Dependence Modeling Between Continuous Time Stochastic Processes PDF Download
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Author: Thomas Deschatre
Publisher:
ISBN:
Category :
Languages : en
Pages : 213
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Book Description
In this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production.
Author: Thomas Deschatre
Publisher:
ISBN:
Category :
Languages : en
Pages : 213
Get Book Here
Book Description
In this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production.
Author: Kees van Montfort
Publisher: Springer
ISBN: 3319772198
Category : Medical
Languages : en
Pages : 442
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Book Description
This unique book provides an overview of continuous time modeling in the behavioral and related sciences. It argues that the use of discrete time models for processes that are in fact evolving in continuous time produces problems that make their application in practice highly questionable. One main issue is the dependence of discrete time parameter estimates on the chosen time interval, which leads to incomparability of results across different observation intervals. Continuous time modeling by means of differential equations offers a powerful approach for studying dynamic phenomena, yet the use of this approach in the behavioral and related sciences such as psychology, sociology, economics and medicine, is still rare. This is unfortunate, because in these fields often only a few discrete time (sampled) observations are available for analysis (e.g., daily, weekly, yearly, etc.). However, as emphasized by Rex Bergstrom, the pioneer of continuous-time modeling in econometrics, neither human beings nor the economy cease to exist in between observations. In 16 chapters, the book addresses a vast range of topics in continuous time modeling, from approaches that closely mimic traditional linear discrete time models to highly nonlinear state space modeling techniques. Each chapter describes the type of research questions and data that the approach is most suitable for, provides detailed statistical explanations of the models, and includes one or more applied examples. To allow readers to implement the various techniques directly, accompanying computer code is made available online. The book is intended as a reference work for students and scientists working with longitudinal data who have a Master's- or early PhD-level knowledge of statistics.
Author: Tomasz R. Bielecki
Publisher: Cambridge University Press
ISBN: 1108895379
Category : Mathematics
Languages : en
Pages : 280
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Book Description
The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.
Author: Howard M. Taylor
Publisher: Academic Press
ISBN: 1483269272
Category : Mathematics
Languages : en
Pages : 410
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Book Description
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Author: Frank Beichelt
Publisher: CRC Press
ISBN: 9781420010459
Category : Mathematics
Languages : en
Pages : 438
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Book Description
This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.
Author: Denis Bosq
Publisher: Springer Science & Business Media
ISBN: 9401587698
Category : Mathematics
Languages : en
Pages : 355
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Book Description
This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math ematically?". The exercises at the end of each lesson will deepen the stu dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.
Author: J. K. Lindsey
Publisher: Cambridge University Press
ISBN: 9781139454513
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
Author: Floyd B. Hanson
Publisher: SIAM
ISBN: 9780898718638
Category : Mathematics
Languages : en
Pages : 472
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Book Description
This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.
Author: Harry Joe
Publisher: World Scientific
ISBN: 981429988X
Category : Business & Economics
Languages : en
Pages : 370
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Book Description
1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka
Author: Kees van Montfort
Publisher:
ISBN: 9783319772202
Category : Differential equations
Languages : en
Pages : 442
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Book Description
This unique book provides an overview of continuous time modeling in the behavioral and related sciences. It argues that the use of discrete time models for processes that are in fact evolving in continuous time produces problems that make their application in practice highly questionable. One main issue is the dependence of discrete time parameter estimates on the chosen time interval, which leads to incomparability of results across different observation intervals. Continuous time modeling by means of differential equations offers a powerful approach for studying dynamic phenomena, yet the use of this approach in the behavioral and related sciences such as psychology, sociology, economics and medicine, is still rare. This is unfortunate, because in these fields often only a few discrete time (sampled) observations are available for analysis (e.g., daily, weekly, yearly, etc.). However, as emphasized by Rex Bergstrom, the pioneer of continuous-time modeling in econometrics, neither human beings nor the economy cease to exist in between observations. In 16 chapters, the book addresses a vast range of topics in continuous time modeling, from approaches that closely mimic traditional linear discrete time models to highly nonlinear state space modeling techniques. Each chapter describes the type of research questions and data that the approach is most suitable for, provides detailed statistical explanations of the models, and includes one or more applied examples. To allow readers to implement the various techniques directly, accompanying computer code is made available online. The book is intended as a reference work for students and scientists working with longitudinal data who have a Master's- or early PhD-level knowledge of statistics.--
