Introduction To Statistical Time Series
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| Author | : Peter J. Brockwell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 429 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475725264 |
Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.
| Author | : Douglas C. Montgomery |
| Publisher | : John Wiley & Sons |
| Total Pages | : 670 |
| Release | : 2015-04-21 |
| Genre | : Mathematics |
| ISBN | : 1118745159 |
Praise for the First Edition "...[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both popular and modern time series methodologies as well as an introduction to Bayesian methods in forecasting. Introduction to Time Series Analysis and Forecasting, Second Edition also includes: Over 300 exercises from diverse disciplines including health care, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®, and R that illustrate the theory and practicality of forecasting techniques in the context of time-oriented data New material on frequency domain and spatial temporal data analysis Expanded coverage of the variogram and spectrum with applications as well as transfer and intervention model functions A supplementary website featuring PowerPoint® slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, Second Edition is an ideal textbook upper-undergraduate and graduate-levels courses in forecasting and time series. The book is also an excellent reference for practitioners and researchers who need to model and analyze time series data to generate forecasts.
| Author | : Rob J Hyndman |
| Publisher | : OTexts |
| Total Pages | : 380 |
| Release | : 2018-05-08 |
| Genre | : Business & Economics |
| ISBN | : 0987507117 |
Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
| Author | : Christian H. Weiss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 300 |
| Release | : 2018-02-05 |
| Genre | : Mathematics |
| ISBN | : 1119096960 |
A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series. The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website. Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series Covers common models for time series of counts as well as for categorical time series, and works out their most important stochastic properties Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions Includes dataset examples with all necessary R code provided on a companion website An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.
| Author | : Chris Chatfield |
| Publisher | : CRC Press |
| Total Pages | : 398 |
| Release | : 2019-04-25 |
| Genre | : Mathematics |
| ISBN | : 1498795641 |
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.
| Author | : Wayne A. Fuller |
| Publisher | : John Wiley & Sons |
| Total Pages | : 738 |
| Release | : 1995-12-29 |
| Genre | : Mathematics |
| ISBN | : 9780471552390 |
The subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accommodate a wide variety of readers, review material,especially on elementary results in Fourier analysis, large samplestatistics, and difference equations, has been included.
| Author | : Paul S.P. Cowpertwait |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 262 |
| Release | : 2009-05-28 |
| Genre | : Mathematics |
| ISBN | : 0387886982 |
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.
| Author | : Gareth James |
| Publisher | : Springer Nature |
| Total Pages | : 617 |
| Release | : 2023-08-01 |
| Genre | : Mathematics |
| ISBN | : 3031387473 |
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance, marketing, and astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. This book is targeted at statisticians and non-statisticians alike, who wish to use cutting-edge statistical learning techniques to analyze their data. Four of the authors co-wrote An Introduction to Statistical Learning, With Applications in R (ISLR), which has become a mainstay of undergraduate and graduate classrooms worldwide, as well as an important reference book for data scientists. One of the keys to its success was that each chapter contains a tutorial on implementing the analyses and methods presented in the R scientific computing environment. However, in recent years Python has become a popular language for data science, and there has been increasing demand for a Python-based alternative to ISLR. Hence, this book (ISLP) covers the same materials as ISLR but with labs implemented in Python. These labs will be useful both for Python novices, as well as experienced users.
| Author | : Manfred Mudelsee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 497 |
| Release | : 2010-08-26 |
| Genre | : Science |
| ISBN | : 9048194822 |
Climate is a paradigm of a complex system. Analysing climate data is an exciting challenge, which is increased by non-normal distributional shape, serial dependence, uneven spacing and timescale uncertainties. This book presents bootstrap resampling as a computing-intensive method able to meet the challenge. It shows the bootstrap to perform reliably in the most important statistical estimation techniques: regression, spectral analysis, extreme values and correlation. This book is written for climatologists and applied statisticians. It explains step by step the bootstrap algorithms (including novel adaptions) and methods for confidence interval construction. It tests the accuracy of the algorithms by means of Monte Carlo experiments. It analyses a large array of climate time series, giving a detailed account on the data and the associated climatological questions. This makes the book self-contained for graduate students and researchers.
| Author | : L. H. Koopmans |
| Publisher | : Academic Press |
| Total Pages | : 383 |
| Release | : 2014-05-12 |
| Genre | : Mathematics |
| ISBN | : 1483218546 |
The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.
