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  Time Series Analysis by State Space Methods,
Second Edition

by J. Durbin and S.J. Koopman


About the book

New to this edition

This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbance terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second edition include the filtering of nonlinear and non-Gaussian series.

Part I of the book obtains the mean and variance of the state, of a variable intended to measure the effect of an interaction and of regression coefficients, in terms of the observations.

Part II extends the treatment to nonlinear and non-normal models. For these, analytical solutions are not available so methods are based on simulation.

Readership: Researchers in statistics, econometrics, biometrics, environmetrics, engineering, system theory and physics. Financial analysts in banking and other financial institutions.


  • Preface to Second Edition
  • Preface to First Edition
    1. Introduction
  • Part I - The linear state space model
    1. Local level model
    2. Linear state space models
    3. Filtering, smoothing and forecasting
    4. Initialisation of filter and smoother
    5. Further computational aspects
    6. Maximum likelihood estimation of parameters
    7. Illustrations of the use of the linear model
  • Part II - Non-Gaussian and nonlinear state space models
    1. Special cases of nonlinear and non-Gaussian state space models
    2. Approximate filtering and smoothing
    3. Importance sampling for smoothing
    4. Particle filtering
    5. Bayesian estimation of parameters
    6. Non-Gaussian and nonlinear illustrations
  • References
  • Author Index
  • Subject Index


    The data used in the book can be downloaded in one zip-file, which contains the following files in text format:

    nile.dat Volume of Nile river at Aswan 1871-1970 (Chapter 2)
    seatbelt.dat Drivers, front and rear seat passengers killed and seriously injured in Great Britain (Section 8.2, 8.3)
    internet.dat Number of users logged on to an internet server (Section 8.4)
    motorcycle.dat Motorcycle accident acceleration (Section 8.5)
    sv.dat Pound/Dollar daily exchange rates (Section 8.6, 14.5)
    van.dat Van drivers killed and seat belt law in Great Britain (Section 14.3)
    gas.dat Gas consumption in UK (Section 14.4)
    boat.dat Boat race Oxford-Cambridge data from 1829-2000 (Section 14.6)


    A five-star review of the second edition by Fin Econ on Amazon:

    This is a top notch text for learning State Space methods. It is sort of a main course to the following appetizer and dessert.

    The appetizer that I recommend that a beginner first read is (An introduction to) State Space Time Series Analysis by Commandeur and Koopman. It is an optimal starting point.

    After progressing from the introductory text to the Durbin and Koopman text, an excellent test is State Space and Unobserved Components Models by Harvey, Koopman and Shephard.

    The models in these books are easily implemented in Oxmetrics - for which a free console version is available for academic use.

    Two quotes from a four-star review of the second edition by Dimitri Shvorob on Amazon:

    "Preface to Second Edition", found via "Search inside", discusses the changes since the first edition, and these do address readers' comments on that book's Amazon page, by expanding coverage of the non-linear/non-normal case.

    ... the overall impression is that of a comprehensive, rigorous and reasonably compact exploration of the field.

    A four-star review of the second edition by Kevin S. Gray on Amazon:

    If you're on the hunt for a comprehensive and detailed mathematical treatment of State Space modeling, this book may be what you're looking for. It's a "heavy" textbook, not a "how-to" cookbook, but is well-organized and well-written. The first author was James Durbin, the renowned statistician who passed away in 2012 at the age of 88. His frequent collaborator, Siem Jan Koopman, is widely published on time series analysis and econometrics topics.

    A quote from a four-star review of the first edition by AGJr on Amazon::

    Part I - The linear Gaussian state space model is a must for the understanding the applications, with plenty of examples. Easy to read and understand, it will certainly help the practicioner in applying its concepts with any statistical software, or even in writing his/her own code.

    A quote from an editorial review of the first edition of the book as it appeared in the Journal of the Royal Statistical Society:

    ... provides an up-to-date exposition and comprehensive treatment of state space models in time series analysis. This book will be helpful to graduate students and applied statisticians working in the area of econometric modelling as well as researchers in the areas of engineering, medicine and biology where state space models are used. ... a good mixture of theory and practical applications ... graduate and research students will definitely enjoy this book. Also practitioners will find the book quite useful. I would also recommend it for library purchase.

    Two quotes from a five-star review of the first edition by A reader on Amazon:

    Chapter 2 of this book must rank among the very best texts ever written on the Kalman Filter: In a few pages, the authors not only give a quick, comprehensible, implementable demo of the Kalman filter (I had an implementation of the equations up and working less than half an hour after I first opened the book); they also motivate the various topics to be treated in the rest of the book, like initialization, smoothing, error control and so on.

    As for rating, the book as a whole might deserve 3 to 4 stars. But that chapter 2... that chapter is worth 5 stars alone.


    A quote from a four-star review of the first edition by Biostatistician on Amazon:

    ... in general, the book introduces the concept of Kalman filter nicely and rigorously.

    Publication and ordering information

    Time Series Analysis by State Space Methods by J. Durbin and S.J. Koopman was first published on June 14, 2001, as Volume 24 in the Oxford Statistical Science Series by Oxford University Press.

    The second edition of Time Series Analysis by State Space Methods by J. Durbin and S.J. Koopman was published on May 3, 2012, as Volume 38 in the Oxford Statistical Science Series by Oxford University Press. The second edition can be ordered from OUP-UK and Amazon, amongst other places.

    The first edition of the book has been translated into Japanese by Hajime Wago, and can be ordered from Amazon Japan.