Simulation and Inference for Stochastic Processes with YUIMA

1. Front Matter

   Pages i-xiii

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2. The Yuima Framework

   1. Front Matter

      Pages 1-1

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   2. The YUIMA Package

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 3-65

3. Models and Inference

   1. Front Matter

      Pages 67-67

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   2. Diffusion Processes

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 69-136

   3. Compound Poisson Processes

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 137-154

   4. Stochastic Differential Equations Driven by Lévy Processes

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 155-202

   5. Stochastic Differential Equations Driven by the Fractional Brownian Motion

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 203-213

   6. CARMA Models

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 215-236

   7. COGARCH Models

      • Stefano M. Iacus, Nakahiro Yoshida

      Pages 237-256

4. Back Matter

   Pages 257-268

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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.

• Lévy processes
• R language
• YUIMA
• computational statistics
• simulation and inference for stochastic processes
• stochastic differential equations
• levy
• Malliavin calculus
• CRAN
• Brownian motion
• Wiener process
• CARMA
• COGARCH
• quasi maximum likelihood estimation
• adaptive Bayes estimation
• structural change point analysis
• hypotheses testing
• asynchronous covariance estimation
• lead-lag estimation
• LASSO model selection

• Department of Economics, Management and Quantitative Methods, University of Milan, Milan, Italy

  Stefano M. Iacus

• Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, Japan

  Nakahiro Yoshida

Stefano M. Iacus, PhD, is full professor of statistics in the Department of Economics, Management and Quantitative Methods at the University of Milan. He has been a member of the R Core Team (1999-2014) for the development of the R statistical environment and is now a member of the R Foundation. His research interests include inference for stochastic processes, simulation, computational statistics, causal inference, text mining, and sentiment analysis.

Nakahiro Yoshida, PhD, is full professor at the Graduate School of Mathematical Sciences, University of Tokyo. He is working in theoretical statistics, probability theory, computational statistics, and financial data analysis. He was awarded the Japan Statistical Society Award in 2009 and the Analysis Prize from the Mathematical Society of Japan in 2006.

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