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Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 12
Book Description
In this paper we take up Bayesian inference in multivariate stable distributions through innovative multivariate stable copulae. The problem that the characteristic function is defined through a difficult object, the spectral measure is completely bypassed by our approach. The new methods are applied to major exchange rates with encouraging results. The copula-based technique is based on non-parametric margins (both data-estimated as well as Dirichlet process priors) and we compare with a multivariate stable copula whose margins can be normal, Student-t or univariate stable.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 12
Book Description
In this paper we take up Bayesian inference in multivariate stable distributions through innovative multivariate stable copulae. The problem that the characteristic function is defined through a difficult object, the spectral measure is completely bypassed by our approach. The new methods are applied to major exchange rates with encouraging results. The copula-based technique is based on non-parametric margins (both data-estimated as well as Dirichlet process priors) and we compare with a multivariate stable copula whose margins can be normal, Student-t or univariate stable.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 41
Book Description
In this paper we take up Bayesian inference in general, multivariate stable distributions. We use approximate Bayesian computation (ABC) along with carefully crafted proposal distributions for the implementation of MCMC. The problem of selecting summary statistics in ABC is resolved through the use of the characteristic function. Two important problems in multivariate stable distributions are: (i) the selection of an optimal con guration of the grid points where the empirical and theoretical characteristic functions are compared, and (ii) the estimation of the spectral measure through which the distributions are de ned in Rd. The problems are resolved successfully and certain new approximations to the spectral measure are proposed and implemented. E fficient proposal/importance distributions are constructed, and tested thoroughly, to ensure good performance in connection with ABC. The new techniques are applied to exchange rate and stock return data and are supplemented by Monte Carlo simulations. In addition, critical values are provided for a closeness statistic between the empirical and theoretical characteristic functions, resolving successfully another major problem in ABC-related inference.
Author: Efthymios G. Tsionas Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their spectral measure. We present e cient MCMC schemes to perform the computations when the spectral measure is approximated discretely or, as we propose, by a normal distribution. Appropriate latent variables are introduced to implement MCMC. In relation to the discrete approximation, we propose e cient computational schemes based on the characteristic function.
Author: Arkady Shemyakin Publisher: John Wiley & Sons ISBN: 1118959019 Category : Mathematics Languages : en Pages : 314
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: Publisher: ISBN: Category : Languages : en Pages : 194
Book Description
There continues to be unfading interest in using parametric max-stable processes to study time dependence and clustered extremes in time series data. However, this comes with some difficulties largely due to inability to find enough models that fit to data directly without transforming the data and the barriers in estimating the often large number of model parameters. In this work, we study the use of sparse maxima of moving maxima (M3) process with random effects and hidden Frechet type shocks from which we get a max-linear model. In this setting, the model is applicable to cases of tail dependence or independence depending on the parameter values. Some of the fine properties of the model include mirroring the dependence structure in real data, dealing with the undesirable signature patterns found in most parametric max-stable processes and being directly applicable to real data. In the multivariate setting, we employ a sparse multivariate maxima of moving maxima (M4) process as the univariate setting does with the M3 process. A copula structure is added to our model, specifically to model the joint distribution of the random Frechet type shocks. For parameter estimation, we use Monte Carlo methods and extend application to high-frequency financial time series data. Finally, since our model has a latent Markov process, we investigate the estimation of the latent process using discrete distribution similar to the well studied Sequential Monte Carlo (SMC) methods. Keywords: Extreme value theory; max-stable processes; time series; Bayesian inference; max-linear models; latent process estimation; high-frequency financial data.
Author: Piotr Jaworski Publisher: Springer Science & Business Media ISBN: 3642354076 Category : Business & Economics Languages : en Pages : 299
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 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.
Author: Roberto Casarin Publisher: ISBN: Category : Languages : en Pages : 50
Book Description
In many different fields such as hydrology, telecommunications, physics of condensed matter and finance, the gaussian model results unsatisfactory and reveals difficulties in fitting data with skewness, heavy tails and multimodality. The use of stable distributions allows for modelling skewness and heavy tails but gives rise to inferential problems related to the estimation of the stable distributions' parameters. Some recent works have proposed characteristic function based estimation method and MCMC simulation based estimation techniques like the MCMC-EM method and the Gibbs sampling method in a full Bayesian approach. The aim of this work is to generalise the stable distribution framework by introducing a model that accounts also for multimodality. In particular we introduce a stable mixture model and a suitable reparametrisation of the mixture, which allow us to make inference on the mixture parameters. We use a full Bayesian approach and MCMC simulation techniques for the estimation of the posterior distribution. Finally we propose some applications of stable mixtures to financial data.
Author: Daniel B. Rowe Publisher: CRC Press ISBN: 9781420035261 Category : Mathematics Languages : en Pages : 360
Book Description
Of the two primary approaches to the classic source separation problem, only one does not impose potentially unreasonable model and likelihood constraints: the Bayesian statistical approach. Bayesian methods incorporate the available information regarding the model parameters and not only allow estimation of the sources and mixing coefficients, but
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Efthymios G. Tsionas
Author: Arkady Shemyakin
Author: Liangwei Wang
Author: 
Author: Piotr Jaworski
Author: Roberto Casarin
Author: Zhaohui Zin
Author: Daniel B. Rowe