# The YUIMA Project Package for SDEs

## Documentation for package ‘yuima’ version 1.15.27

- DESCRIPTION file.
- Package NEWS.

## Help Pages

A B C D E F G H I J L M N P Q R S T V W Y

## -- A --

adaBayes | Adaptive Bayes estimator for the parameters in sde model
adaBayes-method | Adaptive Bayes estimator for the parameters in sde model
ae | Asymptotic Expansion
aeCharacteristic | Asymptotic Expansion - Characteristic Function
aeDensity | Asymptotic Expansion - Density
aeExpectation | Asymptotic Expansion - Functionals
aeKurtosis | Asymptotic Expansion - Kurtosis
aeMarginal | Asymptotic Expansion - Marginals
aeMean | Asymptotic Expansion - Mean
aeMoment | Asymptotic Expansion - Moments
aeSd | Asymptotic Expansion - Standard Deviation
aeSkewness | Asymptotic Expansion - Skewness
asymptotic_term | asymptotic expansion of the expected value of the functional
asymptotic_term-method | asymptotic expansion of the expected value of the functional

## -- B --

bns.test | Barndorff-Nielsen and Shephard's Test for the Presence of Jumps Using Bipower Variation
bns.test-method | Barndorff-Nielsen and Shephard's Test for the Presence of Jumps Using Bipower Variation

## -- C --

CARMA | Continuous Autoregressive Moving Average (p, q) model
Carma | Continuous Autoregressive Moving Average (p, q) model
carma.info-class | Class for information about CARMA(p,q) model
carma.qmle | Class for Quasi Maximum Likelihood Estimation of CARMA(p,q) model
Carma.Recovering | Estimation for the underlying Levy in a carma model
CarmaHawkes | Hawkes Process with a Continuous Autoregressive Moving Average(p, q) intensity
carmaHawkes.info-class | Class for information on the Hawkes process with a CARMA(p,q) intensity
CarmaNoise | Estimation for the underlying Levy in a carma model
CarmaRecovNoise | Estimation for the underlying Levy in a carma model
cbind-method | Class for stochastic differential equations
cbind.yuima | Set and access data of an object of type "yuima.data" or "yuima".
cbind.yuima-method | Class "yuima.data" for the data slot of a "yuima" class object
cce | Nonsynchronous Cumulative Covariance Estimator
cce-method | Class for stochastic differential equations
cce-method | Class "yuima.data" for the data slot of a "yuima" class object
cce.factor | High-Dimensional Cumulative Covariance Estimator by Factor Modeling and Regularization
cdf | Methods for an object of class 'yuima.law'
cdf-method | 'yuima law-class': A mathematical description for the noise.
cdf-method | 'yuima.th-class': A mathematical description for the t-Levy process.
char | Methods for an object of class 'yuima.law'
char-method | 'yuima law-class': A mathematical description for the noise.
char-method | 'yuima.th-class': A mathematical description for the t-Levy process.
COGARCH | Continuous-time GARCH (p,q) process
CoGarch | Continuous-time GARCH (p,q) process
Cogarch | Continuous-time GARCH (p,q) process
cogarch | Continuous-time GARCH (p,q) process
cogarch.est-class | Class for Generalized Method of Moments Estimation for COGARCH(p,q) model
cogarch.est.incr-class | Class for Estimation of COGARCH(p,q) model with underlying increments
cogarch.info-class | Class for information about CoGarch(p,q)
cogarch.Recovering | Estimation for the underlying Levy in a COGARCH(p,q) model
cogarchNoise | Estimation for the underlying Levy in a COGARCH(p,q) model
CogarchRecovNoise | Estimation for the underlying Levy in a COGARCH(p,q) model
CP.qmle | Class for Quasi Maximum Likelihood Estimation of Compound Poisson-based and SDE models
CPoint | Volatility structural change point estimator

## -- D --

Data | Five minutes Log SPX prices
DataPPR | From 'zoo' data to 'yuima.PPR'.
dbgamma | Random numbers and densities
dconst | Fictitious rng for the constant random variable used to generate and describe Poisson jumps.
dens | Methods for an object of class 'yuima.law'
dens-method | 'yuima law-class': A mathematical description for the noise.
dens-method | 'yuima.th-class': A mathematical description for the t-Levy process.
dGH | Random numbers and densities
dGIG | Random numbers and densities
Diagnostic.Carma | Diagnostic Carma model
Diagnostic.Cogarch | Function for checking the statistical properties of the COGARCH(p,q) model
dIG | Random numbers and densities
dim | Set and access data of an object of type "yuima.data" or "yuima".
dim-method | Class for stochastic differential equations
dim-method | Class "yuima.data" for the data slot of a "yuima" class object
dNIG | Random numbers and densities
dvgamma | Random numbers and densities

## -- E --

est.cogarch.incr-class | Class for Estimation of COGARCH(p,q) model with underlying increments
Estimation of t-Levy Regression Model | Estimation of the t-Levy Regression Model
Estimation.LevyIncr | Gaussian quasi-likelihood estimation for Levy driven SDE
estimation_LRM | Estimation of the t-Levy Regression Model
estimation_RLM,yuima.LevyRM-function | 'yuima.LevyRM': A class for the mathematical description of the t-Student regression model.
EstimCarmaHawkes | Estimation Methods for a CARMA(p,q)-Hawkes Counting Process

## -- F --

F0 | Calculate the value of functional
F0-method | Calculate the value of functional
fitCIR | Calculate preliminary estimator and one-step improvements of a Cox-Ingersoll-Ross diffusion
Fnorm | Calculate the value of functional
Fnorm-method | Calculate the value of functional
FromCF2yuima_law | From a Characteristic Function to an 'yuima.law-object'.

## -- G --

get.counting.data | Extract arrival times from an object of class 'yuima.PPR'
get.zoo.data | Set and access data of an object of type "yuima.data" or "yuima".
get.zoo.data-method | Class for stochastic differential equations
get.zoo.data-method | Class "yuima.data" for the data slot of a "yuima" class object
gete | Description of a functional associated with a perturbed stochastic differential equation
gete-method | Classes for stochastic differential equations data object
getF | Description of a functional associated with a perturbed stochastic differential equation
getf | Description of a functional associated with a perturbed stochastic differential equation
getF-method | Classes for stochastic differential equations data object
getf-method | Classes for stochastic differential equations data object
getxinit | Description of a functional associated with a perturbed stochastic differential equation
getxinit-method | Classes for stochastic differential equations data object
gmm | Method of Moments for COGARCH(P,Q).
gmm.COGARCH | Method of Moments for COGARCH(P,Q).

## -- H --

Hawkes.Carma.Intensity | Hawkes Process with a Continuous Autoregressive Moving Average(p, q) intensity
hyavar | Asymptotic Variance Estimator for the Hayashi-Yoshida estimator

## -- I --

IC | Information criteria for the stochastic differential equation
incr.qmleLevy | Class for Quasi Maximum Likelihood Estimation of Levy SDE model
info.Map | Class for information about Map/Operators
info.Map-class | Class for information about Map/Operators
info.PPR | Class for information about Point Process
info.PPR-class | Class for information about Point Process
initialize-method | Class for the mathematical description of integral of a stochastic process
initialize-method | Class for the mathematical description of integral of a stochastic process
initialize-method | Class for information about Map/Operators
initialize-method | Class for information about Point Process
initialize-method | Class for the mathematical description of integral of a stochastic process
initialize-method | Class for information about Map/Operators
initialize-method | Class for the mathematical description of integral of a stochastic process
initialize-method | Class for stochastic differential equations
initialize-method | Class for a mathematical description of a Point Process
initialize-method | Class for the mathematical description of integral of a stochastic process
initialize-method | 'yuima.LevyRM': A class for the mathematical description of the t-Student regression model.
initialize-method | Class for the mathematical description of function of a stochastic process
initialize-method | Class for a mathematical description of a Point Process
initialize-method | Class for the asymptotic expansion of diffusion processes
initialize-method | Class for the mathematical description of CARMA(p,q) model
initialize-method | Class for the mathematical description of a Hawkes process with a CARMA(p,q) intensity
initialize-method | Classe for stochastic differential equations characteristic scheme
initialize-method | Class for the mathematical description of CoGarch(p,q) model
initialize-method | Class "yuima.data" for the data slot of a "yuima" class object
initialize-method | Classes for stochastic differential equations data object
initialize-method | 'yuima law-class': A mathematical description for the noise.
initialize-method | Classes for the mathematical description of stochastic differential equations
initialize-method | Class for the mathematical description of Multi dimensional Jump Diffusion processes
initialize-method | Class for the mathematical description of Compound Poisson processes
initialize-method | Class for Quasi Maximum Likelihood Estimation of Levy SDE model
initialize-method | Classes for stochastic differential equations sampling scheme
initialize-method | 'yuima.th-class': A mathematical description for the t-Levy process.
Integral.sde | Class for the mathematical description of integral of a stochastic process
Integral.sde-class | Class for the mathematical description of integral of a stochastic process
Integrand | Class for the mathematical description of integral of a stochastic process
Integrand-class | Class for the mathematical description of integral of a stochastic process
Intensity.PPR | Intesity Process for the Point Process Regression Model

## -- J --

JBtest | Remove jumps and calculate the Gaussian quasi-likelihood estimator based on the Jarque-Bera normality test

## -- L --

lambdaFromData | Intensity of a Point Process Regression Model
lasso | Adaptive LASSO estimation for stochastic differential equations
LawMethods | Methods for an object of class 'yuima.law'
length | Set and access data of an object of type "yuima.data" or "yuima".
length-method | Class for stochastic differential equations
length-method | Class "yuima.data" for the data slot of a "yuima" class object
Levy.Carma | Estimation for the underlying Levy in a carma model
Levy.cogarch | Estimation for the underlying Levy in a COGARCH(p,q) model
LevySDE | Gaussian quasi-likelihood estimation for Levy driven SDE
limiting.gamma | calculate the value of limiting covariance matrices : Gamma
limiting.gamma-method | Class for stochastic differential equations
limiting.gamma-method | Class for the mathematical description of CARMA(p,q) model
limiting.gamma-method | Class for the mathematical description of CoGarch(p,q) model
limiting.gamma-method | Classes for the mathematical description of stochastic differential equations
llag | Lead Lag Estimator
llag-method | Lead Lag Estimator
llag-method | Class for stochastic differential equations
llag-method | Class "yuima.data" for the data slot of a "yuima" class object
llag.test | Wild Bootstrap Test for the Absence of Lead-Lag Effects
lm.jumptest | Lee and Mykland's Test for the Presence of Jumps Using Normalized Returns
lmm | Spectral Method for Cumulative Covariance Estimation
LogSPX | Five minutes Log SPX prices
lse | Calculate quasi-likelihood and ML estimator of least squares estimator
LSE-method | Class for stochastic differential equations
lseBayes | Adaptive Bayes estimator for the parameters in sde model by using LSE functions
lseBayes-method | Adaptive Bayes estimator for the parameters in sde model by using LSE functions

## -- M --

Map of SDE | Map of a Stochastic Differential Equation
Map of yuima | Map of a Stochastic Differential Equation
medrv | Volatility Estimation and Jump Test Using Nearest Neighbor Truncation
medrv.test | Volatility Estimation and Jump Test Using Nearest Neighbor Truncation
Method of Moment COGARCH | Method of Moments for COGARCH(P,Q).
MethodOfMoments.CarmaHawkes | Estimation Methods for a CARMA(p,q)-Hawkes Counting Process
minrv | Volatility Estimation and Jump Test Using Nearest Neighbor Truncation
minrv.test | Volatility Estimation and Jump Test Using Nearest Neighbor Truncation
ml.ql-method | Class for stochastic differential equations
mllag | Multiple Lead-Lag Detector
mmfrac | mmfrac
model.parameter-class | Class for the parameter description of stochastic differential equations
mpv | Realized Multipower Variation
mpv-method | Realized Multipower Variation
MWK151 | Graybill - Methuselah Walk - PILO - ITRDB CA535

## -- N --

NoisePPR | Extract arrival times from an object of class 'yuima.PPR'
noisy.sampling | Noisy Observation Generator
noisy.sampling-method | Noisy Observation Generator
ntv | Volatility Estimation and Jump Test Using Nearest Neighbor Truncation

## -- P --

param.Integral | Class for the mathematical description of integral of a stochastic process
param.Integral-class | Class for the mathematical description of integral of a stochastic process
param.Map | Class for information about Map/Operators
param.Map-class | Class for information about Map/Operators
phi.test | Phi-divergence test statistic for stochastic differential equations
plot-method | Class for Estimation of COGARCH(p,q) model with underlying increments
plot-method | Class for Generalized Method of Moments Estimation for COGARCH(p,q) model
plot-method | Class for stochastic differential equations
plot-method | Class for Quasi Maximum Likelihood Estimation of Compound Poisson-based and SDE models
plot-method | Class for the asymptotic expansion of diffusion processes
plot-method | Class for Quasi Maximum Likelihood Estimation of CARMA(p,q) model
plot-method | Class "yuima.data" for the data slot of a "yuima" class object
poisson.random.sampling | Poisson random sampling method
poisson.random.sampling-method | Class for stochastic differential equations
poisson.random.sampling-method | Class "yuima.data" for the data slot of a "yuima" class object
PPR.qmle | Class for Quasi Maximum Likelihood Estimation of Point Process Regression Models
pseudologlikelihood | Calculate quasi-likelihood and ML estimator of least squares estimator
pseudologlikelihood.COGARCH | Calculate quasi-likelihood and ML estimator of least squares estimator
pz.test | Podolskij and Ziggel's Test for the Presence of Jumps Using Power Variation with Perturbed Truncation

## -- Q --

qgv | qgv
ql-method | Class for stochastic differential equations
qmle | Calculate quasi-likelihood and ML estimator of least squares estimator
qmle.carma | Class for Quasi Maximum Likelihood Estimation of CARMA(p,q) model
qmle.CarmaHawkes | Estimation Methods for a CARMA(p,q)-Hawkes Counting Process
qmle.CP | Class for Quasi Maximum Likelihood Estimation of Compound Poisson-based and SDE models
qmle.PPR | Class for Quasi Maximum Likelihood Estimation of Point Process Regression Models
qmleL | Volatility structural change point estimator
qmleLevy | Gaussian quasi-likelihood estimation for Levy driven SDE
qmleLevy.incr | Class for Quasi Maximum Likelihood Estimation of Levy SDE model
qmleR | Volatility structural change point estimator
quant | Methods for an object of class 'yuima.law'
quant-method | 'yuima law-class': A mathematical description for the noise.
quant-method | 'yuima.th-class': A mathematical description for the t-Levy process.
quasilogl | Calculate quasi-likelihood and ML estimator of least squares estimator

## -- R --

rand | Methods for an object of class 'yuima.law'
rand-method | Methods for an object of class 'yuima.law'
rand-method | 'yuima law-class': A mathematical description for the noise.
rand-method | 'yuima.th-class': A mathematical description for the t-Levy process.
rbgamma | Random numbers and densities
rconst | Fictitious rng for the constant random variable used to generate and describe Poisson jumps.
Recovering.Noise | Estimation for the underlying Levy in a carma model
Recovering.Noise.cogarch | Estimation for the underlying Levy in a COGARCH(p,q) model
rGH | Random numbers and densities
rGIG | Random numbers and densities
rIG | Random numbers and densities
rng | Random numbers and densities
rNIG | Random numbers and densities
rnts | Random numbers and densities
rpts | Random numbers and densities
rql | Calculate quasi-likelihood and ML estimator of least squares estimator
rql-method | Class for stochastic differential equations
rstable | Random numbers and densities
rvgamma | Random numbers and densities

## -- S --

setCarma | Continuous Autoregressive Moving Average (p, q) model
setCarmaHawkes | Hawkes Process with a Continuous Autoregressive Moving Average(p, q) intensity
setCharacteristic | Set characteristic information and create a 'characteristic' object.
setCogarch | Continuous-time GARCH (p,q) process
setData | Set and access data of an object of type "yuima.data" or "yuima".
setFunctional | Description of a functional associated with a perturbed stochastic differential equation
setFunctional-method | Description of a functional associated with a perturbed stochastic differential equation
setHawkes | Constructor of Hawkes model
setIntegral | Integral of Stochastic Differential Equation
setLaw | Random variable constructor
setLaw_th | Constructior of a t-Levy process.
setLRM | A constructor of a t-Student Regression Model.
setMap | Map of a Stochastic Differential Equation
setModel | Basic description of stochastic differential equations (SDE)
setPoisson | Basic constructor for Compound Poisson processes
setPPR | Point Process
setSampling | Set sampling information and create a 'sampling' object.
setYuima | Creates a "yuima" object by combining "model", "data", "sampling", "characteristic" and "functional"slots.
show-method | Class "yuima.snr" for self-normalized residuals of SDE "yuima" class object
simBmllag | Simulation of increments of bivariate Brownian motions with multi-scale lead-lag relationships
simBmllag.coef | Simulation of increments of bivariate Brownian motions with multi-scale lead-lag relationships
simCIR | Simulation of the Cox-Ingersoll-Ross diffusion
simFunctional | Calculate the value of functional
simFunctional-method | Calculate the value of functional
simulate | Simulator function for multi-dimensional stochastic processes
simulate-method | Class for Estimation of COGARCH(p,q) model with underlying increments
simulate-method | Class for stochastic differential equations
simulate-method | Class for a mathematical description of a Point Process
simulate-method | Class for the mathematical description of integral of a stochastic process
simulate-method | 'yuima.LevyRM': A class for the mathematical description of the t-Student regression model.
simulate-method | Class for the mathematical description of function of a stochastic process
simulate-method | Class for a mathematical description of a Point Process
simulate-method | Class for the mathematical description of CARMA(p,q) model
simulate-method | Class for the mathematical description of CoGarch(p,q) model
simulate-method | Classes for the mathematical description of stochastic differential equations
simulate-method | Class for the mathematical description of Multi dimensional Jump Diffusion processes
snr | Calculating self-normalized residuals for SDEs.
spectralcov | Spectral Method for Cumulative Covariance Estimation
subsampling | subsampling
subsampling-method | Class for stochastic differential equations
subsampling-method | Class "yuima.data" for the data slot of a "yuima" class object

## -- T --

t-Levy process | 'yuima.th-class': A mathematical description for the t-Levy process.
toLatex | Additional Methods for LaTeX Representations for Yuima objects
toLatex.yuima | Additional Methods for LaTeX Representations for Yuima objects
toLatex.yuima.carma | Additional Methods for LaTeX Representations for Yuima objects
toLatex.yuima.cogarch | Additional Methods for LaTeX Representations for Yuima objects
toLatex.yuima.model | Additional Methods for LaTeX Representations for Yuima objects

## -- V --

variable.Integral | Class for the mathematical description of integral of a stochastic process
variable.Integral-class | Class for the mathematical description of integral of a stochastic process

## -- W --

wllag | Scale-by-scale lead-lag estimation

## -- Y --

ybook | R code for the Yuima Book
yuima-class | Class for stochastic differential equations
yuima.ae-class | Class for the asymptotic expansion of diffusion processes
yuima.carma-class | Class for the mathematical description of CARMA(p,q) model
yuima.carma.qmle-class | Class for Quasi Maximum Likelihood Estimation of CARMA(p,q) model
yuima.carmaHawkes-class | Class for the mathematical description of a Hawkes process with a CARMA(p,q) intensity
yuima.characteristic-class | Classe for stochastic differential equations characteristic scheme
yuima.cogarch-class | Class for the mathematical description of CoGarch(p,q) model
yuima.CP.qmle-class | Class for Quasi Maximum Likelihood Estimation of Compound Poisson-based and SDE models
yuima.data-class | Class "yuima.data" for the data slot of a "yuima" class object
yuima.functional-class | Classes for stochastic differential equations data object
yuima.Hawkes | Class for a mathematical description of a Point Process
yuima.Hawkes-class | Class for a mathematical description of a Point Process
yuima.Integral | Class for the mathematical description of integral of a stochastic process
yuima.Integral-class | Class for the mathematical description of integral of a stochastic process
yuima.law | 'yuima law-class': A mathematical description for the noise.
yuima.law-class | 'yuima law-class': A mathematical description for the noise.
yuima.LevyRM | 'yuima.LevyRM': A class for the mathematical description of the t-Student regression model.
yuima.LevyRM-class | 'yuima.LevyRM': A class for the mathematical description of the t-Student regression model.
yuima.Map | Class for the mathematical description of function of a stochastic process
yuima.Map-class | Class for the mathematical description of function of a stochastic process
yuima.model | Classes for the mathematical description of stochastic differential equations
yuima.model-class | Classes for the mathematical description of stochastic differential equations
yuima.multimodel | Class for the mathematical description of Multi dimensional Jump Diffusion processes
yuima.multimodel-class | Class for the mathematical description of Multi dimensional Jump Diffusion processes
yuima.poisson-class | Class for the mathematical description of Compound Poisson processes
yuima.PPR | Class for a mathematical description of a Point Process
yuima.PPR-class | Class for a mathematical description of a Point Process
yuima.PPR.qmle-class | Class for Quasi Maximum Likelihood Estimation of Point Process Regression Models
yuima.PPR.qmle-method | Class for Quasi Maximum Likelihood Estimation of Point Process Regression Models
yuima.qmle-class | Class for Quasi Maximum Likelihood Estimation of Compound Poisson-based and SDE models
yuima.qmleLevy.incr-class | Class for Quasi Maximum Likelihood Estimation of Levy SDE model
yuima.qmleLevy.incr-method | Class for Quasi Maximum Likelihood Estimation of Levy SDE model
yuima.sampling-class | Classes for stochastic differential equations sampling scheme
yuima.snr-class | Class "yuima.snr" for self-normalized residuals of SDE "yuima" class object
yuima.th | 'yuima.th-class': A mathematical description for the t-Levy process.
yuima.th-class | 'yuima.th-class': A mathematical description for the t-Levy process.