A Class Of Non Gaussian State Space Models With Exact Likelihood Inference

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A Class of Non-Gaussian State Space Models with Exact Likelihood Inference

Author : Drew Creal
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis A Class of Non-Gaussian State Space Models with Exact Likelihood Inference by : Drew Creal

Download or read book A Class of Non-Gaussian State Space Models with Exact Likelihood Inference written by Drew Creal and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The likelihood function for general non-linear, non-Gaussian state space models is a high- dimensional integral with no closed-form solution. In this paper, I show how to calculate the likelihood function exactly for a large class of non-Gaussian state space models that includes stochastic intensity, stochastic volatility, and stochastic duration models among others. The state variables in this class follow a non-negative stochastic process that is popular in econometrics for modeling volatility and intensities. In addition to calculating the maximum likelihood estimator, I also show how to perform filtering and smoothing to estimate the latent variables in the model. Finally, it is also possible to take random draws from the joint posterior distribution of the latent states conditional on the data and the model's parameters, which is valuable for inference of more complex models.

A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood

Author : Dani Gamerman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood by : Dani Gamerman

Download or read book A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood written by Dani Gamerman and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Gaussian assumption generally employed in many state-space models is usually not satisfied for real time series. Thus, in this work, a broad family of non-Gaussian models is defined by integrating and expanding previous work in the literature. The expansion is obtained at two levels: at the observational level, it allows for many distributions not previously considered, and at the latent state level, it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion considerably increases the applicability of the models and solves many previously existing problems such as long-term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed because of the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared with other non-Gaussian state-space models available. The methodology is applied to Gaussian and non-Gaussian dynamic linear models with time-varying means and variances and provides a computationally simple solution to inference in these models. The methodology is illustrated in a number of examples.

Non gaussian state space models for count data: the durbin and koopman methodology

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (181 download)

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Book Synopsis Non gaussian state space models for count data: the durbin and koopman methodology by :

Download or read book Non gaussian state space models for count data: the durbin and koopman methodology written by and published by . This book was released on 1902 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: O objetivo desta tese é o de apresentar e investigar a metodologia de Durbin e Koopman (DK) usada para estimar o espaço de estado de modelos de séries temporais não-Gaussianos, dentro do contexto de modelos estruturais. A abordagem de DK está baseada na avaliação da verossimilhança usando uma eficiente simulação de Monte Carlo, por meio de amostragem por importância e técnicas de redução de variância, tais como variáveis antitéticas e variáveis de controle. Ela também integra conhecidas técnicas existentes no caso Gaussiano tais como o Filtro de Kalman Siavizado e o algoritmo de simulação suavizada. Uma vez que os hiperparâmetros do modelo são estimados, o estado, que contém as componentes do modelo, é estimado pela avaliação da moda a posteriori. Propomos então aproximações para avaliar a média e a variância da distribuição preditiva. São consideradas aplicações usando o modelo de Poisson.

Bayesian Inference of State Space Models

Author : Kostas Triantafyllopoulos
Publisher : Springer Nature
ISBN 13 : 303076124X
Total Pages : 503 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Bayesian Inference of State Space Models by : Kostas Triantafyllopoulos

Download or read book Bayesian Inference of State Space Models written by Kostas Triantafyllopoulos and published by Springer Nature. This book was released on 2021-11-12 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.

On Importance Sampling for State Space Models

Author : Borus Martinus Johannes Petrus Jungbacker
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (255 download)

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Book Synopsis On Importance Sampling for State Space Models by : Borus Martinus Johannes Petrus Jungbacker

Download or read book On Importance Sampling for State Space Models written by Borus Martinus Johannes Petrus Jungbacker and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Time Series Analysis by State Space Methods

Author : James Durbin
Publisher : OUP Oxford
ISBN 13 : 0191627194
Total Pages : 369 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Time Series Analysis by State Space Methods by : James Durbin

Download or read book Time Series Analysis by State Space Methods written by James Durbin and published by OUP Oxford. This book was released on 2012-05-03 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Time Series Analysis and Its Applications

Author : Robert H. Shumway
Publisher :
ISBN 13 : 9781475732627
Total Pages : 568 pages
Book Rating : 4.7/5 (326 download)

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Book Synopsis Time Series Analysis and Its Applications by : Robert H. Shumway

Download or read book Time Series Analysis and Its Applications written by Robert H. Shumway and published by . This book was released on 2014-01-15 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Term Structure Modeling and Estimation in a State Space Framework

Author : Wolfgang Lemke
Publisher : Springer Science & Business Media
ISBN 13 : 3540283447
Total Pages : 224 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Term Structure Modeling and Estimation in a State Space Framework by : Wolfgang Lemke

Download or read book Term Structure Modeling and Estimation in a State Space Framework written by Wolfgang Lemke and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been prepared during my work as a research assistant at the Institute for Statistics and Econometrics of the Economics Department at the University of Bielefeld, Germany. It was accepted as a Ph.D. thesis titled "Term Structure Modeling and Estimation in a State Space Framework" at the Department of Economics of the University of Bielefeld in November 2004. It is a pleasure for me to thank all those people who have been helpful in one way or another during the completion of this work. First of all, I would like to express my gratitude to my advisor Professor Joachim Frohn, not only for his guidance and advice throughout the com pletion of my thesis but also for letting me have four very enjoyable years teaching and researching at the Institute for Statistics and Econometrics. I am also grateful to my second advisor Professor Willi Semmler. The project I worked on in one of his seminars in 1999 can really be seen as a starting point for my research on state space models. I thank Professor Thomas Braun for joining the committee for my oral examination.

Bayesian Filtering and Smoothing

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 110703065X
Total Pages : 255 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Bayesian Filtering and Smoothing by : Simo Särkkä

Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Introduction to Time Series and Forecasting

Author : Peter J. Brockwell
Publisher : Springer Science & Business Media
ISBN 13 : 1475725264
Total Pages : 429 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Time Series and Forecasting by : Peter J. Brockwell

Download or read book Introduction to Time Series and Forecasting written by Peter J. Brockwell and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.

State Space and Unobserved Component Models

Author : James Durbin
Publisher : Cambridge University Press
ISBN 13 : 9780521835954
Total Pages : 398 pages
Book Rating : 4.8/5 (359 download)

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Book Synopsis State Space and Unobserved Component Models by : James Durbin

Download or read book State Space and Unobserved Component Models written by James Durbin and published by Cambridge University Press. This book was released on 2004-06-10 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of developments in the theory and application of state space modeling, first published in 2004.

Inference in Hidden Markov Models

Author : Olivier Cappé
Publisher : Springer Science & Business Media
ISBN 13 : 0387289828
Total Pages : 656 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Inference in Hidden Markov Models by : Olivier Cappé

Download or read book Inference in Hidden Markov Models written by Olivier Cappé and published by Springer Science & Business Media. This book was released on 2006-04-12 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

Author : Siem Jan Koopman
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (837 download)

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Book Synopsis Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models by : Siem Jan Koopman

Download or read book Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models written by Siem Jan Koopman and published by . This book was released on 2011 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Readings in Unobserved Components Models

Author : Andrew C. Harvey
Publisher : Oxford University Press, USA
ISBN 13 : 0199278695
Total Pages : 475 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Readings in Unobserved Components Models by : Andrew C. Harvey

Download or read book Readings in Unobserved Components Models written by Andrew C. Harvey and published by Oxford University Press, USA. This book was released on 2005 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of readings which give the reader an idea of the nature and scope of unobserved components (UC) models and the methods used to deal with them. The book is intended to give a self-contained presentation of the methods and applicative issues. Harvey has made major contributions to this field and provides substantial introductions throughout the book to form a unified view of the literature. About the Series Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.

An Introduction to State Space Time Series Analysis

Author : Jacques J. F. Commandeur
Publisher : OUP Oxford
ISBN 13 : 0191607800
Total Pages : 192 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis An Introduction to State Space Time Series Analysis by : Jacques J. F. Commandeur

Download or read book An Introduction to State Space Time Series Analysis written by Jacques J. F. Commandeur and published by OUP Oxford. This book was released on 2007-07-19 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gaussian Processes for Machine Learning

Author : Carl Edward Rasmussen
Publisher : MIT Press
ISBN 13 : 026218253X
Total Pages : 266 pages
Book Rating : 4.2/5 (621 download)

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Book Synopsis Gaussian Processes for Machine Learning by : Carl Edward Rasmussen

Download or read book Gaussian Processes for Machine Learning written by Carl Edward Rasmussen and published by MIT Press. This book was released on 2005-11-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements

Author : James C. Spall
Publisher :
ISBN 13 :
Total Pages : 3 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements by : James C. Spall

Download or read book Validation of State-Space Models from a Single Realization of Non-Gaussian Measurements written by James C. Spall and published by . This book was released on 1985 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: A methodology is presented for testing whether a dynamic model in linear state-space form accurately describes the system under consideration. Unlike existing procedures it is not necessary to assume that all of the random terms in the model are normally distributed. The methodology is based on a single realization of observations and is relatively easy to implement since it relies on a normalized Kalman filter state estimate. The testing procedure rests on an asymptotic distribution theory for the filter estimate. Control theory; Reprints. (jhd).