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Introduction to Time Series Analysis and Forecasting, 2nd Edition
by Cheryl L. Jennings Murat Kulahci Douglas C. MontgomeryAn accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data.Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.Seven easy-to-follow chapters provide intuitive explanations and in-depth coverage of key forecasting topics, including:Regression-based methods, heuristic smoothing methods, and general time series modelsBasic statistical tools used in analyzing time series dataMetrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over timeCross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squaresExponential smoothing techniques for time series with polynomial components and seasonal dataForecasting and prediction interval construction with a discussion on transfer function models as well as intervention modeling and analysisMultivariate time series problems, ARCH and GARCH models, and combinations of forecastsThe ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time seriesThe intricate role of computer software in successful time series analysis is acknowledged with the use of Minitab, JMP, and SAS software applications, which illustrate how the methods are imple-mented in practice. An extensive FTP site is available for readers to obtain data sets, Microsoft Office PowerPoint slides, and selected answers to problems in the book. Requiring only a basic working knowledge of statistics and complete with exercises at the end of each chapter as well as examples from a wide array of fields, Introduction to Time Series Analysis and Forecasting is an ideal text for forecasting and time series courses at the advanced undergraduate and beginning graduate levels. The book also serves as an indispensable reference for practitioners in business, economics, engineering, statistics, mathematics, and the social, environmental, and life sciences.
Introduction to Time Series and Forecasting
by Peter J. Brockwell Richard A. DavisThis book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied to economics, engineering and the natural and social sciences. It assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This third edition contains detailed instructions for the use of the professional version of the Windows-based computer package ITSM2000, now available as a free download from the Springer Extras website. The logic and tools of time series model-building are developed in detail. Numerous exercises are included and the software can be used to analyze and forecast data sets of the user''s own choosing. The book can also be used in conjunction with other time series packages such as those included in R. The programs in ITSM2000 however are menu-driven and can be used with minimal investment of time in the computational details. 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. Many additional special topics are also covered. New to this edition: A chapter devoted to Financial Time Series Introductions to Brownian motion, Lévy processes and Itô calculus An expanded section on continuous-time ARMA processes Peter J. Brockwell and Richard A. Davis are Fellows of the American Statistical Association and the Institute of Mathematical Statistics and elected members of the International Statistics Institute. Richard A. Davis is the current President of the Institute of Mathematical Statistics and, with W. T. M. Dunsmuir, winner of the Koopmans Prize. Professors Brockwell and Davis are coauthors of the widely used advanced text, Time Series: Theory and Methods, Second Edition (Springer-Verlag, 1991). From reviews of the first edition: This book, like a good science fiction novel, is hard to put down. . . . Fascinating examples hold one''s attention and are taken from an astonishing variety of topics and fields. . . . Given that time series forecasting is really a simple idea, it is amazing how much beautiful mathematics this book encompasses. Each chapter is richly filled with examples that serve to illustrate and reinforce the basic concepts. The exercises at the end of each chapter are well designed and make good use of numerical problems. Combined with the ITSM package, this book is ideal as a textbook for the self-study student or the introductory course student. Overall then, as a text for a university-level course or as a learning aid for an industrial forecaster, I highly recommend the book. --SIAM Review In addition to including ITSM, the book details all of the algorithms used in the package --a quality which sets this text apart from all others at this level. This is an excellent idea for at least two reasons. It gives the practitioner the opportunity to use ITSM more intelligently by providing an extra source of intuition for understanding estimation and forecasting, and it allows the more adventurous practitioners to code their own algorithms for their individual purposes. . . . Overall I find Introduction to Time Series and Forecasting to be a very useful and enlightening introduction to time series. --Journal of the American Statistical Association The emphasis is on hands-on experience and the friendly software that accompanies the book serves the purpose admirably. . . . The authors should be congratulated for making the subject accessible and fun to learn. The book is a pleasure to read and highly recommended. I regard it as the best introductory text in town. --Short Book Reviews, International Statistical Review
Introduction to Time Series Modeling with Applications in R (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Genshiro KitagawaPraise for the first edition: [This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. … [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework. –Statistics in Medicine What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters. –MAA Reviews Introduction to Time Series Modeling with Applications in R, Second Edition covers numerous stationary and nonstationary time series models and tools for estimating and utilizing them. The goal of this book is to enable readers to build their own models to understand, predict and master time series. The second edition makes it possible for readers to reproduce examples in this book by using the freely available R package TSSS to perform computations for their own real-world time series problems. This book employs the state-space model as a generic tool for time series modeling and presents the Kalman filter, the non-Gaussian filter and the particle filter as convenient tools for recursive estimation for state-space models. Further, it also takes a unified approach based on the entropy maximization principle and employs various methods of parameter estimation and model selection, including the least squares method, the maximum likelihood method, recursive estimation for state-space models and model selection by AIC. Along with the standard stationary time series models, such as the AR and ARMA models, the book also introduces nonstationary time series models such as the locally stationary AR model, the trend model, the seasonal adjustment model, the time-varying coefficient AR model and nonlinear non-Gaussian state-space models. About the Author: Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
Introduction to Topological Groups (Dover Books on Mathematics)
by Dr Taqdir HusainSuitable for advanced undergraduates and graduate students in mathematics, this introduction to topological groups presumes familiarity with the elementary concepts of set theory, elements of functional analysis, functions of real and complex variables, and the theory of functions of several variables. Chapters I to V deal with the algebraico-topological aspect of the subject, and Chapters VI to IX emphasize its analytical aspect.After an introductory chapter on the fundamentals of topology and group theory, the treatment explores semitopological groups and the general theory of topological groups. An elementary study of locally compact topological groups is followed by proofs of the open homomorphism and closed graph theorems in a very general setting. Succeeding chapters examine the rudiments of analysis on topological groups. Topics include the Harr measure, finite-dimensional representations of groups, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras.
Introduction to Topology: Second Edition (Dover Books on Mathematics)
by Theodore W. Gamelin Robert Everist GreeneOne of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two. The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, important applications become immediately evident without the necessity of a large formal program.Prerequisites are familiarity with real numbers and some basic set theory. Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition), while a list of notations and bibliographical references appear at the end of the book.
Introduction to Topology: Third Edition
by Bert MendelsonHighly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.
Introduction to Topology
by Tej Bahadur SinghTopology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.
Introduction To Topology And Geometry
by Saul Stahl Catherine StensonAn easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained. " --CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: * Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being * Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods * Bridges seemingly disparate topics by creating thoughtful and logical connections * Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
An Introduction to Traffic Flow Theory (Springer Optimization and Its Applications #84)
by Lily ElefteriadouThis text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today's highway transportation system. It provides the fundamental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc. ). Newer concepts of Intelligent transportation systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art in traffic flow research and microscopic traffic analysis and traffic simulation have significantly advanced and are also discussed in this text. Real world examples and useful problem sets complement each chapter. This textbook is meant for use in advanced undergraduate/graduate level courses in traffic flow theory with prerequisites including two semesters of calculus, statistics, and an introductory course in transportation. The text would also be of interest to transportation professionals as a refresher in traffic flow theory, or as a reference. Students and engineers of diverse backgrounds will find this text accessible and applicable to today's traffic issues.
An Introduction to Traffic Flow Theory (Springer Optimization and Its Applications #84)
by Lily ElefteriadouThis second edition of An Introduction to Traffic Flow Theory adds new material in several chapters related to advanced technologies including autonomy, the use of sensors and communications, and particularly congestion mitigation solutions that leverage connected and autonomous vehicles (CAVs). It also includes a new chapter that briefly outlines several mathematical analysis techniques commonly used in traffic flow theory, aiming to introduce students to some of the most frequently used tools available for traffic operational-related analysis. This new edition also includes several updates related to the most recent versions of the Highway Capacity Manual and the Green Book. This textbook is meant for use in advanced undergraduate/graduate level courses in traffic flow theory with prerequisites including two semesters of calculus, statistics, and an introductory course in transportation. The text would also be of interest to transportation professionals as a refresherin traffic flow theory or as a reference. Students and engineers of diverse backgrounds will find this text accessible and applicable to today’s traffic issues.This text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today’s highway transportation system. It provides the fundamental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc.). Newer concepts of Intelligent transportation systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art traffic flow research, microscopic traffic analysis, and traffic simulation have significantly advanced and are also discussed in this text. Real-world examples and useful problem sets complement each chapter.
Introduction to Transients in Electrical Circuits: Analytical and Digital Solution Using an EMTP-based Software (Power Systems)
by José Carlos Goulart de Siqueira Benedito Donizeti BonattoThis book integrates analytical and digital solutions through Alternative Transients Program (ATP) software, recognized for its use all over the world in academia and in the electric power industry, utilizing a didactic approach appropriate for graduate students and industry professionals alike.This book presents an approach to solving singular-function differential equations representing the transient and steady-state dynamics of a circuit in a structured manner, and without the need for physical reasoning to set initial conditions to zero plus (0+). It also provides, for each problem presented, the exact analytical solution as well as the corresponding digital solution through a computer program based on the Electromagnetics Transients Program (EMTP).Of interest to undergraduate and graduate students, as well as industry practitioners, this book fills the gap between classic works in the field of electrical circuits and more advanced works in the field of transients in electrical power systems, facilitating a full understanding of digital and analytical modeling and solution of transients in basic circuits.
Introduction to Traveling Waves
by Anna R. Ghazaryan Stéphane Lafortune Vahagn ManukianIntroduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts. Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves. Features Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations. Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling. Contains numerous examples to support the theoretical material. Supplementary MATLAB codes available via GitHub.
An Introduction to Ultrametric Summability Theory (Forum for Interdisciplinary Mathematics #2)
by P. N. NatarajanUltrametric analysis has emerged as an important branch of mathematics in recent years. This book presents, for the first time, a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis.
An Introduction to Unconstrained Optimisation
by J. McKeown D. Meegan D. SprevakIntegrating computer graphics and computer-based exercises with the text, An Introduction to Unconstrained Optimisation illustrates key methods with many examples and exercises using the computer. The book takes an elementary approach to this advanced topic, allowing readers to concentrate on learning and understanding the concepts of numerical optimization without unnecessary involvement in the intricacies of the subject. In addition, the modular approach of the software provides the opportunity to explore the algorithms used and to develop them further or try alternative approaches. Most of the algorithms are based upon a "hill-climbing" concept which, in two dimensions, is illustrated dynamically on the computer screen in the form of contour plots and search directions. The text is not specific to any particular microcomputer. Software is available for the BBC series of machines (40/80 track disc formats) and PC-compatible machines. The software is not available from your local bookstore, but is easily obtainable using the order form in the book.Keeping proofs and lists of methods to a minimum, the book is at a level suitable for a first course in numerical analysis, with a basic knowledge of calculus and vector algebra assumed. This book/software package will be of interest to professionals, teachers, and undergraduate students in mathematics, operational research, science, and engineering as well as economics and management courses that deal with quantitative methods.
Introduction to Unconstrained Optimization with R
by Shashi Kant Mishra Bhagwat RamThis book discusses unconstrained optimization with R—a free, open-source computing environment, which works on several platforms, including Windows, Linux, and macOS. The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. Each method is accompanied by worked examples and R scripts. To help readers apply these methods in real-world situations, the book features a set of exercises at the end of each chapter. Primarily intended for graduate students of applied mathematics, operations research and statistics, it is also useful for students of mathematics, engineering, management, economics, and agriculture.
An Introduction to Undergraduate Research in Computational and Mathematical Biology: From Birdsongs to Viscosities (Foundations for Undergraduate Research in Mathematics)
by Hannah Callender Highlander Alex Capaldi Carrie Diaz EatonSpeaking directly to the growing importance of research experience in undergraduate mathematics programs, this volume offers suggestions for undergraduate-appropriate research projects in mathematical and computational biology for students and their faculty mentors. The aim of each chapter is twofold: for faculty, to alleviate the challenges of identifying accessible topics and advising students through the research process; for students, to provide sufficient background, additional references, and context to excite students in these areas and to enable them to successfully undertake these problems in their research.Some of the topics discussed include: • Oscillatory behaviors present in real-world applications, from seasonal outbreaks of childhood diseases to action potentials in neurons• Simulating bacterial growth, competition, and resistance with agent-based models and laboratory experiments• Network structure and the dynamics of biological systems• Using neural networks to identify bird species from birdsong samples• Modeling fluid flow induced by the motion of pulmonary ciliaAimed at undergraduate mathematics faculty and advanced undergraduate students, this unique guide will be a valuable resource for generating fruitful research collaborations between students and faculty.
An Introduction to Using Mapping Sentences
by Paul M. Hackett Katelyn LustigThis book acts as an introductory guide to understanding and using the mapping sentence as a tool in social science and humanities research. The book fills the need for a concise text that simply instructs how and when to use a mapping sentence and provides practical examples. Mapping sentences are a major research component and tool of facet theory. The book begins by covering the background to mapping sentence, including the philosophy and theory underpinning it. The following chapter discuss what mapping sentence is, what different kinds of mapping sentences exist, and knowing when and which to use it in a given situation. The book then moves into describing how to write a mapping sentence and how to analyse the information gained from mapping sentence research. It ends with a consideration of the future developments of mapping sentences and their applications across the social sciences and humanities, including in particular psychology, marketing, behavioural biology, art and health.
Introduction to Vector and Tensor Analysis
by Robert C. WredeA broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L (SpringerBriefs in Mathematics)
by Nikos KatzourakisThe purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.
Introductory Algebra An Applied Approach 9th Edition
by Richard N. Aufmann Joanne S. LockwoodAs in previous editions, the focus in INTRODUCTORY ALGEBRA remains on the Aufmann Interactive Method (AIM). Students are encouraged to be active participants in the classroom and in their own studies as they work through the examples. Student engagement is crucial to success.
Introductory Algebra for College Students (Sixth Edition)
by Robert BlitzerThis book provides comprehensive, in-depth coverage of the topics required in a one-term course in beginning or introductory algebra.
Introductory Algebra Student Workbook, Vol. 2 (Fifth Edition)
by Scottsdale Community College Mathematics DepartmentIntroductory Algebra Student Workbook V2 is designed to lead students through Introductory Algebra
Introductory Analysis: An Inquiry Approach
by John D. Ross Kendall C. RichardsIntroductory Analysis: An Inquiry Approach aims to provide a self-contained, inquiry-oriented approach to undergraduate-level real analysis. The presentation of the material in the book is intended to be "inquiry-oriented'" in that as each major topic is discussed, details of the proofs are left to the student in a way that encourages an active approach to learning. The book is "self-contained" in two major ways: it includes scaffolding (i.e., brief guiding prompts marked as Key Steps in the Proof) for many of the theorems. Second, it includes preliminary material that introduces students to the fundamental framework of logical reasoning and proof-writing techniques. Students will be able to use the guiding prompts (and refer to the preliminary work) to develop their proof-writing skills. Features Structured in such a way that approximately one week of class can be devoted to each chapter Suitable as a primary text for undergraduates, or as a supplementary text for some postgraduate courses Strikes a unique balance between enquiry-based learning and more traditional approaches to teaching
Introductory and Intermediate Algebra for College Students (Fifth Edition)
by Robert F. BlitzerNOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value-this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. For courses in introductory and intermediate algebra. Gets them engaged. Keeps them engaged. Bob Blitzer's use of realistic applications instantly piques students' curiosity about the presence of mathematical concepts in the world around them. These applications are apparent throughout the entire program-from his relatable examples, friendly writing style, and thought-provoking features in the textbook, to the enhanced digital resources in the MyMathLab course. Blitzer pulls from topics that are relevant to college students, often from pop culture and everyday life, to ensure that students will actually use their learning resources to achieve success. With an expansion of the series to now include a Developmental Math "all-in-one" text (with content spanning prealgebra through intermediate algebra), and with an enhanced media program accompanying this revision, developmental students at all levels will see how math applies to their daily lives and culture. Also available with MyMathLab #65533; MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.