Simulation and Inference for Stochastic Processes with YUIMA: A Comprehensive R Framework for SDEs and Other Stochastic Processes (Use R!)

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.

YUIMA套件是第一個基於S4類別和方法的全面R框架，可模擬由Wiener過程、Lévy過程或分數布朗運動驅動的隨機微分方程，以及CARMA、COGARCH和點過程。該套件執行各種中心統計分析，如準最大概似估計、自適應貝葉斯估計、結構變化點分析、假設檢驗、非同步協方差估計、領先-落後估計、LASSO模型選擇等。YUIMA還通過Malliavin微積分的自動漸近展開，通過快速計算隨機過程的函數期望值來支持隨機數值分析。所有模型都可以是多維、多參數或非參數的。本書簡要解釋了幾類隨機過程的模擬和推斷的基本理論，然後介紹了模擬實驗和對實際數據的應用。儘管這些過程最初是在物理學中提出的，最近在金融學中也變得流行，但由於時間序列實驗數據現在可用，它們在生物學中也變得受歡迎。YUIMA套件可在CRAN上免費下載，本書將使用者能夠從第一頁開始進行分析。