Laplace transform

A comparison between transformations


Stochastic processes


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


Identification, estimation, and model checking


Estimation of covariance and correlation functions


Estimation of parameters in standard models

Selection of the model order

Model checking

Case study: Electricity consumption


Spectral analysis

The periodogram

Consistent estimates of the spectrum

The cross-spectrum

Estimation of the cross-spectrum


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


Model checking

Prediction in transfer-function models

Intervention models


Multivariate time series

Stationary stochastic processes and their moments

Linear processes

The multivariate ARMA process

Non-stationary models


Identification of multivariate models

Estimation of parameters

Model checking


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


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



About the Originator

About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General