modern spectrum analysis of time series fast algorithms and error control techniques

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Modern Spectrum Analysis Of Time Series

Author : Prabhakar S. Naidu
ISBN : 0849324645
Genre : Mathematics
File Size : 41. 33 MB
Format : PDF, Kindle
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Spectrum analysis can be considered as a topic in statistics as well as a topic in digital signal processing (DSP). This book takes a middle course by emphasizing the time series models and their impact on spectrum analysis. The text begins with elements of probability theory and goes on to introduce the theory of stationary stochastic processes. The depth of coverage is extensive. Many topics of concern to spectral characterization of Gaussian and non-Gaussian time series, scalar and vector time series are covered. A section is devoted to the emerging areas of non-stationary and cyclostationary time series. The book is organized more as a textbook than a reference book. Each chapter includes many examples to illustrate the concepts described. Several exercises are included at the end of each chapter. The level is appropriate for graduate and research students.

Spectral Analysis Of Signals

Author : Yanwei Wang
ISBN : 9781598290011
Genre : Technology & Engineering
File Size : 41. 93 MB
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Spectral estimation is important in many fields including astronomy, meteorology, seismology, communications, economics, speech analysis, medical imaging, radar, sonar, and underwater acoustics. Most existing spectral estimation algorithms are devised for uniformly sampled complete-data sequences. However, the spectral estimation for data sequences with missing samples is also important in many applications ranging from astronomical time series analysis to synthetic aperture radar imaging with angular diversity. For spectral estimation in the missing-data case, the challenge is how to extend the existing spectral estimation techniques to deal with these missing-data samples. Recently, nonparametric adaptive filtering based techniques have been developed successfully for various missing-data problems. Collectively, these algorithms provide a comprehensive toolset for the missing-data problem based exclusively on the nonparametric adaptive filter-bank approaches, which are robust and accurate, and can provide high resolution and low sidelobes. In this book, we present these algorithms for both one-dimensional and two-dimensional spectral estimation problems.

Analysis Of Time Series Structure

Author : Nina Golyandina
ISBN : 1420035843
Genre : Mathematics
File Size : 49. 5 MB
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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.

Time Series Theory And Methods

Author : Peter J. Brockwell
ISBN : 9781441903198
Genre : Business & Economics
File Size : 35. 42 MB
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This paperback edition is a reprint of the 1991 edition. Time Series: Theory and Methods is a systematic account of linear time series models and their application to the modeling and prediction of data collected sequentially in time. The aim is to provide specific techniques for handling data and at the same time to provide a thorough understanding of the mathematical basis for the techniques. Both time and frequency domain methods are discussed, but the book is written in such a way that either approach could be emphasized. The book is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It contains substantial chapters on multivariate series and state-space models (including applications of the Kalman recursions to missing-value problems) and shorter accounts of special topics including long-range dependence, infinite variance processes, and nonlinear models. Most of the programs used in the book are available in the modeling package ITSM2000, the student version of which can be downloaded from http://www.stat.colostate.edu/~pjbrock/student06.

Time Series Analysis And Its Applications

Author : Robert H. Shumway
ISBN : 9783319524528
Genre : Mathematics
File Size : 45. 99 MB
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The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, stochastic volatility, wavelets, and Markov chain Monte Carlo integration methods. This edition includes R code for each numerical example in addition to Appendix R, which provides a reference for the data sets and R scripts used in the text in addition to a tutorial on basic R commands and R time series. An additional file is available on the book’s website for download, making all the data sets and scripts easy to load into R.

Proceedings Of The First Us Japan Conference On The Frontiers Of Statistical Modeling An Informational Approach

Author : H. Bozdogan
ISBN : 0792325974
Genre : Mathematics
File Size : 68. 8 MB
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Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models."

Sas For Forecasting Time Series

Author : John C. Brocklebank
ISBN : 0471395668
Genre : Mathematics
File Size : 23. 34 MB
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Easy-to-read and comprehensive, this book shows how the SAS System performs multivariate time series analysis and features the advanced SAS procedures STATSPACE, ARIMA, and SPECTRA. The interrelationship of SAS/ETS procedures is demonstrated with an accompanying discussion of how the choice of a procedure depends on the data to be analysed and the reults desired. Other topics covered include detecting sinusoidal components in time series models and performing bivariate corr-spectral analysis and comparing the results with the standard transfer function methodology. The authors? unique approach to integrating students in a variety of disciplines and industries. Emphasis is on correct interpretation of output to draw meaningful conclusions. The volume, co-pubished by SAS and JWS, features both theory and practicality, and accompanies a soon-to-be extensive library of SAS hands-on manuals in a multitude of statistical areas. The book can be used with a number of hardware-specific computing machines including CMS, Mac, MVS, Opem VMS Alpha, Opmen VMS VAX, OS/390, OS/2, UNIX, and Windows.

Modern Spectrum Analysis Ii

Author : Stanislav B. Kesler
ISBN : 0879422033
Genre : Science
File Size : 55. 81 MB
Format : PDF
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Time Series Forecasting

Author : Chris Chatfield
ISBN : 9781420036206
Genre : Mathematics
File Size : 71. 98 MB
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From the author of the bestselling "Analysis of Time Series," Time-Series Forecasting offers a comprehensive, up-to-date review of forecasting methods. It provides a summary of time-series modelling procedures, followed by a brief catalogue of many different time-series forecasting methods, ranging from ad-hoc methods through ARIMA and state-space modelling to multivariate methods and including recent arrivals, such as GARCH models, neural networks, and cointegrated models. The author compares the more important methods in terms of their theoretical inter-relationships and their practical merits. He also considers two other general forecasting topics that have been somewhat neglected in the literature: the computation of prediction intervals and the effect of model uncertainty on forecast accuracy. Although the search for a "best" method continues, it is now well established that no single method will outperform all other methods in all situations-the context is crucial. Time-Series Forecasting provides an outstanding reference source for the more generally applicable methods particularly useful to researchers and practitioners in forecasting in the areas of economics, government, industry, and commerce.

Climate Time Series Analysis

Author : Manfred Mudelsee
ISBN : 9048194822
Genre : Science
File Size : 26. 62 MB
Format : PDF
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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.

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