Time Series Analysis

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Features

  • Describes both linear systems and linear time series, linking systems theory with time series theory
  • Explores static and dynamic models to show the differences between model types
  • Examines the significant topics of ARMA and ARIMA processes, the autocovariance function, and the Kalman filter
  • Includes numerous real-world examples from economics, physics, and engineering as well as several exercises at the end of most chapters
  • Provides a web page with computer-based exercises and a complete collection of slides
  • Summary

    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.

    Table of Contents

    Preface
    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

    Author Bio(s)

    Editorial Reviews

    "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