Author: Ivan Medovikov Publisher: ISBN: Category : Languages : en Pages : 204
Book Description
The essence of almost any multivariate econometric analysis is the analysis of dependence between sets of random quantities of interest. A series of new, powerful and omnibus non- parametric tools for the analysis of dependence emerged recently in the econometric literature, which are based on the statistical theory of copulas. A copula function completely, and in the case of random variables with continuous marginal distribution functions, uniquely character- izes their interdependence. The term?copula? emphasizes the manner in which it?couples? the marginal distributions into joint by specifying the dependence structure. This dissertation con- sists of four chapters and aims to contribute to both the theory and the applications of copulas to problems in economics, econometrics and finance. The second chapter is empirical in nature. It adopts the copula approach to the analysis of the relationship between macroeconomic news and financial markets. A large body of literature which studies the impact of news on equity markets exists. A common finding reported in such studies is that news relating to dividends, profits, and the overall state of the economy explains only a small part of the variability in the aggregate stock market returns. A common limitation of such studies is the use of the narrow measures of news, such as, for example, scheduled releases of economic data. The second chapter proposes a broad measure of macroeconomic news which is termed the?Macroeconomic News Index?. The index is based on a manual review and classification of thousands of news releases. Using the copula approach, new find- ings relating to the relationship between macroeconomic news measured using the Index and the stock markets are revealed. In particular, it is found that macroeconomic news has a much larger impact on the equity markets than reported in earlier studies, and that the relationship is highly asymmetric. The third chapter is theoretical, and aims to improve the existing non-parametric copula- based tools which help formally and rigorously establish the presence of dependence in the data. It provides an extension to the independence test statistic proposed in Genest and Remil- lard (2004) and recently Kojadinovic and Holmes (2009), which is obtained through the intro- duction of a weighted functional norm. The addition of the weights creates a channel through which the power properties of the test can be manipulated. The choice of the weights which favors observations closer to the median of the distribution is shown have the ability to give the statistic a significant power advantage. Quessy (2010) recently showed how a test for in- dependence can be used to test for the goodness of fit of parametric copulas. The addition of the weights may be particularly beneficial in this context, since it permits the imposition of asymmetric losses which arise as a consequence of modeling error. The third chapter provides additional results which enable the application of the test statistic to the problems which in- volve estimated quantities such as regression model residuals. In an illustrative application of these results, the test is used to probe the presence of conditional heteroscedasticity in a linear regression model, and is shown to have a power advantage over the test of White (1980) in several settings. This appears to be one of the first applications of the copula theory to the problem of residual-based testing which deserves closer attention and future work. The test statistic proposed in the third chapter cannot be directly applied to the analysis of time series. The fourth chapter provides a serial extension to the statistic, which is closely related to the serial test of Kojadinovic and Yan (2009). The ability to adjust the power of the test through the di erent choices of the weights is retained in the serial case. The fourth chapter further extends the results of Quessy (2010) to the serial setting, which permits the application of the statistic to the testing for the goodness of fit of serial copulas. One limitation of the statistics of Kojadinovic and Holmes (2009), Kojadinovic and Yan (2009), and the weighted statistic proposed in the third chapter is the lack of standardization, meaning that they cannot be used as measures of dependence. An upper bound for the statistic is derived in Chapter 4, which is subject to the empirical marginal copulas. A standardized version of the statistic is proposed, which can serve as an omnibus measure of vectorial dependence. A computational formula for the new copula-based dependence measure is provided.
Author: Lan Zhang Publisher: Cambridge University Press ISBN: 110847425X Category : Mathematics Languages : en Pages : 621
Book Description
Illustration of copula theory with detailed real-world case study examples in the fields of hydrology and water resources engineering.
Author: Piotr Jaworski Publisher: Springer Science & Business Media ISBN: 3642124658 Category : Mathematics Languages : en Pages : 338
Book Description
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
Author: Publisher: ScholarlyEditions ISBN: 1490110127 Category : Mathematics Languages : en Pages : 1001
Book Description
Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Alexander Lipton Publisher: World Scientific ISBN: 9812709495 Category : Business & Economics Languages : en Pages : 178
Book Description
The recent growth of credit derivatives has been explosive. The global credit derivatives market grew in notional value from $1 trillion to $20 trillion from 2000 to 2006. However, understanding the true nature of these instruments still poses both theoretical and practical challenges. For a long time now, the framework of Gaussian copulas parameterized by correlation, and more recently base correlation, has provided an adequate, if unintuitive, description of the market. However, the increased liquidity in credit indices and index tranches, as well as the proliferation of exotic instruments such as forward starting tranches, options on tranches, leveraged super senior tranches, and the like, have made it imperative to come up with models that describe market reality better.This book, originally and concurrently published in the International Journal of Theoretical and Applied Finance, Vol. 10, No. 4, 2007, agrees that base correlation has outlived its usefulness; opinions of how to replace it, however, are divided. Both the top-down and bottom-up approaches for describing the dynamics of credit baskets are presented, and pro and contra arguments are put forward. Readers will decide which direction is the most promising one at the moment. However, it is hoped that, in the near future, models that transcend base correlation will be proposed and accepted by the market.
Author: Arkady Shemyakin Publisher: John Wiley & Sons ISBN: 1118959035 Category : Mathematics Languages : en Pages : 350
Book Description
Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.
Author: Robert Engle Publisher: Princeton University Press ISBN: 1400830192 Category : Business & Economics Languages : en Pages : 176
Book Description
Financial markets respond to information virtually instantaneously. Each new piece of information influences the prices of assets and their correlations with each other, and as the system rapidly changes, so too do correlation forecasts. This fast-evolving environment presents econometricians with the challenge of forecasting dynamic correlations, which are essential inputs to risk measurement, portfolio allocation, derivative pricing, and many other critical financial activities. In Anticipating Correlations, Nobel Prize-winning economist Robert Engle introduces an important new method for estimating correlations for large systems of assets: Dynamic Conditional Correlation (DCC). Engle demonstrates the role of correlations in financial decision making, and addresses the economic underpinnings and theoretical properties of correlations and their relation to other measures of dependence. He compares DCC with other correlation estimators such as historical correlation, exponential smoothing, and multivariate GARCH, and he presents a range of important applications of DCC. Engle presents the asymmetric model and illustrates it using a multicountry equity and bond return model. He introduces the new FACTOR DCC model that blends factor models with the DCC to produce a model with the best features of both, and illustrates it using an array of U.S. large-cap equities. Engle shows how overinvestment in collateralized debt obligations, or CDOs, lies at the heart of the subprime mortgage crisis--and how the correlation models in this book could have foreseen the risks. A technical chapter of econometric results also is included. Based on the Econometric and Tinbergen Institutes Lectures, Anticipating Correlations puts powerful new forecasting tools into the hands of researchers, financial analysts, risk managers, derivative quants, and graduate students.
Author: Rustam Ibragimov Publisher: ISBN: 9789814689809 Category : BUSINESS & ECONOMICS Languages : en Pages : 303
Book Description
"This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence."--Publisher's website.
Author: Neild, Nena Raschelle Publisher: IGI Global ISBN: 1668458403 Category : Language Arts & Disciplines Languages : en Pages : 371
Book Description
There is a need in the current educational field to develop classroom strategies and environments that support deaf learners. It is critical for educators to understand the best practices and challenges within deaf education in order to provide these learners with a thorough education. Strategies for Promoting Independence and Literacy for Deaf Learners With Disabilities provides teachers with information and strategies to support deaf learners with disabilities. It also discusses background information on special education law and topics related to transition. Covering key topics such as social skills, technology, communication, and classroom environments, this premier reference source is ideal for policymakers, administrators, researchers, academicians, scholars, practitioners, instructors, preservice teachers, teacher educators, and students.
Author: Ivan Medovikov
Author: Lan Zhang
Author: Piotr Jaworski
Author: 
Author: Alexander Lipton
Author: Arkady Shemyakin
Author: Robert Engle
Author: Rustam Ibragimov
Author: 
Author: Neild, Nena Raschelle