The YUIMA software aims at developing a complete environment for estimation and simulation of Stochastic Differential Equations.
In the yuima R package Stochastic Differential Equations can be of very abstract type, e.g. uni or multidimensional, driven by Wiener process of fractional Brownian motion with general Hurst parameter, with or without jumps specified as Lévy noise. Estimation and simulation routines for Contiuous ARMA (CARMA) and Contiuous GARCH (COGARCH) models are available as well.
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. It 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 yuimaGUI package provides a user-friendly interface for yuima, including also additional tools related to Quantitative Finance such as data retrival (stock prices and economic indicators) , time series clustering, change point analysis, lead-lag estimation and more.