Parameter Estimation in Fractional Diffusion Models PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Parameter Estimation in Fractional Diffusion Models PDF full book. Access full book title Parameter Estimation in Fractional Diffusion Models by Kęstutis Kubilius. Download full books in PDF and EPUB format.
Author: Kęstutis Kubilius Publisher: Springer ISBN: 3319710303 Category : Mathematics Languages : en Pages : 403
Book Description
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.
Author: Kęstutis Kubilius Publisher: Springer ISBN: 3319710303 Category : Mathematics Languages : en Pages : 403
Book Description
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.
Author: Christopher C. Heyde Publisher: Springer Science & Business Media ISBN: 0387226796 Category : Mathematics Languages : en Pages : 236
Book Description
The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
Author: Anca Patricia Vacarescu Publisher: Stanford University ISBN: Category : Languages : en Pages : 192
Book Description
We consider the nonlinear filtering problem for partially observed Generalized Hawkes Processes, which can be applied in the context of portfolio credit risk. The problem belongs to the larger class of hidden Markov models, where the counting process is observed at discrete points in time and the observations are sparse, while the intensity driving process in unobservable. We construct the conditional distribution of the process given the information filtration and we discuss the analytical and numerical properties of the corresponding filters. In particular, we study the sensitivity of the filters with respect to the parameters of the model, and we obtain a monotonicity result with respect to the jump and the volatility terms driving the intensity. Using the scaled process, we provide necessary and sufficient conditions for the frequency of time observations in terms of the parameters of the model, to ensure a good performance of the filter. We also address the problem of parameter estimation for the Generalized Hawkes Process in the framework of the EM algorithm, and we analyze the effect of the self-exciting feature of our process on the asymptotic and numerical properties of the estimators.
Author: Christiane Fuchs Publisher: Springer Science & Business Media ISBN: 3642259693 Category : Mathematics Languages : en Pages : 439
Book Description
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.
Author: David Lunn Publisher: CRC Press ISBN: 1466586664 Category : Mathematics Languages : en Pages : 393
Book Description
Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents
Author: Erich L. Lehmann Publisher: Springer Science & Business Media ISBN: 0387227288 Category : Mathematics Languages : en Pages : 610
Book Description
This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".
Author: Jaya P. N. Bishwal Publisher: Springer Nature ISBN: 3031038614 Category : Mathematics Languages : en Pages : 634
Book Description
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Author: Yury A. Kutoyants Publisher: Springer Science & Business Media ISBN: 144713866X Category : Mathematics Languages : en Pages : 493
Book Description
The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.
Author: Jaya P. N. Bishwal Publisher: Springer ISBN: 3540744487 Category : Mathematics Languages : en Pages : 271
Book Description
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
Author: Kęstutis Kubilius
Author: Kęstutis Kubilius
Author: Christopher C. Heyde
Author: Anca Patricia Vacarescu
Author: Christiane Fuchs
Author: David Lunn
Author: Erich L. Lehmann
Author: Jaya P. N. Bishwal
Author: Simo Särkkä
Author: Yury A. Kutoyants
Author: Jaya P. N. Bishwal