This book presents a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models . Time Series Analysis by State Space Methods by Durbin and Koopman - Ebook download as PDF File .pdf), Text File .txt) or read book online. The course is organised around the book “Time Series Analysis by State Space Methods” of Durbin and. Koopman (Second Edition,
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S.J.-Time Series Analysis by State Space Methods-Oxford University Press ( ).pdf · bigger ok, 2 years ago. echecs16.info · bigger . The purpose of this document is to summarize Part I of the book “Time Series Analysis by State Space. Methods ”, written by James Durbin and. PDF | This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis. The distinguishing feature of state space .
He is also an associate professor of econometrics at Universidad Complutense de Madrid. Alfredo Garcia-Hiernaux is an associate professor of econometrics at Universidad Complutense de Madrid and a freelance consultant. Miguel Jerez is an associate professor of econometrics at Universidad Complutense de Madrid and a freelance consultant. He was previously executive vice-president at Caja de Madrid for six years. Sonia Sotoca is an associate professor of econometrics at Universidad Complutense de Madrid. Casals, Garcia-Hiernaux, Jerez, and Sotoca are all engaged in a long-term research project to apply state-space techniques to standard econometric problems.
We give a general treatment in which some elements of the initial state vector have known distributions while others are diffuse, that is, treated as random variables with infinite variance, or are treated as unknown constants to be estimated by maximum likelihood. The treatment is based on recent work and we regard it as more transparent than earlier discussions of the problem.
Chapter 6 discusses computational aspects of filtering and smoothing and begins by considering the estimation of the regression component of the model.
It next considers the square root filter and smoother which may be used when the Kalman filter and smoother show signs of numerical instability. It goes on to discuss how multivariate time series can be treated as univariate series by bringing elements of the observational vectors into the system one at a time, with compu- tational savings relative to the multivariate treatment in some cases.
The chapter concludes by discussing computer algorithms. In Chapter 7, maximum likelihood estimation of unknown parameters is con- sidered both for the case where the distribution of the initial state vector is known and for the case where at least some elements of the vector are diffuse or are treated as fixed and unknown.
The use of the score vector and the EM algorithm is discussed. The effect of parameter estimation on variance estimation is examined. Up to this point the exposition has been based on the classical approach to inference in which formulae are worked out on the assumption that parameters 1.
In Bayesian analysis the parameters are treated as random variables with a specified or a non-informative prior joint density. In Chapter 8 we consider Bayesian analysis of the linear Gaussian model both for the case where the prior density is proper and for the case where it is non-informative. We give formulae from which the posterior mean can be calculated for functions of the state vector, either by numerical integration or by simulation.
We restrict attention to functions which, for given values of the parameters, can be calculated by the Kalman filter and smoother; this however includes a substantial number of quantities of interest.
In Chapter 9 we illustrate the use of the methodology by applying the techniques that have been developed to a number of analyses based on real data. These include a study of the effect of the seat belt law on road accidents in Great Britain, forecasting the number of users logged on to an Internet server, fitting acceleration against time for a simulated motorcycle accident and modelling the volatility of financial time series.
The analyses are based on simulation using the approach developed by Durbin and Koopman Chapter 10 illustrates the range of non-Gaussian and nonlinear models that can be analysed using the methods of Part H. This includes exponential family models such as the Poisson distribution for the conditional distribution of the observations given the state.
It also includes heavy-tailed distributions for the observational and state disturbances, such as the i-distribution and mixtures of normal densities. Departures from linearity of the models are studied for cases where the basic state space structure is preserved. Financial models such as stochastic volatility models are investigated from the state space point of view.
The simulation techniques employed in this book for handling non-Gaussian models are based on importance sampling and antithetic variables. The methods that we use are described in Chapter We first show how to calculate the conditional mode of the state given the observations for the non-Gaussian model by iterated use of the Kalman filter and smoother.
We then find the linear Gaussian model with the same conditional mode given the observations and we use the conditional density of the state given the observations for this model as the impor- tance density.
Since this density is Gaussian we can draw random samples from it for the simulation using the simulation smoother described in Chapter 4.
To improve efficiency we introduce two antithetic variables intended to balance the simulation sample for location and scale. Finally, we show how cases where the observation or state errors have f-distributions or distributions which are mixtures of normal densities can be treated without using importance sampling.
Chapter 12 discusses the implementation of importance sampling numerically. It also shows how variances due to simulation can be estimated by means of simple formulae. It next discusses the estimation of unknown parameters by maximum likelihood.
The final topic considered is the effect of errors in the estimation of the parameters on the estimates. In Chapter 13 we show that by an extension of the importance sampling techniques of Chapter 11 we can obtain a Bayesian treatment for non-Gaussian and nonlinear models.
Estimates of posterior means, variances, densities and distribution functions of functions of elements of the state vector are provided.
We also estimate the posterior densities of the parameters of the model. Estimates of variances due to simulation are obtained. We provide examples in Chapter 14 which illustrate the methods that have been developed in Part II for analysing observations using non-Gaussian and nonlinear state space models.
It is sort of a main course to the following appetizer and dessert. It is an optimal starting point. The models in these books are easily implemented in Oxmetrics - for which a free console version is available for academic use.
A four-star review of the second edition by Kevin S. Gray on site : 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 at the age of 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 site :: Part I - The linear Gaussian state space model is a must for the understanding the applications, with plenty of examples. A quote from an editorial review of the first edition of the book as it appeared in the Journal of the Royal Statistical Society