State Space Models
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Identifiability Of State Space Models
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Author : E. Walter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Identifiability Of State Space Models written by E. Walter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.
Time Series Analysis For The State Space Model With R Stan
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Author : Junichiro Hagiwara
language : en
Publisher: Springer Nature
Release Date : 2021-08-30
Time Series Analysis For The State Space Model With R Stan written by Junichiro Hagiwara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-30 with Mathematics categories.
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.
State Space Modeling Of Time Series
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Author : Masanao Aoki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
State Space Modeling Of Time Series written by Masanao Aoki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Business & Economics categories.
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.
Bayesian Inference Of State Space Models
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Author : Kostas Triantafyllopoulos
language : en
Publisher: Springer
Release Date : 2022-11-13
Bayesian Inference Of State Space Models written by Kostas Triantafyllopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-13 with Mathematics categories.
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.
State Space Methods For Time Series Analysis
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Author : Jose Casals
language : en
Publisher: CRC Press
Release Date : 2018-09-03
State Space Methods For Time Series Analysis written by Jose Casals and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
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.
Partially Observed Markov Decision Processes
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Author : Vikram Krishnamurthy
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-21
Partially Observed Markov Decision Processes written by Vikram Krishnamurthy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-21 with Mathematics categories.
This book covers formulation, algorithms, and structural results of partially observed Markov decision processes, whilst linking theory to real-world applications in controlled sensing. Computations are kept to a minimum, enabling students and researchers in engineering, operations research, and economics to understand the methods and determine the structure of their optimal solution.
Advanced State Space Methods For Neural And Clinical Data
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Author : Zhe Chen
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-15
Advanced State Space Methods For Neural And Clinical Data written by Zhe Chen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-15 with Computers categories.
An authoritative and in-depth treatment of state space methods, with a range of applications in neural and clinical data.
Practical Time Series Analysis
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Author : Aileen Nielsen
language : en
Publisher: O'Reilly Media
Release Date : 2019-09-20
Practical Time Series Analysis written by Aileen Nielsen and has been published by O'Reilly Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-20 with Computers categories.
Time series data analysis is increasingly important due to the massive production of such data through the internet of things, the digitalization of healthcare, and the rise of smart cities. As continuous monitoring and data collection become more common, the need for competent time series analysis with both statistical and machine learning techniques will increase. Covering innovations in time series data analysis and use cases from the real world, this practical guide will help you solve the most common data engineering and analysis challengesin time series, using both traditional statistical and modern machine learning techniques. Author Aileen Nielsen offers an accessible, well-rounded introduction to time series in both R and Python that will have data scientists, software engineers, and researchers up and running quickly. You’ll get the guidance you need to confidently: Find and wrangle time series data Undertake exploratory time series data analysis Store temporal data Simulate time series data Generate and select features for a time series Measure error Forecast and classify time series with machine or deep learning Evaluate accuracy and performance
Time Series Analysis And Its Applications
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Author : Robert H. Shumway
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Time Series Analysis And Its Applications written by Robert H. Shumway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The goals of this book are to develop an appreciation for the richness and versatility of modern time series analysis as a tool for analyzing data, and still maintain a commitment to theoretical integrity, as exemplified by the seminal works of Brillinger (1981) and Hannan (1970) and the texts by Brockwell and Davis (1991) and Fuller (1995). The advent of more powerful computing, es pecially in the last three years, has provided both real data and new software that can take one considerably beyond the fitting of·simple time domain mod els, such as have been elegantly described in the landmark work of Box and Jenkins (1970). The present book is designed to be useful as a text for courses in time series on several different levels and as a reference work for practition ers facing the analysis of time-correlated data in the physical, biological, and social sciences. We believe the book will be useful as a text at both the undergraduate and graduate levels. An undergraduate course can be accessible to students with a background in regression analysis and might include Sections 1. 1-1. 8, 2. 1-2. 9, and 3. 1-3. 8. Similar courses have been taught at the University of California (Berkeley and Davis) in the past using the earlier book on applied time series analysis by Shumway (1988). Such a course is taken by undergraduate students in mathematics, economics, and statistics and attracts graduate students from the agricultural, biological, and environmental sciences.
Time Series Analysis By State Space Methods
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Author : James Durbin
language : en
Publisher: Oxford University Press
Release Date : 2012-05-03
Time Series Analysis By State Space Methods written by James Durbin and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-03 with Business & Economics categories.
This is a comprehensive treatment of the state space approach to time series analysis. A distinguishing feature of state space time series models is that observations are regarded as made up of distinct components, which are each modelled separately.