Dynamic Time Series Models using R-INLA

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Publisher : CRC Press
ISBN 13 : 1000622606
Total Pages : 297 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Dynamic Time Series Models using R-INLA by : Nalini Ravishanker

Download or read book Dynamic Time Series Models using R-INLA written by Nalini Ravishanker and published by CRC Press. This book was released on 2022-08-10 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic Time Series Models using R-INLA: An Applied Perspective is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework. The book is an ideal reference for statisticians and scientists who work with time series data. It provides an excellent resource for teaching a course on Bayesian analysis using state space models for time series. Key Features: Introduction and overview of R-INLA for time series analysis. Gaussian and non-Gaussian state space models for time series. State space models for time series with exogenous predictors. Hierarchical models for a potentially large set of time series. Dynamic modelling of stochastic volatility and spatio-temporal dependence.

Time Series

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Publisher : CRC Press
ISBN 13 : 1498747043
Total Pages : 473 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Time Series by : Raquel Prado

Download or read book Time Series written by Raquel Prado and published by CRC Press. This book was released on 2021-07-27 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Expanded on aspects of core model theory and methodology. • Multiple new examples and exercises. • Detailed development of dynamic factor models. • Updated discussion and connections with recent and current research frontiers.

Spatial and Spatio-temporal Bayesian Models with R - INLA

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118326555
Total Pages : 322 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis Spatial and Spatio-temporal Bayesian Models with R - INLA by : Marta Blangiardo

Download or read book Spatial and Spatio-temporal Bayesian Models with R - INLA written by Marta Blangiardo and published by John Wiley & Sons. This book was released on 2015-06-02 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

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Author :
Publisher : CRC Press
ISBN 13 : 0429629850
Total Pages : 284 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA by : Elias T. Krainski

Download or read book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA written by Elias T. Krainski and published by CRC Press. This book was released on 2018-12-07 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Bayesian inference with INLA

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Publisher : CRC Press
ISBN 13 : 1351707205
Total Pages : 330 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Bayesian inference with INLA by : Virgilio Gomez-Rubio

Download or read book Bayesian inference with INLA written by Virgilio Gomez-Rubio and published by CRC Press. This book was released on 2020-02-20 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

Time Series

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Publisher : CRC Press
ISBN 13 : 1420093363
Total Pages : 375 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Time Series by : Raquel Prado

Download or read book Time Series written by Raquel Prado and published by CRC Press. This book was released on 2010-05-21 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers. The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB® code, and other material are available on the authors’ websites. Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.

The Analysis of Time Series

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Publisher : CRC Press
ISBN 13 : 1498795641
Total Pages : 398 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Analysis of Time Series by : Chris Chatfield

Download or read book The Analysis of Time Series written by Chris Chatfield and published by CRC Press. This book was released on 2019-04-25 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of this classic title, now in its seventh edition, presents a balanced and comprehensive introduction to the theory, implementation, and practice of time series analysis. The book covers a wide range of topics, including ARIMA models, forecasting methods, spectral analysis, linear systems, state-space models, the Kalman filters, nonlinear models, volatility models, and multivariate models. It also presents many examples and implementations of time series models and methods to reflect advances in the field. Highlights of the seventh edition: A new chapter on univariate volatility models A revised chapter on linear time series models A new section on multivariate volatility models A new section on regime switching models Many new worked examples, with R code integrated into the text The book can be used as a textbook for an undergraduate or a graduate level time series course in statistics. The book does not assume many prerequisites in probability and statistics, so it is also intended for students and data analysts in engineering, economics, and finance.

Time Series Models

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Author :
Publisher : Springer Nature
ISBN 13 : 3031132130
Total Pages : 213 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Time Series Models by : Manfred Deistler

Download or read book Time Series Models written by Manfred Deistler and published by Springer Nature. This book was released on 2022-10-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.

Applied Time Series Analysis with R

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Publisher : CRC Press
ISBN 13 : 1498734316
Total Pages : 460 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Applied Time Series Analysis with R by : Wayne A. Woodward

Download or read book Applied Time Series Analysis with R written by Wayne A. Woodward and published by CRC Press. This book was released on 2017-02-17 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Features Gives readers the ability to actually solve significant real-world problems Addresses many types of nonstationary time series and cutting-edge methodologies Promotes understanding of the data and associated models rather than viewing it as the output of a "black box" Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website. Over 150 exercises and extensive support for instructors The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).

Ordered Data Analysis, Modeling and Health Research Methods

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Publisher : Springer
ISBN 13 : 3319254332
Total Pages : 268 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Ordered Data Analysis, Modeling and Health Research Methods by : Pankaj Choudhary

Download or read book Ordered Data Analysis, Modeling and Health Research Methods written by Pankaj Choudhary and published by Springer. This book was released on 2015-12-14 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an eclectic mix of original research articles in areas covering the analysis of ordered data, stochastic modeling and biostatistics. These areas were featured in a conference held at the University of Texas at Dallas from March 7 to 9, 2014 in honor of Professor H. N. Nagaraja’s 60th birthday and his distinguished contributions to statistics. The articles were written by leading experts who were invited to contribute to the volume from among the conference participants. The volume is intended for all researchers with an interest in order statistics, distribution theory, analysis of censored data, stochastic modeling, time series analysis, and statistical methods for the health sciences, including statistical genetics.

Hands-On Time Series Analysis with R

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Author :
Publisher : Packt Publishing Ltd
ISBN 13 : 1788624041
Total Pages : 438 pages
Book Rating : 4.7/5 (886 download)

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Book Synopsis Hands-On Time Series Analysis with R by : Rami Krispin

Download or read book Hands-On Time Series Analysis with R written by Rami Krispin and published by Packt Publishing Ltd. This book was released on 2019-05-31 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Build efficient forecasting models using traditional time series models and machine learning algorithms. Key FeaturesPerform time series analysis and forecasting using R packages such as Forecast and h2oDevelop models and find patterns to create visualizations using the TSstudio and plotly packagesMaster statistics and implement time-series methods using examples mentionedBook Description Time series analysis is the art of extracting meaningful insights from, and revealing patterns in, time series data using statistical and data visualization approaches. These insights and patterns can then be utilized to explore past events and forecast future values in the series. This book explores the basics of time series analysis with R and lays the foundations you need to build forecasting models. You will learn how to preprocess raw time series data and clean and manipulate data with packages such as stats, lubridate, xts, and zoo. You will analyze data and extract meaningful information from it using both descriptive statistics and rich data visualization tools in R such as the TSstudio, plotly, and ggplot2 packages. The later section of the book delves into traditional forecasting models such as time series linear regression, exponential smoothing (Holt, Holt-Winter, and more) and Auto-Regressive Integrated Moving Average (ARIMA) models with the stats and forecast packages. You'll also cover advanced time series regression models with machine learning algorithms such as Random Forest and Gradient Boosting Machine using the h2o package. By the end of this book, you will have the skills needed to explore your data, identify patterns, and build a forecasting model using various traditional and machine learning methods. What you will learnVisualize time series data and derive better insightsExplore auto-correlation and master statistical techniquesUse time series analysis tools from the stats, TSstudio, and forecast packagesExplore and identify seasonal and correlation patternsWork with different time series formats in RExplore time series models such as ARIMA, Holt-Winters, and moreEvaluate high-performance forecasting solutionsWho this book is for Hands-On Time Series Analysis with R is ideal for data analysts, data scientists, and all R developers who are looking to perform time series analysis to predict outcomes effectively. A basic knowledge of statistics is required; some knowledge in R is expected, but not mandatory.

Practical Time Series Forecasting with R

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Publisher : Axelrod Schnall Publishers
ISBN 13 : 0997847956
Total Pages : 250 pages
Book Rating : 4.9/5 (978 download)

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Book Synopsis Practical Time Series Forecasting with R by : Galit Shmueli

Download or read book Practical Time Series Forecasting with R written by Galit Shmueli and published by Axelrod Schnall Publishers. This book was released on with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical Time Series Forecasting with R: A Hands-On Guide, Third Edition provides an applied approach to time-series forecasting. Forecasting is an essential component of predictive analytics. The book introduces popular forecasting methods and approaches used in a variety of business applications. The book offers clear explanations, practical examples, and end-of-chapter exercises and cases. Readers will learn to use forecasting methods using the free open-source R software to develop effective forecasting solutions that extract business value from time series data. This edition features the R fable package, full color, enhanced organization, and new material. It includes: - Popular forecasting methods including smoothing algorithms, regression models, ARIMA, neural networks, deep learning, and ensembles - A practical approach to evaluating the performance of forecasting solutions - A business-analytics exposition focused on linking time-series forecasting to business goals - Guided cases for integrating the acquired knowledge using real data - End-of-chapter problems to facilitate active learning - Data, R code, and instructor materials on companion website - Affordable and globally-available textbook, available in hardcover, paperback, and Kindle formats Practical Time Series Forecasting with R: A Hands-On Guide, Third Edition is the perfect textbook for upper-undergraduate, graduate and MBA-level courses as well as professional programs in data science and business analytics. The book is also designed for practitioners in the fields of operations research, supply chain management, marketing, economics, information systems, finance, and management.

Introductory Time Series with R

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0387886982
Total Pages : 262 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Introductory Time Series with R by : Paul S.P. Cowpertwait

Download or read book Introductory Time Series with R written by Paul S.P. Cowpertwait and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives you a step-by-step introduction to analysing time series using the open source software R. Each time series model is motivated with practical applications, and is defined in mathematical notation. Once the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence enhances understanding of both the time series model and the R function used to fit the model to data. Finally, the model is used to analyse observed data taken from a practical application. By using R, the whole procedure can be reproduced by the reader. All the data sets used in the book are available on the website http://staff.elena.aut.ac.nz/Paul-Cowpertwait/ts/. The book is written for undergraduate students of mathematics, economics, business and finance, geography, engineering and related disciplines, and postgraduate students who may need to analyse time series as part of their taught programme or their research.

Time Series Analysis

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Publisher : John Wiley & Sons
ISBN 13 : 1118674928
Total Pages : 709 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Time Series Analysis by : George E. P. Box

Download or read book Time Series Analysis written by George E. P. Box and published by John Wiley & Sons. This book was released on 2015-05-29 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Fourth Edition "The book follows faithfully the style of the original edition. The approach is heavily motivated by real-world time series, and by developing a complete approach to model building, estimation, forecasting and control." —Mathematical Reviews Bridging classical models and modern topics, the Fifth Edition of Time Series Analysis: Forecasting and Control maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, the Fifth Edition continues to serve as one of the most influential and prominent works on the subject. Time Series Analysis: Forecasting and Control, Fifth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series and describes their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. Along with these classical uses, the new edition covers modern topics with new features that include: A redesigned chapter on multivariate time series analysis with an expanded treatment of Vector Autoregressive, or VAR models, along with a discussion of the analytical tools needed for modeling vector time series An expanded chapter on special topics covering unit root testing, time-varying volatility models such as ARCH and GARCH, nonlinear time series models, and long memory models Numerous examples drawn from finance, economics, engineering, and other related fields The use of the publicly available R software for graphical illustrations and numerical calculations along with scripts that demonstrate the use of R for model building and forecasting Updates to literature references throughout and new end-of-chapter exercises Streamlined chapter introductions and revisions that update and enhance the exposition Time Series Analysis: Forecasting and Control, Fifth Edition is a valuable real-world reference for researchers and practitioners in time series analysis, econometrics, finance, and related fields. The book is also an excellent textbook for beginning graduate-level courses in advanced statistics, mathematics, economics, finance, engineering, and physics.

Spatio-Temporal Statistics with R

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Author :
Publisher : CRC Press
ISBN 13 : 0429649789
Total Pages : 380 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Spatio-Temporal Statistics with R by : Christopher K. Wikle

Download or read book Spatio-Temporal Statistics with R written by Christopher K. Wikle and published by CRC Press. This book was released on 2019-02-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.

Recursive Estimation and Time-Series Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 3642219810
Total Pages : 505 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Recursive Estimation and Time-Series Analysis by : Peter C. Young

Download or read book Recursive Estimation and Time-Series Analysis written by Peter C. Young and published by Springer Science & Business Media. This book was released on 2011-08-04 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised version of the 1984 book of the same name but considerably modified and enlarged to accommodate the developments in recursive estimation and time series analysis that have occurred over the last quarter century. Also over this time, the CAPTAIN Toolbox for recursive estimation and time series analysis has been developed at Lancaster, for use in the MatlabTM software environment (see Appendix G). Consequently, the present version of the book is able to exploit the many computational routines that are contained in this widely available Toolbox, as well as some of the other routines in MatlabTM and its other toolboxes. The book is an introductory one on the topic of recursive estimation and it demonstrates how this approach to estimation, in its various forms, can be an impressive aid to the modelling of stochastic, dynamic systems. It is intended for undergraduate or Masters students who wish to obtain a grounding in this subject; or for practitioners in industry who may have heard of topics dealt with in this book and, while they want to know more about them, may have been deterred by the rather esoteric nature of some books in this challenging area of study.

Time Series Analysis and Forecasting by Example

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118056957
Total Pages : 346 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Time Series Analysis and Forecasting by Example by : Søren Bisgaard

Download or read book Time Series Analysis and Forecasting by Example written by Søren Bisgaard and published by John Wiley & Sons. This book was released on 2011-08-24 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intuition-based approach enables you to master time series analysis with ease Time Series Analysis and Forecasting by Example provides the fundamental techniques in time series analysis using various examples. By introducing necessary theory through examples that showcase the discussed topics, the authors successfully help readers develop an intuitive understanding of seemingly complicated time series models and their implications. The book presents methodologies for time series analysis in a simplified, example-based approach. Using graphics, the authors discuss each presented example in detail and explain the relevant theory while also focusing on the interpretation of results in data analysis. Following a discussion of why autocorrelation is often observed when data is collected in time, subsequent chapters explore related topics, including: Graphical tools in time series analysis Procedures for developing stationary, non-stationary, and seasonal models How to choose the best time series model Constant term and cancellation of terms in ARIMA models Forecasting using transfer function-noise models The final chapter is dedicated to key topics such as spurious relationships, autocorrelation in regression, and multiple time series. Throughout the book, real-world examples illustrate step-by-step procedures and instructions using statistical software packages such as SAS, JMP, Minitab, SCA, and R. A related Web site features PowerPoint slides to accompany each chapter as well as the book's data sets. With its extensive use of graphics and examples to explain key concepts, Time Series Analysis and Forecasting by Example is an excellent book for courses on time series analysis at the upper-undergraduate and graduate levels. it also serves as a valuable resource for practitioners and researchers who carry out data and time series analysis in the fields of engineering, business, and economics.