Simulation and Inference for Stochastic Processes with YUIMA

A Comprehensive R Framework for SDEs and Other Stochastic Processes

Stefano M. Iacus, Nakahiro Yoshida (Autoren)

Buch | Softcover

XIII, 268 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-55567-6 (ISBN)

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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.

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.

1 Introduction.- 2 Diffusion processes.- 3 Compound Poisson processes.- 4 Stochastic differential equations driven by Lévy processes.- 5 Stochastic differential equations driven by the fractional Brownian motion.- 6 CARMA models.- 7 COGARCH models.- Reference.- Index.

"The book is written in an accessible style ... . a wide audience can benefit for a through overview of the topic and the R package." (Irina Ioana Mohorianu, zbMATH 1458.60004, 2021)

Erscheinungsdatum	24.06.2018
Reihe/Serie	Use R!
Zusatzinfo	XIII, 268 p. 83 illus., 32 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	434 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	adaptive Bayes estimation • asynchronous covariance estimation • Brownian motion • CARMA • COGARCH • Computational Statistics • CRAN • hypotheses testing • LASSO model selection • lead-lag estimation • Levy • Lévy processes • Malliavin calculus • Mathematical & statistical software • Mathematical & statistical software • mathematics and statistics • Maths for computer scientists • probability & statistics • Probability and Statistics in Computer Science • Probability & statistics • Probability theory and stochastic processes • quasi maximum likelihood estimation • R language • simulation and inference for stochastic processes • Statistics and Computing/Statistics Programs • Stochastic differential equations • stochastics • structural change point analysis • Wiener process • YUIMA
ISBN-10	3-319-55567-7 / 3319555677
ISBN-13	978-3-319-55567-6 / 9783319555676
Zustand	Neuware