[Yuima-commits] r598 - pkg/yuima/man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Mar 27 07:55:20 CEST 2017
Author: eguchi
Date: 2017-03-27 07:55:20 +0200 (Mon, 27 Mar 2017)
New Revision: 598
Added:
pkg/yuima/man/qmleLevy.Rd
Log:
added
Added: pkg/yuima/man/qmleLevy.Rd
===================================================================
--- pkg/yuima/man/qmleLevy.Rd (rev 0)
+++ pkg/yuima/man/qmleLevy.Rd 2017-03-27 05:55:20 UTC (rev 598)
@@ -0,0 +1,159 @@
+\encoding{UTF-8}
+\name{qmleLevy}
+\alias{qmleLevy}
+%- Also NEED an '\alias' for EACH other topic documented here.
+\title{
+Gaussian quasi-likelihood estimation for Levy driven SDE
+}
+\description{
+Calculate the Gaussian quasi-likelihood and Gaussian quasi-likelihood estimators of Levy driven SDE.
+}
+\usage{
+qmleLevy(yuima, start, lower, upper, joint = FALSE, third = FALSE)
+}
+\arguments{
+ \item{yuima}{a yuima object.}
+ \item{lower}{a named list for specifying lower bounds of parameters.}
+ \item{upper}{a named list for specifying upper bounds of parameters.}
+ \item{start}{initial values to be passed to the optimizer.}
+ \item{joint}{perform joint estimation or two stage estimation? by default joint=FALSE. If there exists an overlapping parameter, joint=TRUE does not work for the theoretical reason}
+ \item{third}{perform third estimation? by default third=FALSE. If there exists an overlapping parameter, third=TRUE does not work for the
+ theoretical reason.}
+}
+\details{
+This function performs Gaussian quasi-likelihood estimation for Levy driven SDE.
+}
+\value{
+\item{first}{estimated values of first estimation (scale parameters)}
+
+\item{second}{estimated values of second estimation (drift parameters)}
+
+\item{third}{estimated values of third estimation (scale parameters)}
+}
+
+\note{
+The function \code{qmleLevy} uses the function \code{qmle} internally.
+It can be applied only for the standardized Levy noise whose moments of any order exist.
+In present \code{yuima} package, birateral gamma (bgamma) process, normal inverse Gaussian (NIG) process, variance gamma (VG) process, and normal tempered stable process are such candidates.
+In the current version, the standardization condition on the driving noise is internally checked only for the one-dimensional noise.
+The standardization condition for the multivariate noise is given in
+
+\href{https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnx5dW1hdWVoYXJhMTkyOHxneDo1OGIxNGQ2YjBlYWIxNzA3}{https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnx5dW1hdWVoYXJhMTkyOHxneDo3ZTdlMTA1OTMyZTBkYjQ2}
+
+or
+
+\href{https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnx5dW1hdWVoYXJhMTkyOHxneDo3ZTdlMTA1OTMyZTBkYjQ2}{https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnx5dW1hdWVoYXJhMTkyOHxneDo3ZTdlMTA1OTMyZTBkYjQ2}.
+
+They also contain more presice explanation of this function.
+}
+\references{
+
+Masuda, H. (2013). Convergence of Gaussian quasi-likelihood random fields for ergodic Levy driven SDE observed at high frequency. The Annals of Statistics, 41(3), 1593-1641.
+
+Masuda, H. and Uehara, Y. (2017). On stepwise estimation of Levy driven
+stochastic differential equation (Japanese) ., Proc. Inst. Statist. Math., accepted.
+}
+\author{
+The YUIMA Project Team
+
+Contacts: Yuma Uehara \email{y-uehara at math.kyushu-u.ac.jp}
+}
+
+
+
+\seealso{
+}
+\examples{
+## One-dimensional case 1
+dri<-"-theta0*x" ## set drift
+
+jum<-"theta1/(1+x^2)^(-1/2)" ## set jump
+
+yuima<-setModel(drift = dri
+ ,jump.coeff = jum
+ ,solve.variable = "x",state.variable = "x"
+ ,measure.type = "code"
+ ,measure = list(df="rbgamma(z,1,sqrt(2),1,sqrt(2))")) ## set true model
+
+n<-100000
+tp<-0.1
+N<-floor(n*tp) ## the number of samples
+T<-100 ## terminal
+hn<-T/N ## stepsize
+
+sam<-setSampling(Terminal = T, n=n) ## set sampling scheme
+subsam<-setSampling(Terminal = T, n=N)
+yuima<-setYuima(model = yuima, sampling = sam) ## model
+
+true<-list(theta0 = 1,theta1 = 2) ## true values
+upper<-list(theta0 = 4, theta1 = 4) ## set upper bound
+lower<-list(theta0 = 0.5, theta1 = 1) ## set lower bound
+set.seed(123)
+yuima<-simulate(yuima, xinit = 0, true.parameter = true,sampling = sam, subsampling = subsam) ## generate a path
+start<-list(theta0 = runif(1,0.5,4), theta1 = runif(1,1,4)) ## set initial values
+qmleLevy(yuima,start=start,lower=lower,upper=upper, joint = FALSE, third = TRUE)
+
+## One-dimensional case 2
+
+dri<-"-theta0*x" ## set drift
+jum<-"exp(-theta1/(1+x^2))" ## set jump
+yuima<-setModel(drift = dri ,jump.coeff = jum,solve.variable = "x",
+ state.variable = "x",measure.type = "code"
+ ,measure = list(df="rNIG(z,5,0,5,0)")) ## set model
+n<-100000 ## the number of total generation
+tp<-0.1
+N<-floor(n*tp) ## the number of samples
+T<-100 ## terminal
+hn<-T/N ## stepsize
+sam<-setSampling(Terminal = T, n=n) ## set sampling scheme
+subsam<-setSampling(Terminal = T, n=N)
+yuima<-setYuima(model = yuima, sampling = sam)
+true<-list(theta0 = 1,theta1 = 2) ## true values
+upper<-list(theta0 = 40, theta1 = 40) ## set upper bound
+lower<-list(theta0 = 0.5, theta1 = 1) ## set lower bound
+set.seed(123)
+yuima<-simulate(yuima, xinit = 0, true.parameter = true,sampling = sam,
+subsampling = subsam) ## generate a path
+plot(yuima)
+start<-list(theta0 = runif(1,0.5,40), theta1 = runif(1,1,40)) ## set initial values
+qmleLevy(yuima,start=start,lower=lower,upper=upper, joint = TRUE)
+
+## Multi-dimensional case
+
+lambda<-1/2
+alpha<-1
+beta<-c(0,0)
+mu<-c(0,0)
+Lambda<-matrix(c(1,0,0,1),2,2) ## set parameters in noise
+
+dri<-c("1-theta0*x1-x2","-theta1*x2")
+jum<-matrix(c("x1*theta2+1","0","0","1"),2,2) ## set coefficients
+
+yuima <- setModel(drift=dri,
+ solve.variable=c("x1","x2"),state.variable = c("x1","x2"), jump.coeff=jum, measure.type="code",
+ measure=list(df="rvgamma(z, lambda, alpha, beta, mu, Lambda)"))
+
+n<-100000 ## the number of total samples
+tp<-0.1 ## the degree of thinning
+N<-floor(n*tp) ## the number of samples used for optimization
+T<-100 ## terminal
+hn<-T/N ## stepsize
+
+sam<-setSampling(Terminal = T, n=n) ## set sampling scheme
+subsam<-setSampling(Terminal = T, n=N)
+yuima<-setYuima(model = yuima, sampling = sam) ## model
+
+true<-list(theta0 = 1,theta1 = 2,theta2 = 3,lambda=lambda, alpha=alpha, beta=beta,
+ mu=mu, Lambda=Lambda) ## true values
+upper<-list(theta0 = 4, theta1 = 4, theta2 = 5) ## set upper bound
+lower<-list(theta0 = 0.5, theta1 = 1, theta2 = 1) ## set lower bound
+set.seed(123)
+yuima<-simulate(yuima, xinit = c(0,0), true.parameter = true,sampling = sam, subsampling = subsam) ## generate a path
+plot(yuima)
+start<-list(theta0 = runif(1,0.5,4), theta1 = runif(1,1,4), theta2 = runif(1,1,5)) ## set initial values
+qmleLevy(yuima,start=start,lower=lower,upper=upper,joint = FALSE,third = TRUE)
+
+}
+
+\keyword{ ~kwd1 }% use one of RShowDoc("KEYWORDS")
+\keyword{ ~kwd2 }% __ONLY ONE__ keyword per line
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