Download or read book Heavy Tailed Functional Time Series written by Thomas Meinguet and published by Presses univ. de Louvain. This book was released on 2010-08 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this thesis is to treat the temporal tail dependence and the cross-sectional tail dependence of heavy tailed functional time series. Functional time series are aimed at modelling spatio-temporal phenomena; for instance rain, temperature, pollution on a given geographical area, with temporally dependent observations. Heavy tails mean that the series can exhibit much higher spikes than with Gaussian distributions for instance. In such cases, second moments cannot be assumed to exist, violating the basic assumption in standard functional data analysis based on the sequence of autocovariance operators. As for random variables, regular variation provides the mathematical backbone for a coherent theory of extreme values. The main tools introduced in this thesis for a regularly varying functional time series are its tail process and its spectral process. These objects capture all the aspects of the probability distribution of extreme values jointly over time and space. The development of the tail and spectral process for heavy tailed functional time series is followed by three theoretical applications. The first application is a characterization of a variety of indices and objects describing the extremal behavior of the series: the extremal index, tail dependence coefficients, the extremogram and the point process of extremes. The second is the computation of an explicit expression of the tail and spectral processes for heavy tailed linear functional time series. The third and final application is the introduction and the study of a model for the spatio-temporal dependence for functional time series called maxima of moving maxima of continuous functions (CM3 processes), with the development of an estimation method.
Download or read book Heavy Tailed Time Series written by Rafal Kulik and published by Springer Nature. This book was released on 2020-07-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.
Download or read book Heavy Tail and Plug In Robust Consistent Conditional Moment Tests of Functional Form written by Jonathan B. Hill and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present asymptotic power-one tests of regression model functional form for heavy tailed time series. Under the null hypothesis of correct specification the model errors must have a finite mean, and otherwise only need to have a fractional moment. If the errors have an infinite variance then in principle any consistent plug-in is allowed, depending on the model, including those with non-Gaussian limits and/or a sub-root(n)-convergence rate. One test statistic exploits an orthogonalized test equation that promotes plug-in robustness irrespective of tails. We derive chi-squared weak limits of the statistics, we characterize an empirical process method for smoothing over a trimming parameter, and we study the finite sample properties of the test statistics.
Download or read book A Practical Guide to Heavy Tails written by Robert Adler and published by Springer Science & Business Media. This book was released on 1998-10-26 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Download or read book Heavy Tail Phenomena written by Sidney I. Resnick and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Download or read book Inference for Heavy Tailed Data written by Liang Peng and published by Academic Press. This book was released on 2017-08-11 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tailed data appears frequently in social science, internet traffic, insurance and finance. Statistical inference has been studied for many years, which includes recent bias-reduction estimation for tail index and high quantiles with applications in risk management, empirical likelihood based interval estimation for tail index and high quantiles, hypothesis tests for heavy tails, the choice of sample fraction in tail index and high quantile inference. These results for independent data, dependent data, linear time series and nonlinear time series are scattered in different statistics journals. Inference for Heavy-Tailed Data Analysis puts these methods into a single place with a clear picture on learning and using these techniques. Contains comprehensive coverage of new techniques of heavy tailed data analysis Provides examples of heavy tailed data and its uses Brings together, in a single place, a clear picture on learning and using these techniques
Download or read book Extreme Value Theory for Time Series written by Thomas Mikosch and published by Springer Nature. This book was released on with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Analysis of Univariate Heavy Tailed Data written by Natalia Markovich and published by John Wiley & Sons. This book was released on 2008-03-11 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.
Download or read book Heavy Tail Phenomena written by Sidney I. Resnick and published by Springer Science & Business Media. This book was released on 2007 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Download or read book Heavy Tail Modeling in Time Series and Telecommunications written by Eric Hendrik Van den Berg and published by . This book was released on 1999 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Linear Time Series written by Kamil Feridun Turkman and published by Springer. This book was released on 2014-09-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time series.
Download or read book Analysis of Heavy tailed Time Series written by and published by . This book was released on 2017 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Statistics written by Herve Dimy Anguima Ibondzi and published by LAP Lambert Academic Publishing. This book was released on 2014-05-29 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial data have, among others, a particular feature: large values of such series cluster, we are concerned with estimation of clustering probabilities for univariate heavy tailed time series. We describe regular variation as a tool to model heavy tails. We summarize some results on the central limit theorem (CLT) and tightness of stochastic processes. These tools are needed to prove asymptotic normality of our estimator. We employ functional convergence of a bivariate tail empirical process, regular variation property and Lindeberg's CLT and the mixing property with geometric rates to conclude asymptotic normality of an estimator of the clustering probabilities. Theoretical results are illustrated by simulation studies.
Download or read book Handbook of Heavy Tailed Distributions in Finance written by S.T Rachev and published by Elsevier. This book was released on 2003-03-05 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series.This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.
Download or read book Cyclostationarity Theory and Methods IV written by Fakher Chaari and published by Springer. This book was released on 2019-07-31 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions presented at the 10th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2017. It includes twelve interesting papers covering current topics related to both cyclostationary and general non stationary processes. Moreover, this book, which covers both theoretical and practical issues, offers a practice-oriented guide to the analysis of data sets with non-stationary behavior and a bridge between basic and applied research on nonstationary processes. It provides students, researchers and professionals with a timely guide on cyclostationary systems, nonstationary processes and relevant engineering applications.
Download or read book Moment Condition Tests for Heavy Tailed Time Series written by Jonathan B. Hill and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop an asymptotically chi-squared statistic for testing moment conditions E[m(b0)] = 0, where m(b) may be weakly dependent, scalar components of m(b0) may have an infinite variance, and E[m(b)] need not exist for any b under the alternative. Score tests are a natural application, and in general a variety of tests can be heavy-tail robustified by our method, including white noise, GARCH affects, omitted variables, distribution, functional form, causation, volatility spillover and over-identification. The test statistic is derived from a tail-trimmed sample version of the moments evaluated at a consistent plug-in b_hat for b0. Depending on the test in question and heaviness of tails, b_hat may be any consistent estimator including sub-root-T-convergent and/or asymptotically non-Gaussian ones, since b_hat can be assured not to affect the test statistic asymptotically. We adapt bootstrap, p-value occupation time, and covariance determinant methods for selecting the trimming fractile in any sample, and apply our statistic to tests of white noise, omitted variables and volatility spillover. We find it obtains sharp empirical size and strong power, while conventional tests exhibit size distortions.
