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.
The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.
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.
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.
The latest cutting-edge research on market microstructure Based on the December 2010 conference on market microstructure, organized with the help of the Institut Louis Bachelier, this guide brings together the leading thinkers to discuss this important field of modern finance. It provides readers with vital insight on the origin of the well-known anomalous "stylized facts" in financial prices series, namely heavy tails, volatility, and clustering, and illustrates their impact on the organization of markets, execution costs, price impact, organization liquidity in electronic markets, and other issues raised by high-frequency trading. World-class contributors cover topics including analysis of high-frequency data, statistics of high-frequency data, market impact, and optimal trading. This is a must-have guide for practitioners and academics in quantitative finance.
This book deals with the mathematical aspects of survival analysis and reliability as well as other topics, reflecting recent developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics. The work will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering.
Martingale Methods in Statistics provides a unique introduction to statistics of stochastic processes written with the author’s strong desire to present what is not available in other textbooks. While the author chooses to omit the well-known proofs of some of fundamental theorems in martingale theory by making clear citations instead, the author does his best to describe some intuitive interpretations or concrete usages of such theorems. On the other hand, the exposition of relatively new theorems in asymptotic statistics is presented in a completely self-contained way. Some simple, easy-to-understand proofs of martingale central limit theorems are included. The potential readers include those who hope to build up mathematical bases to deal with high-frequency data in mathematical finance and those who hope to learn the theoretical background for Cox’s regression model in survival analysis. A highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics, such as the asymptotic representation of Z-estimators, the theory of asymptotically optimal inference based on the LAN concept and the unified approach to the change point problems via "Z-process method". Some new inequalities for maxima of finitely many martingales are presented in the Appendix. Readers will find many tips for solving concrete problems in modern statistics of stochastic processes as well as in more fundamental models such as i.i.d. and Markov chain models.
