Author: Nina Golyandina
Publisher: CRC Press
ISBN: 9781420035841
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing. However, despite the promise it holds for time series applications in other disciplines, SSA is not widely known among statisticians and econometrists, and although the basic SSA algorithm looks simple, understanding what it does and where its pitfalls lay is by no means simple. Analysis of Time Series Structure: SSA and Related Techniques provides a careful, lucid description of its general theory and methodology. Part I introduces the basic concepts, and sets forth the main findings and results, then presents a detailed treatment of the methodology. After introducing the basic SSA algorithm, the authors explore forecasting and apply SSA ideas to change-point detection algorithms. Part II is devoted to the theory of SSA. Here the authors formulate and prove the statements of Part I. They address the singular value decomposition (SVD) of real matrices, time series of finite rank, and SVD of trajectory matrices. Based on the authors' original work and filled with applications illustrated with real data sets, this book offers an outstanding opportunity to obtain a working knowledge of why, when, and how SSA works. It builds a strong foundation for successfully using the technique in applications ranging from mathematics and nonlinear physics to economics, biology, oceanology, social science, engineering, financial econometrics, and market research.
Author: Nina Golyandina
Publisher: Chapman and Hall/CRC
ISBN: 9781584881940
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing. However, despite the promise it holds for time series applications in other disciplines, SSA is not widely known among statisticians and econometrists, and although the basic SSA algorithm looks simple, understanding what it does and where its pitfalls lay is by no means simple. Analysis of Time Series Structure: SSA and Related Techniques provides a careful, lucid description of its general theory and methodology. Part I introduces the basic concepts, and sets forth the main findings and results, then presents a detailed treatment of the methodology. After introducing the basic SSA algorithm, the authors explore forecasting and apply SSA ideas to change-point detection algorithms. Part II is devoted to the theory of SSA. Here the authors formulate and prove the statements of Part I. They address the singular value decomposition (SVD) of real matrices, time series of finite rank, and SVD of trajectory matrices. Based on the authors' original work and filled with applications illustrated with real data sets, this book offers an outstanding opportunity to obtain a working knowledge of why, when, and how SSA works. It builds a strong foundation for successfully using the technique in applications ranging from mathematics and nonlinear physics to economics, biology, oceanology, social science, engineering, financial econometrics, and market research.
Author: L. H. Koopmans
Publisher: Academic Press
ISBN: 1483218546
Category : Mathematics
Languages : en
Pages : 383
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Book Description
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.
Author: Holger Kantz
Publisher: Cambridge University Press
ISBN: 9780521529020
Category : Mathematics
Languages : en
Pages : 390
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Book Description
The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.
Author: Nina Golyandina
Publisher: Springer Nature
ISBN: 3662624362
Category : Mathematics
Languages : en
Pages : 156
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Book Description
This book gives an overview of singular spectrum analysis (SSA). SSA is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA is multi-purpose and naturally combines both model-free and parametric techniques, which makes it a very special and attractive methodology for solving a wide range of problems arising in diverse areas. Rapidly increasing number of novel applications of SSA is a consequence of the new fundamental research on SSA and the recent progress in computing and software engineering which made it possible to use SSA for very complicated tasks that were unthinkable twenty years ago. In this book, the methodology of SSA is concisely but at the same time comprehensively explained by two prominent statisticians with huge experience in SSA. The book offers a valuable resource for a very wide readership, including professional statisticians, specialists in signal and image processing, as well as specialists in numerous applied disciplines interested in using statistical methods for time series analysis, forecasting, signal and image processing. The second edition of the book contains many updates and some new material including a thorough discussion on the place of SSA among other methods and new sections on multivariate and multidimensional extensions of SSA.
Author: Gregory C. Reinsel
Publisher: Springer Science & Business Media
ISBN: 146840198X
Category : Mathematics
Languages : en
Pages : 278
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Book Description
The use of methods of time series analysis in the study of multivariate time series has become of increased interest in recent years. Although the methods are rather well developed and understood for univarjate time series analysis, the situation is not so complete for the multivariate case. This book is designed to introduce the basic concepts and methods that are useful in the analysis and modeling of multivariate time series, with illustrations of these basic ideas. The development includes both traditional topics such as autocovariance and auto correlation matrices of stationary processes, properties of vector ARMA models, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and model checking diagnostics for residuals, as well as topics of more recent interest for vector ARMA models such as reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate unit-root models and cointegration structure, and state-space models and Kalman filtering techniques and applications. This book concentrates on the time-domain analysis of multivariate time series, and the important subject of spectral analysis is not considered here. For that topic, the reader is referred to the excellent books by Jenkins and Watts (1968), Hannan (1970), Priestley (1981), and others.
Author: Paul Teetor
Publisher: "O'Reilly Media, Inc."
ISBN: 1449307264
Category : Computers
Languages : en
Pages : 438
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Book Description
With more than 200 practical recipes, this book helps you perform data analysis with R quickly and efficiently. The R language provides everything you need to do statistical work, but its structure can be difficult to master. This collection of concise, task-oriented recipes makes you productive with R immediately, with solutions ranging from basic tasks to input and output, general statistics, graphics, and linear regression. Each recipe addresses a specific problem, with a discussion that explains the solution and offers insight into how it works. If you’re a beginner, R Cookbook will help get you started. If you’re an experienced data programmer, it will jog your memory and expand your horizons. You’ll get the job done faster and learn more about R in the process. Create vectors, handle variables, and perform other basic functions Input and output data Tackle data structures such as matrices, lists, factors, and data frames Work with probability, probability distributions, and random variables Calculate statistics and confidence intervals, and perform statistical tests Create a variety of graphic displays Build statistical models with linear regressions and analysis of variance (ANOVA) Explore advanced statistical techniques, such as finding clusters in your data "Wonderfully readable, R Cookbook serves not only as a solutions manual of sorts, but as a truly enjoyable way to explore the R language—one practical example at a time."—Jeffrey Ryan, software consultant and R package author
Author: Andrew C. Harvey
Publisher: Cambridge University Press
ISBN: 9780521405737
Category : Business & Economics
Languages : en
Pages : 574
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Book Description
A synthesis of concepts and materials, that ordinarily appear separately in time series and econometrics literature, presents a comprehensive review of theoretical and applied concepts in modeling economic and social time series.
Author: Rami Krispin
Publisher: Packt Publishing Ltd
ISBN: 1788624041
Category : Computers
Languages : en
Pages : 438
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Book Description
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.
Author: Saul I. Gass
Publisher: Springer Science & Business Media
ISBN: 079237827X
Category : Management science
Languages : en
Pages : 969
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Book Description
Audience: Anyone concerned with the science, techniques and ideas of how decisions are made."--BOOK JACKET.
