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Introduction To Time Series Modeling

Author: Genshiro Kitagawa
Publisher: CRC Press
ISBN: 9781584889229
Size: 13.39 MB
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In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to learn fundamental methods of time series modeling. Illustrating how to build models for time series using basic methods, Introduction to Time Series Modeling covers numerous time series models and the various tools for handling them. The book employs the state-space model as a generic tool for time series modeling and presents convenient recursive filtering and smoothing methods, including the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, for the state-space models. Taking a unified approach to model evaluation based on the entropy maximization principle advocated by Dr. Akaike, the author derives various methods of parameter estimation, such as the least squares method, the maximum likelihood method, recursive estimation for state-space models, and model selection by the Akaike information criterion (AIC). Along with simulation methods, he also covers standard stationary time series models, such as AR and ARMA models, as well as nonstationary time series models, including the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model. With a focus on the description, modeling, prediction, and signal extraction of times series, this book provides basic tools for analyzing time series that arise in real-world problems. It encourages readers to build models for their own real-life problems.

Models For Dependent Time Series

Author: Granville Tunnicliffe Wilson
Publisher: CRC Press
ISBN: 1420011502
Size: 78.90 MB
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Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data. The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational material for the remaining chapters, which cover the construction of structural models and the extension of vector autoregressive modeling to high frequency, continuously recorded, and irregularly sampled series. The final chapter combines these approaches with spectral methods for identifying causal dependence between time series. Web Resource A supplementary website provides the data sets used in the examples as well as documented MATLAB® functions and other code for analyzing the examples and producing the illustrations. The site also offers technical details on the estimation theory and methods and the implementation of the models.

Hidden Markov Models For Time Series

Author: Walter Zucchini
Publisher: CRC Press
ISBN: 1482253844
Size: 52.88 MB
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Hidden Markov Models for Time Series: An Introduction Using R, Second Edition illustrates the great flexibility of hidden Markov models (HMMs) as general-purpose models for time series data. The book provides a broad understanding of the models and their uses. After presenting the basic model formulation, the book covers estimation, forecasting, decoding, prediction, model selection, and Bayesian inference for HMMs. Through examples and applications, the authors describe how to extend and generalize the basic model so that it can be applied in a rich variety of situations. The book demonstrates how HMMs can be applied to a wide range of types of time series: continuous-valued, circular, multivariate, binary, bounded and unbounded counts, and categorical observations. It also discusses how to employ the freely available computing environment R to carry out the computations. Features Presents an accessible overview of HMMs Explores a variety of applications in ecology, finance, epidemiology, climatology, and sociology Includes numerous theoretical and programming exercises Provides most of the analysed data sets online New to the second edition A total of five chapters on extensions, including HMMs for longitudinal data, hidden semi-Markov models and models with continuous-valued state process New case studies on animal movement, rainfall occurrence and capture–recapture data

Diagnostic Checks In Time Series

Author: Wai Keung Li
Publisher: CRC Press
ISBN: 9780203485606
Size: 57.76 MB
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Diagnostic checking is an important step in the modeling process. But while the literature on diagnostic checks is quite extensive and many texts on time series modeling are available, it still remains difficult to find a book that adequately covers methods for performing diagnostic checks. Diagnostic Checks in Time Series helps to fill that gap. Author Wai Keung Li--one of the world's top authorities in time series modeling--concentrates on diagnostic checks for stationary time series and covers a range of different linear and nonlinear models, from various ARMA, threshold type, and bilinear models to conditional non-Gaussian and autoregressive heteroscedasticity (ARCH) models. Because of its broad applicability, the portmanteau goodness-of-fit test receives particular attention, as does the score test. Unlike most treatments, the author's approach is a practical one, and he looks at each topic through the eyes of a model builder rather than a mathematical statistician. This book brings together the widely scattered literature on the subject, and with clear explanations and focus on applications, it guides readers through the final stages of their modeling efforts. With Diagnostic Checks in Time Series, you will understand the relative merits of the models discussed, know how to estimate these models, and often find ways to improve a model.

State Space Methods For Time Series Analysis

Author: Jose Casals
Publisher: CRC Press
ISBN: 1482219603
Size: 34.24 MB
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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.

Generalized Additive Models

Author: T.J. Hastie
Publisher: Routledge
ISBN: 1351445960
Size: 22.47 MB
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This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.

Statistical Methods For Spatio Temporal Systems

Author: Barbel Finkenstadt
Publisher: CRC Press
ISBN: 1420011057
Size: 10.14 MB
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Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts with an introduction of the topic and progresses to recent research results. Presenting specific examples of epidemic data of bovine tuberculosis, gastroenteric disease, and the U.K. foot-and-mouth outbreak, the first chapter uses stochastic models, such as point process models, to provide the probabilistic backbone that facilitates statistical inference from data. The next chapter discusses the critical issue of modeling random growth objects in diverse biological systems, such as bacteria colonies, tumors, and plant populations. The subsequent chapter examines data transformation tools using examples from ecology and air quality data, followed by a chapter on space-time covariance functions. The contributors then describe stochastic and statistical models that are used to generate simulated rainfall sequences for hydrological use, such as flood risk assessment. The final chapter explores Gaussian Markov random field specifications and Bayesian computational inference via Gibbs sampling and Markov chain Monte Carlo, illustrating the methods with a variety of data examples, such as temperature surfaces, dioxin concentrations, ozone concentrations, and a well-established deterministic dynamical weather model.

Local Polynomial Modelling And Its Applications

Author: Jianqing Fan
Publisher: Routledge
ISBN: 1351434802
Size: 32.82 MB
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Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.

Joint Modeling Of Longitudinal And Time To Event Data

Author: Robert Elashoff
Publisher: CRC Press
ISBN: 1439807833
Size: 72.73 MB
Format: PDF
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Longitudinal studies often incur several problems that challenge standard statistical methods for data analysis. These problems include non-ignorable missing data in longitudinal measurements of one or more response variables, informative observation times of longitudinal data, and survival analysis with intermittently measured time-dependent covariates that are subject to measurement error and/or substantial biological variation. Joint modeling of longitudinal and time-to-event data has emerged as a novel approach to handle these issues. Joint Modeling of Longitudinal and Time-to-Event Data provides a systematic introduction and review of state-of-the-art statistical methodology in this active research field. The methods are illustrated by real data examples from a wide range of clinical research topics. A collection of data sets and software for practical implementation of the joint modeling methodologies are available through the book website. This book serves as a reference book for scientific investigators who need to analyze longitudinal and/or survival data, as well as researchers developing methodology in this field. It may also be used as a textbook for a graduate level course in biostatistics or statistics.

Dynamic Prediction In Clinical Survival Analysis

Author: Hans van Houwelingen
Publisher: CRC Press
ISBN: 1439835438
Size: 73.23 MB
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There is a huge amount of literature on statistical models for the prediction of survival after diagnosis of a wide range of diseases like cancer, cardiovascular disease, and chronic kidney disease. Current practice is to use prediction models based on the Cox proportional hazards model and to present those as static models for remaining lifetime after diagnosis or treatment. In contrast, Dynamic Prediction in Clinical Survival Analysis focuses on dynamic models for the remaining lifetime at later points in time, for instance using landmark models. Designed to be useful to applied statisticians and clinical epidemiologists, each chapter in the book has a practical focus on the issues of working with real life data. Chapters conclude with additional material either on the interpretation of the models, alternative models, or theoretical background. The book consists of four parts: Part I deals with prognostic models for survival data using (clinical) information available at baseline, based on the Cox model Part II is about prognostic models for survival data using (clinical) information available at baseline, when the proportional hazards assumption of the Cox model is violated Part III is dedicated to the use of time-dependent information in dynamic prediction Part IV explores dynamic prediction models for survival data using genomic data Dynamic Prediction in Clinical Survival Analysis summarizes cutting-edge research on the dynamic use of predictive models with traditional and new approaches. Aimed at applied statisticians who actively analyze clinical data in collaboration with clinicians, the analyses of the different data sets throughout the book demonstrate how predictive models can be obtained from proper data sets.