Heavy Tailed Time Series

Author : Rafal Kulik,Philippe Soulier
Publisher : Springer Nature
Page : 677 pages
File Size : 54,8 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9781071607374

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Heavy-Tailed Time Series by Rafal Kulik,Philippe Soulier Pdf

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.

Author : Robert Adler,Raya Feldman,Murad Taqqu
Publisher : Springer Science & Business Media
Page : 560 pages
File Size : 47,5 Mb
Release : 1998-10-26
Category : Mathematics
ISBN : 0817639519

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A Practical Guide to Heavy Tails by Robert Adler,Raya Feldman,Murad Taqqu Pdf

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

Author : Jayakrishnan Nair,Adam Wierman,Bert Zwart
Publisher : Cambridge University Press
Page : 265 pages
File Size : 42,9 Mb
Release : 2022-06-09
Category : Business & Economics
ISBN : 9781316511732

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The Fundamentals of Heavy Tails by Jayakrishnan Nair,Adam Wierman,Bert Zwart Pdf

An accessible yet rigorous package of probabilistic and statistical tools for anyone who must understand or model extreme events.

Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 42,8 Mb
Release : 2007
Category : Business & Economics
ISBN : 9780387242729

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Heavy-Tail Phenomena by Sidney I. Resnick Pdf

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.

Author : Thomas Meinguet
Publisher : Presses univ. de Louvain
Page : 173 pages
File Size : 47,6 Mb
Release : 2010-08
Category : Science
ISBN : 9782874632358

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Heavy Tailed Functional Time Series by Thomas Meinguet Pdf

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.

Author : Andrew C. Harvey
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,6 Mb
Release : 2013-04-22
Category : Business & Economics
ISBN : 9781107328785

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Dynamic Models for Volatility and Heavy Tails by Andrew C. Harvey Pdf

The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.

Author : S.T Rachev
Publisher : Elsevier
Page : 707 pages
File Size : 44,9 Mb
Release : 2003-03-05
Category : Business & Economics
ISBN : 9780080557731

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Handbook of Heavy Tailed Distributions in Finance by S.T Rachev Pdf

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.

Author : Eric Hendrik Van den Berg
Publisher : Unknown
Page : 274 pages
File Size : 45,5 Mb
Release : 1999
Category : Electronic
ISBN : CORNELL:31924086216052

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Heavy Tail Modeling in Time Series and Telecommunications by Eric Hendrik Van den Berg Pdf

Author : Sergey Foss,Dmitry Korshunov,Stan Zachary
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 50,8 Mb
Release : 2013-05-21
Category : Mathematics
ISBN : 9781461471011

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An Introduction to Heavy-Tailed and Subexponential Distributions by Sergey Foss,Dmitry Korshunov,Stan Zachary Pdf

Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions. One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way. Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

Author : Natalia Markovich
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 47,9 Mb
Release : 2008-03-11
Category : Mathematics
ISBN : 0470723599

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Nonparametric Analysis of Univariate Heavy-Tailed Data by Natalia Markovich Pdf

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.

Author : Marat Ibragimov,Rustam Ibragimov,Johan Walden
Publisher : Springer
Page : 131 pages
File Size : 52,7 Mb
Release : 2015-05-23
Category : Business & Economics
ISBN : 9783319168777

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Heavy-Tailed Distributions and Robustness in Economics and Finance by Marat Ibragimov,Rustam Ibragimov,Johan Walden Pdf

This book focuses on general frameworks for modeling heavy-tailed distributions in economics, finance, econometrics, statistics, risk management and insurance. A central theme is that of (non-)robustness, i.e., the fact that the presence of heavy tails can either reinforce or reverse the implications of a number of models in these fields, depending on the degree of heavy-tailed ness. These results motivate the development and applications of robust inference approaches under heavy tails, heterogeneity and dependence in observations. Several recently developed robust inference approaches are discussed and illustrated, together with applications.

Author : Michele Leonardo Bianchi,Stoyan V Stoyanov,Gian Luca Tassinari,Frank J Fabozzi,Sergio Focardi
Publisher : World Scientific
Page : 598 pages
File Size : 47,6 Mb
Release : 2019-03-08
Category : Business & Economics
ISBN : 9789813276215

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Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management by Michele Leonardo Bianchi,Stoyan V Stoyanov,Gian Luca Tassinari,Frank J Fabozzi,Sergio Focardi Pdf

The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.

Author : Svetlozar T. Rachev
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 44,8 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817681807

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Handbook of Computational and Numerical Methods in Finance by Svetlozar T. Rachev Pdf

The subject of numerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance, and numerical analysis. The methods employed bridge the gap between financial theory and computational practice, and provide solutions for complex problems that are difficult to solve by traditional analytical methods. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research and survey articles focusing on various numerical methods in finance. The book is designed for the academic community and will also serve professional investors.

Author : Kamil Feridun Turkman,Manuel González Scotto,Patrícia de Zea Bermudez
Publisher : Springer
Page : 255 pages
File Size : 55,5 Mb
Release : 2014-09-29
Category : Mathematics
ISBN : 9783319070285

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Non-Linear Time Series by Kamil Feridun Turkman,Manuel González Scotto,Patrícia de Zea Bermudez Pdf

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.

Author : Liang Peng,Yongcheng Qi
Publisher : Academic Press
Page : 180 pages
File Size : 48,9 Mb
Release : 2017-08-11
Category : Mathematics
ISBN : 9780128047507

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Inference for Heavy-Tailed Data by Liang Peng,Yongcheng Qi Pdf

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