Introduction

1.1 Overview of the project

1.2 Who should read this book?

1.3 Structure of the book

1.4 How to get the R code for this book

1.5 Main contribution to the Yuima package

1.6 Further developments of Yuima Package

1.7 Things to know about R

1.7.1 How to get R

1.7.2 R and S4 objects

1.8 The yuima package

1.8.1 How to obtain the package

1.8.2 The main object and classes

1.8.3 The yuima.model class

1.9 On model specification

1.9.2 User-specified state and time variables

1.9.3 Specification of parametric models

1.10 Basic facts on simulation

1.10.1 Customization of simulation arguments

1.10.2 Simulation of models with user-specified notation

1.10.3 Simulation of parametric models

1.11 Sampling and simulate

1.11.1 Sampling and subsampling

1.12 How to make data available into a yuima object

1.12.1 Getting data from data providers

1.13 How to extract data from a yuima object

1.14.1 Review of some time series objects in R

1.14.2 How to handle real time stamps

1.14.3 Dates manipulation

1.14.4 Using dates to index time series

1.14.5 Joining two or more time series

1.14.6 Subsetting a time series

1.15 Miscellanea

1.15.1 From Yuima to LATEX

1.15.2 The Yuima GUI

Part II Models and Inference

2 Diffusion processes

2.1 One dimensional model specification

2.1.1 Ornstein-Uhlenbeck (OU)

2.1.3 Vasicek model (VAS)

2.1.4 Constant elasticity of variance (CEV)

2.1.5 Cox-Ingersoll-Ross process (CIR)

2.1.6 Chan-Karolyi-Longstaff-Sanders process (CKLS)

2.1.7 Hyperbolic diffusion processes

2.2 More about simulation

2.3 Space-discretized Euler-Maruyama simulation scheme

2.4 Multidimensional processes

2.4.1 The Heston model

2.5 Parametric inference

2.5.1 Quasi maximum likelihood estimation

2.5.2 Adaptive Bayes estimation

2.6 Example of real data estimation for gBm

2.8 Hypotheses testing

2.9 AIC Model Selection

2.9.1 An example of AIC model selection for exchange rates data

2.10 LASSO model selection

2.10.1 An example of Lasso model selection for interest rates data

2.11 Change point estimation

2.11.1 Example of volatility change-point estimation for 2-dimensional SDE's

2.11.2 An example of two stage estimation

2.11.3 Example of volatility change-point estimation in real data

2.12 Asynchronous covariance estimation

2.12.1 Other covariance estimators

2.13.1 Application of the lead-lag estimator to real data

2.14 Asymptotic expansion

2.14.1 Asymptotic expansion for general stochastic processes

3 Compound Poisson processes

3.1 Inhomogenous Compound Poisson Process

3.1.1 Linear intensity function

3.1.2 The Weibull model

3.1.3 The exponentially decaying intensity model

3.1.4 Modulated and periodical intensity model

3.1.5 Frequency modulation model

3.2 Multidimensional Compound Poisson Processes

3.2.2 User specified jump distribution

3.3 Estimation

3.3.1 Compound Poisson process with Gaussian jumps

3.3.2 NIG Compound Poisson process

3.3.3 Exponential jump Compound Poisson process

3.3.4 The Weibull Compound Poisson process

4 Stochastic differential equations driven by Lévy processes

4.1
About the Author:

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.