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.

State space time series analysis emerged in the 1960s in engineering, but its applications have spread to other fields. Durbin (statistics, London School of Economics and Political Science) and Koopman (econometrics, Free U., Amsterdam) extol the virtues of such models over the main analytical system currently used for time series data, Box-Jenkins' ARIMA. What distinguishes state space time models is that they separately model components such as trend, seasonal, regression elements and disturbance terms. Part I focuses on traditional and new techniques based on the linear Gaussian model. Part II presents new material extending the state space model to non-Gaussian observations. c. Book News Inc.

The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values. Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form. After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables. Web Resource The authors’ E4 MATLAB® toolbox offers all the computational procedures, administrative and analytical functions, and related materials for time series analysis. This flexible, powerful, and free software tool enables readers to replicate the practical examples in the text and apply the procedures to their own work.

This book provides a comprehensive and concrete illustration of time series analysis focusing on the state-space model, which has recently attracted increasing attention in a broad range of fields. The major feature of the book lies in its consistent Bayesian treatment regarding whole combinations of batch and sequential solutions for linear Gaussian and general state-space models: MCMC and Kalman/particle filter. The reader is given insight on flexible modeling in modern time series analysis. The main topics of the book deal with the state-space model, covering extensively, from introductory and exploratory methods to the latest advanced topics such as real-time structural change detection. Additionally, a practical exercise using R/Stan based on real data promotes understanding and enhances the reader’s analytical capability.

A comprehensive overview of developments in the theory and application of state space modeling, first published in 2004.

Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor with state space methods. The only background required in order to understand the material presented in the book is a basic knowledge of classical linear regression models, of which a brief review is provided to refresh the reader's knowledge. Also, a few sections assume familiarity with matrix algebra, however, these sections may be skipped without losing the flow of the exposition. The book offers a step by step approach to the analysis of the salient features in time series such as the trend, seasonal, and irregular components. Practical problems such as forecasting and missing values are treated in some detail. This useful book will appeal to practitioners and researchers who use time series on a daily basis in areas such as the social sciences, quantitative history, biology and medicine. It also serves as an accompanying textbook for a basic time series course in econometrics and statistics, typically at an advanced undergraduate level or graduate level.

model's predictive capability? These are some of the questions that need to be answered in proposing any time series model construction method. This book addresses these questions in Part II. Briefly, the covariance matrices between past data and future realizations of time series are used to build a matrix called the Hankel matrix. Information needed for constructing models is extracted from the Hankel matrix. For example, its numerically determined rank will be the di mension of the state model. Thus the model dimension is determined by the data, after balancing several sources of error for such model construction. The covariance matrix of the model forecasting error vector is determined by solving a certain matrix Riccati equation. This matrix is also the covariance matrix of the innovation process which drives the model in generating model forecasts. In these model construction steps, a particular model representation, here referred to as balanced, is used extensively. This mode of model representation facilitates error analysis, such as assessing the error of using a lower dimensional model than that indicated by the rank of the Hankel matrix. The well-known Akaike's canonical correlation method for model construc tion is similar to the one used in this book. There are some important differ ences, however. Akaike uses the normalized Hankel matrix to extract canonical vectors, while the method used in this book does not normalize the Hankel ma trix.

A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors—noted experts in the field—explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models. The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational methods. Parametric and nonparametric methods and nonlinear and non-Gaussian state space models provide a much wider range of tools for time series analysis. In addition, advances in computing and data collection have made available large data sets and high-frequency data. These new data make it not only feasible, but also necessary to take into consideration the nonlinearity embedded in most real-world time series. This vital guide: • Offers research developed by leading scholars of time series analysis • Presents R commands making it possible to reproduce all the analyses included in the text • Contains real-world examples throughout the book • Recommends exercises to test understanding of material presented • Includes an instructor solutions manual and companion website Written for students, researchers, and practitioners who are interested in exploring nonlinearity in time series, Nonlinear Time Series Analysis offers a comprehensive text that explores the advantages and limitations of the nonlinear models and methods and demonstrates the improvements upon linear time series models.

Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic models, likelihood calculation, prediction intervals and procedures for model selection, was not developed until recently. This book brings together all of the important new results on the state space framework for exponential smoothing. It will be of interest to people wanting to apply the methods in their own area of interest as well as for researchers wanting to take the ideas in new directions. Part 1 provides an introduction to exponential smoothing and the underlying models. The essential details are given in Part 2, which also provide links to the most important papers in the literature. More advanced topics are covered in Part 3, including the mathematical properties of the models and extensions of the models for specific problems. Applications to particular domains are discussed in Part 4.

A synthesis of concepts and materials, that ordinarily appear separately in time series and econometrics literature, presents a comprehensive review of theoretical and applied concepts in modeling economic and social time series.