[Yuima-commits] r746 - pkg/yuima/man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Fri Feb 26 11:36:20 CET 2021
Author: eguchi
Date: 2021-02-26 11:36:19 +0100 (Fri, 26 Feb 2021)
New Revision: 746
Modified:
pkg/yuima/man/qmle.Rd
Log:
modified
Modified: pkg/yuima/man/qmle.Rd
===================================================================
--- pkg/yuima/man/qmle.Rd 2021-02-26 10:35:47 UTC (rev 745)
+++ pkg/yuima/man/qmle.Rd 2021-02-26 10:36:19 UTC (rev 746)
@@ -1,444 +1,444 @@
-\encoding{UTF-8}
-\name{qmle}
-%\alias{ql}
-%\alias{ml.ql}
-\alias{qmle}
-\alias{quasilogl}
-%\alias{LSE}
-%\alias{ml.ql2}
-\alias{rql}
-\alias{lse}
-\alias{pseudologlikelihood}
-\alias{pseudologlikelihood.COGARCH}
-%\alias{ql,ANY-method}
-%\alias{ml.ql,ANY-method}
-%\alias{ml.ql2,ANY-method}
-%\alias{rql,ANY-method}
-\title{Calculate quasi-likelihood and ML estimator of least squares estimator}
-\description{Calculate the quasi-likelihood and estimate of the parameters of the
- stochastic differential equation by the maximum likelihood method or least squares estimator
- of the drift parameter.}
-\usage{
-%ml.ql(yuima,theta2,theta1,h,theta2.lim=matrix(c(0,1),1,2),theta1.lim=matrix(c(0,1),1,2),print=FALSE,method,param,interval)
-%ql(yuima,theta2,theta1,h,print=FALSE,param)
-%rql(yuima,theta2,theta1,ptheta2,ptheta1,h,print=FALSE,param,prevparam)
-qmle(yuima, start, method = "BFGS", fixed = list(), print =
-FALSE, lower, upper, joint = FALSE, Est.Incr =
-"NoIncr", aggregation = TRUE, threshold = NULL, rcpp =
-FALSE, ...)
-quasilogl(yuima, param, print = FALSE, rcpp = FALSE)
-lse(yuima, start, lower, upper, method = "BFGS", ...)
-}
-\arguments{
- \item{yuima}{a yuima object.}
-% \item{theta2,theta1}{parameters of the sdeModel.}
-% \item{h}{ time span of observations.}
-% \item{theta2.lim, theta1.lim}{matrixes to specify the domains of the
-% parameters. Vector can be available only if theta is a scalar.}
-% \item{ptheta2,ptheta1}{}
- \item{print}{you can see a progress of the estimation when print is TRUE.}
- \item{method}{see Details.}
- \item{param}{\code{list} of parameters for the quasi loglikelihood.}
-% \item{interval}{}
-% \item{prevparam}{}
- \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{fixed}{for conditional (quasi)maximum likelihood estimation.}
- \item{joint}{perform joint estimation or two stage estimation? by default \code{joint=FALSE}.}
- \item{Est.Incr}{If the yuima model is an object of \code{\link{yuima.carma-class}} or \code{\link{yuima.cogarch-class}} the \code{qmle} returns an object of \code{\link{yuima.carma.qmle-class}}, \code{\link{cogarch.est.incr-class}},\code{\link{cogarch.est-class}} or object of class \code{mle-class}. By default \code{Est.Incr="NoIncr"}, alternative values are \code{IncrPar} and \code{Incr}. }
- \item{aggregation}{If \code{aggregation=TRUE}, before the estimation of the levy parameters we aggregate the increments.}
- \item{threshold}{If the model has Compund Poisson type jumps, the threshold is
- used to perform thresholding of the increments.}
- \item{...}{passed to \code{\link{optim}} method. See Examples.}
- \item{rcpp}{use C++ code?}
-}
-\details{
-% A function ql calculate the quasi-likelihood of a time series data X with any
-% parameters. A function ml.pl estimates parameters of the sdeModel by
-% maximizing the quasi-likelihood.
- \code{qmle} behaves more likely the standard \code{mle} function in \pkg{stats4} and
- argument \code{method} is one of the methods available in \code{\link{optim}}.
-
- \code{lse} calculates least squares estimators of the drift parameters. This is
- useful for initial guess of \code{qmle} estimation.
- \code{quasilogl} returns the value of the quasi loglikelihood for a given
- \code{yuima} object and list of parameters \code{coef}.
-
-}
-\value{
- \item{QL}{a real value.}
- \item{opt}{a list with components the same as 'optim' function.}
- \item{carmaopt}{if the model is an object of \code{\link{yuima.carma-class}}, \code{qmle} returns an object \code{\link{yuima.carma.qmle-class}}}
- \item{cogarchopt}{if the model is an object of \code{\link{yuima.cogarch-class}}, \code{qmle} returns an object of class \code{\link{cogarch.est-class}}. The estimates are obtained by maximizing the pseudo-loglikelihood function as shown in Iacus et al. (2015)}
-}
-\references{
-## Non-ergodic diffucion
-
-Genon-Catalot, V., & Jacod, J. (1993). On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. In Annales de l'IHP \enc{Probabilités}{Probabilit?s} et statistiques, 29(1), 119-151.
-
-Uchida, M., & Yoshida, N. (2013). Quasi likelihood analysis of volatility and nondegeneracy of statistical random field. Stochastic Processes and their Applications, 123(7), 2851-2876.
-
-## Ergodic diffusion
-
-Kessler, M. (1997). Estimation of an ergodic diffusion from discrete observations. Scandinavian Journal of Statistics, 24(2), 211-229.
-
-## Jump diffusion
-
-Shimizu, Y., & Yoshida, N. (2006). Estimation of parameters for diffusion processes with jumps from discrete observations. Statistical Inference for Stochastic Processes, 9(3), 227-277.
-
-Ogihara, T., & Yoshida, N. (2011). Quasi-likelihood analysis for the stochastic differential equation with jumps. Statistical Inference for Stochastic Processes, 14(3), 189-229.
-
-## COGARCH
-
-Iacus S. M., Mercuri L. and Rroji E.(2015) Discrete time approximation of a COGARCH (p, q) model and its estimation. \href{https://arxiv.org/abs/1511.00253}{https://arxiv.org/abs/1511.00253}
-
-## CARMA
-
-Iacus S. M., Mercuri L. (2015) Implementation of Levy CARMA model in Yuima package. Comp. Stat. (30) 1111-1141. \href{https://link.springer.com/article/10.1007/s00180-015-0569-7}{https://link.springer.com/article/10.1007/s00180-015-0569-7}
-}
-
-\author{The YUIMA Project Team}
-\note{
- %The function ml.ql uses the function optim internally.
- The function qmle uses the function optim internally.
-
- The function qmle uses the function \code{\link{CarmaNoise}} internally for estimation of underlying Levy if the model is an object of \code{\link{yuima.carma-class}}.
-}
-
-\examples{
-#dXt^e = -theta2 * Xt^e * dt + theta1 * dWt
-diff.matrix <- matrix(c("theta1"), 1, 1)
-ymodel <- setModel(drift=c("(-1)*theta2*x"), diffusion=diff.matrix,
- time.variable="t", state.variable="x", solve.variable="x")
-n <- 100
-
-ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
-yuima <- setYuima(model=ymodel, sampling=ysamp)
-set.seed(123)
-yuima <- simulate(yuima, xinit=1, true.parameter=list(theta1=0.3,
-theta2=0.1))
-QL <- quasilogl(yuima, param=list(theta2=0.8, theta1=0.7))
-##QL <- ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)))
-QL
-
-## another way of parameter specification
-##param <- list(theta2=0.8, theta1=0.7)
-##QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
-##QL
-
-
-## old code
-##system.time(
-##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1))
-##)
-##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
-##print(coef(opt))
-
-
-system.time(
-opt2 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
- upper=list(theta1=1,theta2=1), method="L-BFGS-B")
-)
-cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
-print(coef(opt2))
-
-## initial guess for theta2 by least squares estimator
-tmp <- lse(yuima, start=list(theta2=0.7), lower=list(theta2=0), upper=list(theta2=1))
-tmp
-
-system.time(
-opt3 <- qmle(yuima, start=list(theta1=0.8, theta2=tmp), lower=list(theta1=0,theta2=0),
- upper=list(theta1=1,theta2=1), method="L-BFGS-B")
-)
-cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
-print(coef(opt3))
-
-
-## perform joint estimation? Non-optimal, just for didactic purposes
-system.time(
-opt4 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
- upper=list(theta1=1,theta2=1), method="L-BFGS-B", joint=TRUE)
-)
-cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
-print(coef(opt4))
-
-## old code
-##system.time(
-##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1), method="Newton")
-##)
-##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
-##print(coef(opt))
-
-
-\dontrun{
-###multidimension case
-##dXt^e = - drift.matrix * Xt^e * dt + diff.matrix * dWt
-diff.matrix <- matrix(c("theta1.1","theta1.2", "1", "1"), 2, 2)
-
-drift.c <- c("-theta2.1*x1", "-theta2.2*x2", "-theta2.2", "-theta2.1")
-drift.matrix <- matrix(drift.c, 2, 2)
-
-ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
- state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
-n <- 100
-ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
-yuima <- setYuima(model=ymodel, sampling=ysamp)
-set.seed(123)
-
-##xinit=c(x1, x2) #true.parameter=c(theta2.1, theta2.2, theta1.1, theta1.2)
-yuima <- simulate(yuima, xinit=c(1, 1),
-true.parameter=list(theta2.1=0.5, theta2.2=0.3, theta1.1=0.6, theta1.2=0.2))
-
-## theta2 <- c(0.8, 0.2) #c(theta2.1, theta2.2)
-##theta1 <- c(0.7, 0.1) #c(theta1.1, theta1.2)
-## QL <- ql(yuima, theta2, theta1, h=1/((n)^(2/3)))
-## QL
-
-## ## another way of parameter specification
-## #param <- list(theta2=theta2, theta1=theta1)
-## #QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
-## #QL
-
-## theta2.1.lim <- c(0, 1)
-## theta2.2.lim <- c(0, 1)
-## theta1.1.lim <- c(0, 1)
-## theta1.2.lim <- c(0, 1)
-## theta2.lim <- t( matrix( c(theta2.1.lim, theta2.2.lim), 2, 2) )
-## theta1.lim <- t( matrix( c(theta1.1.lim, theta1.2.lim), 2, 2) )
-
-## system.time(
-## opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim)
-## )
-## opt at coef
-
-system.time(
-opt2 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1),
- lower=list(theta1.1=.1,theta1.2=.1,theta2.1=.1,theta2.2=.1),
- upper=list(theta1.1=4,theta1.2=4,theta2.1=4,theta2.2=4), method="L-BFGS-B")
-)
-opt2 at coef
-summary(opt2)
-
-## unconstrained optimization
-system.time(
-opt3 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
-)
-opt3 at coef
-summary(opt3)
-
-quasilogl(yuima, param=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
-
-##system.time(
-##opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim, method="Newton")
-##)
-##opt at coef
-##
-
-# carma(p=2,q=0) driven by a brownian motion without location parameter
-
-mod0<-setCarma(p=2,
- q=0,
- scale.par="sigma")
-
-true.parm0 <-list(a1=1.39631,
- a2=0.05029,
- b0=1,
- sigma=0.23)
-
-samp0<-setSampling(Terminal=100,n=250)
-set.seed(123)
-sim0<-simulate(mod0,
- true.parameter=true.parm0,
- sampling=samp0)
-
-system.time(
-carmaopt0 <- qmle(sim0, start=list(a1=1.39631,a2=0.05029,
- b0=1,
- sigma=0.23))
-)
-
-summary(carmaopt0)
-
-# carma(p=2,q=1) driven by a brownian motion without location parameter
-
-mod1<-setCarma(p=2,
- q=1)
-
-true.parm1 <-list(a1=1.39631,
- a2=0.05029,
- b0=1,
- b1=2)
-
-samp1<-setSampling(Terminal=100,n=250)
-set.seed(123)
-sim1<-simulate(mod1,
- true.parameter=true.parm1,
- sampling=samp1)
-
-system.time(
- carmaopt1 <- qmle(sim1, start=list(a1=1.39631,a2=0.05029,
- b0=1,b1=2),joint=TRUE)
-)
-
-summary(carmaopt1)
-
-# carma(p=2,q=1) driven by a compound poisson process where the jump size is normally distributed.
-
-mod2<-setCarma(p=2,
- q=1,
- measure=list(intensity="1",df=list("dnorm(z, 0, 1)")),
- measure.type="CP")
-
-true.parm2 <-list(a1=1.39631,
- a2=0.05029,
- b0=1,
- b1=2)
-
-samp2<-setSampling(Terminal=100,n=250)
-set.seed(123)
-sim2<-simulate(mod2,
- true.parameter=true.parm2,
- sampling=samp2)
-
-system.time(
- carmaopt2 <- qmle(sim2, start=list(a1=1.39631,a2=0.05029,
- b0=1,b1=2),joint=TRUE)
-)
-
-summary(carmaopt2)
-
-# carma(p=2,q=1) driven by a normal inverse gaussian process
-mod3<-setCarma(p=2,q=1,
- measure=list(df=list("rNIG(z, alpha, beta, delta1, mu)")),
- measure.type="code")
-#
-
-# True param
-true.param3<-list(a1=1.39631,
- a2=0.05029,
- b0=1,
- b1=2,
- alpha=1,
- beta=0,
- delta1=1,
- mu=0)
-
-samp3<-setSampling(Terminal=100,n=200)
-set.seed(123)
-
-sim3<-simulate(mod3,
- true.parameter=true.param3,
- sampling=samp3)
-
-
-carmaopt3<-qmle(sim3,start=true.param3)
-
-summary(carmaopt3)
-
-# Simulation and Estimation of COGARCH(1,1) with CP driven noise
-
-# Model parameters
-eta<-0.053
-b1 <- eta
-beta <- 0.04
-a0 <- beta/b1
-phi<- 0.038
-a1 <- phi
-
-
-# Definition
-
-cog11<-setCogarch(p = 1,q = 1,
- measure = list(intensity = "1",
- df = list("dnorm(z, 0, 1)")),
- measure.type = "CP",
- XinExpr=TRUE)
-
-# Parameter
-paramCP11 <- list(a1 = a1, b1 = b1,
- a0 = a0, y01 = 50.31)
-# Sampling scheme
-samp11 <- setSampling(0, 3200, n=64000)
-
-# Simulation
-set.seed(125)
-
-SimTime11 <- system.time(
- sim11 <- simulate(object = cog11,
- true.parameter = paramCP11,
- sampling = samp11,
- method="mixed")
-)
-
-plot(sim11)
-
-# Estimation
-
-timeComp11<-system.time(
- res11 <- qmle(yuima = sim11,
- start = paramCP11,
- grideq = TRUE,
- method = "Nelder-Mead")
-)
-
-timeComp11
-
-unlist(paramCP11)
-
-coef(res11)
-
-# COGARCH(2,2) model driven by CP
-
-cog22 <- setCogarch(p = 2,q = 2,
- measure = list(intensity = "1",
- df = list("dnorm(z, 0, 1)")),
- measure.type = "CP",
- XinExpr=TRUE)
-
-# Parameter
-
-paramCP22 <- list(a1 = 0.04, a2 = 0.001,
- b1 = 0.705, b2 = 0.1, a0 = 0.1, y01 = (1 + 2 / 3),
- y02=0)
-
-# Use diagnostic.cog for checking the stat and positivity
-
-check22 <- Diagnostic.Cogarch(cog22, param = paramCP22)
-
-# Sampling scheme
-
-samp22 <- setSampling(0, 3600, n = 64000)
-
-# Simulation
-
-set.seed(125)
-SimTime22 <- system.time(
- sim22 <- simulate(object = cog22,
- true.parameter = paramCP22,
- sampling = samp22,
- method = "Mixed")
-)
-
-plot(sim22)
-
-timeComp22 <- system.time(
- res22 <- qmle(yuima = sim22,
- start = paramCP22,
- grideq=TRUE,
- method = "Nelder-Mead")
-)
-
-timeComp22
-
-unlist(paramCP22)
-
-coef(res22)
-
-}
-}
-
-
-% Add one or more standard keywords, see file 'KEYWORDS' in the
-% R documentation directory.
-\keyword{ts}
+\encoding{UTF-8}
+\name{qmle}
+%\alias{ql}
+%\alias{ml.ql}
+\alias{qmle}
+\alias{quasilogl}
+%\alias{LSE}
+%\alias{ml.ql2}
+\alias{rql}
+\alias{lse}
+\alias{pseudologlikelihood}
+\alias{pseudologlikelihood.COGARCH}
+%\alias{ql,ANY-method}
+%\alias{ml.ql,ANY-method}
+%\alias{ml.ql2,ANY-method}
+%\alias{rql,ANY-method}
+\title{Calculate quasi-likelihood and ML estimator of least squares estimator}
+\description{Calculate the quasi-likelihood and estimate of the parameters of the
+ stochastic differential equation by the maximum likelihood method or least squares estimator
+ of the drift parameter.}
+\usage{
+%ml.ql(yuima,theta2,theta1,h,theta2.lim=matrix(c(0,1),1,2),theta1.lim=matrix(c(0,1),1,2),print=FALSE,method,param,interval)
+%ql(yuima,theta2,theta1,h,print=FALSE,param)
+%rql(yuima,theta2,theta1,ptheta2,ptheta1,h,print=FALSE,param,prevparam)
+qmle(yuima, start, method = "L-BFGS-B", fixed = list(),
+print = FALSE, lower, upper, joint = FALSE, Est.Incr ="NoIncr",
+aggregation = TRUE, threshold = NULL, rcpp =FALSE, ...)
+
+quasilogl(yuima, param, print = FALSE, rcpp = FALSE)
+lse(yuima, start, lower, upper, method = "BFGS", ...)
+}
+\arguments{
+ \item{yuima}{a yuima object.}
+% \item{theta2,theta1}{parameters of the sdeModel.}
+% \item{h}{ time span of observations.}
+% \item{theta2.lim, theta1.lim}{matrixes to specify the domains of the
+% parameters. Vector can be available only if theta is a scalar.}
+% \item{ptheta2,ptheta1}{}
+ \item{print}{you can see a progress of the estimation when print is TRUE.}
+ \item{method}{see Details.}
+ \item{param}{\code{list} of parameters for the quasi loglikelihood.}
+% \item{interval}{}
+% \item{prevparam}{}
+ \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{fixed}{for conditional (quasi)maximum likelihood estimation.}
+ \item{joint}{perform joint estimation or two stage estimation? by default \code{joint=FALSE}.}
+ \item{Est.Incr}{If the yuima model is an object of \code{\link{yuima.carma-class}} or \code{\link{yuima.cogarch-class}} the \code{qmle} returns an object of \code{\link{yuima.carma.qmle-class}}, \code{\link{cogarch.est.incr-class}},\code{\link{cogarch.est-class}} or object of class \code{mle-class}. By default \code{Est.Incr="NoIncr"}, alternative values are \code{IncrPar} and \code{Incr}. }
+ \item{aggregation}{If \code{aggregation=TRUE}, before the estimation of the levy parameters we aggregate the increments.}
+ \item{threshold}{If the model has Compund Poisson type jumps, the threshold is
+ used to perform thresholding of the increments.}
+ \item{...}{passed to \code{\link{optim}} method. See Examples.}
+ \item{rcpp}{use C++ code?}
+}
+\details{
+% A function ql calculate the quasi-likelihood of a time series data X with any
+% parameters. A function ml.pl estimates parameters of the sdeModel by
+% maximizing the quasi-likelihood.
+ \code{qmle} behaves more likely the standard \code{mle} function in \pkg{stats4} and
+ argument \code{method} is one of the methods available in \code{\link{optim}}.
+
+ \code{lse} calculates least squares estimators of the drift parameters. This is
+ useful for initial guess of \code{qmle} estimation.
+ \code{quasilogl} returns the value of the quasi loglikelihood for a given
+ \code{yuima} object and list of parameters \code{coef}.
+
+}
+\value{
+ \item{QL}{a real value.}
+ \item{opt}{a list with components the same as 'optim' function.}
+ \item{carmaopt}{if the model is an object of \code{\link{yuima.carma-class}}, \code{qmle} returns an object \code{\link{yuima.carma.qmle-class}}}
+ \item{cogarchopt}{if the model is an object of \code{\link{yuima.cogarch-class}}, \code{qmle} returns an object of class \code{\link{cogarch.est-class}}. The estimates are obtained by maximizing the pseudo-loglikelihood function as shown in Iacus et al. (2015)}
+}
+\references{
+## Non-ergodic diffucion
+
+Genon-Catalot, V., & Jacod, J. (1993). On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. In Annales de l'IHP \enc{Probabilités}{Probabilit?s} et statistiques, 29(1), 119-151.
+
+Uchida, M., & Yoshida, N. (2013). Quasi likelihood analysis of volatility and nondegeneracy of statistical random field. Stochastic Processes and their Applications, 123(7), 2851-2876.
+
+## Ergodic diffusion
+
+Kessler, M. (1997). Estimation of an ergodic diffusion from discrete observations. Scandinavian Journal of Statistics, 24(2), 211-229.
+
+## Jump diffusion
+
+Shimizu, Y., & Yoshida, N. (2006). Estimation of parameters for diffusion processes with jumps from discrete observations. Statistical Inference for Stochastic Processes, 9(3), 227-277.
+
+Ogihara, T., & Yoshida, N. (2011). Quasi-likelihood analysis for the stochastic differential equation with jumps. Statistical Inference for Stochastic Processes, 14(3), 189-229.
+
+## COGARCH
+
+Iacus S. M., Mercuri L. and Rroji E.(2015) Discrete time approximation of a COGARCH (p, q) model and its estimation. \href{https://arxiv.org/abs/1511.00253}{https://arxiv.org/abs/1511.00253}
+
+## CARMA
+
+Iacus S. M., Mercuri L. (2015) Implementation of Levy CARMA model in Yuima package. Comp. Stat. (30) 1111-1141. \href{https://link.springer.com/article/10.1007/s00180-015-0569-7}{https://link.springer.com/article/10.1007/s00180-015-0569-7}
+}
+
+\author{The YUIMA Project Team}
+\note{
+ %The function ml.ql uses the function optim internally.
+ The function qmle uses the function optim internally.
+
+ The function qmle uses the function \code{\link{CarmaNoise}} internally for estimation of underlying Levy if the model is an object of \code{\link{yuima.carma-class}}.
+}
+
+\examples{
+#dXt^e = -theta2 * Xt^e * dt + theta1 * dWt
+diff.matrix <- matrix(c("theta1"), 1, 1)
+ymodel <- setModel(drift=c("(-1)*theta2*x"), diffusion=diff.matrix,
+ time.variable="t", state.variable="x", solve.variable="x")
+n <- 100
+
+ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
+yuima <- setYuima(model=ymodel, sampling=ysamp)
+set.seed(123)
+yuima <- simulate(yuima, xinit=1, true.parameter=list(theta1=0.3,
+theta2=0.1))
+QL <- quasilogl(yuima, param=list(theta2=0.8, theta1=0.7))
+##QL <- ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)))
+QL
+
+## another way of parameter specification
+##param <- list(theta2=0.8, theta1=0.7)
+##QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
+##QL
+
+
+## old code
+##system.time(
+##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1))
+##)
+##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+##print(coef(opt))
+
+
+system.time(
+opt2 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B")
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt2))
+
+## initial guess for theta2 by least squares estimator
+tmp <- lse(yuima, start=list(theta2=0.7), lower=list(theta2=0), upper=list(theta2=1))
+tmp
+
+system.time(
+opt3 <- qmle(yuima, start=list(theta1=0.8, theta2=tmp), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B")
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt3))
+
+
+## perform joint estimation? Non-optimal, just for didactic purposes
+system.time(
+opt4 <- qmle(yuima, start=list(theta1=0.8, theta2=0.7), lower=list(theta1=0,theta2=0),
+ upper=list(theta1=1,theta2=1), method="L-BFGS-B", joint=TRUE)
+)
+cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+print(coef(opt4))
+
+## old code
+##system.time(
+##opt <- ml.ql(yuima, 0.8, 0.7, h=1/((n)^(2/3)), c(0, 1), c(0, 1), method="Newton")
+##)
+##cat(sprintf("\nTrue param. theta2 = .3, theta1 = .1\n"))
+##print(coef(opt))
+
+
+\dontrun{
+###multidimension case
+##dXt^e = - drift.matrix * Xt^e * dt + diff.matrix * dWt
+diff.matrix <- matrix(c("theta1.1","theta1.2", "1", "1"), 2, 2)
+
+drift.c <- c("-theta2.1*x1", "-theta2.2*x2", "-theta2.2", "-theta2.1")
+drift.matrix <- matrix(drift.c, 2, 2)
+
+ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
+ state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
+n <- 100
+ysamp <- setSampling(Terminal=(n)^(1/3), n=n)
+yuima <- setYuima(model=ymodel, sampling=ysamp)
+set.seed(123)
+
+##xinit=c(x1, x2) #true.parameter=c(theta2.1, theta2.2, theta1.1, theta1.2)
+yuima <- simulate(yuima, xinit=c(1, 1),
+true.parameter=list(theta2.1=0.5, theta2.2=0.3, theta1.1=0.6, theta1.2=0.2))
+
+## theta2 <- c(0.8, 0.2) #c(theta2.1, theta2.2)
+##theta1 <- c(0.7, 0.1) #c(theta1.1, theta1.2)
+## QL <- ql(yuima, theta2, theta1, h=1/((n)^(2/3)))
+## QL
+
+## ## another way of parameter specification
+## #param <- list(theta2=theta2, theta1=theta1)
+## #QL <- ql(yuima, h=1/((n)^(2/3)), param=param)
+## #QL
+
+## theta2.1.lim <- c(0, 1)
+## theta2.2.lim <- c(0, 1)
+## theta1.1.lim <- c(0, 1)
+## theta1.2.lim <- c(0, 1)
+## theta2.lim <- t( matrix( c(theta2.1.lim, theta2.2.lim), 2, 2) )
+## theta1.lim <- t( matrix( c(theta1.1.lim, theta1.2.lim), 2, 2) )
+
+## system.time(
+## opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim)
+## )
+## opt at coef
+
+system.time(
+opt2 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1),
+ lower=list(theta1.1=.1,theta1.2=.1,theta2.1=.1,theta2.2=.1),
+ upper=list(theta1.1=4,theta1.2=4,theta2.1=4,theta2.2=4), method="L-BFGS-B")
+)
+opt2 at coef
+summary(opt2)
+
+## unconstrained optimization
+system.time(
+opt3 <- qmle(yuima, start=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
+)
+opt3 at coef
+summary(opt3)
+
+quasilogl(yuima, param=list(theta2.1=0.8, theta2.2=0.2, theta1.1=0.7, theta1.2=0.1))
+
+##system.time(
+##opt <- ml.ql(yuima, theta2, theta1, h=1/((n)^(2/3)), theta2.lim, theta1.lim, method="Newton")
+##)
+##opt at coef
+##
+
+# carma(p=2,q=0) driven by a brownian motion without location parameter
+
+mod0<-setCarma(p=2,
+ q=0,
+ scale.par="sigma")
+
+true.parm0 <-list(a1=1.39631,
+ a2=0.05029,
+ b0=1,
+ sigma=0.23)
+
+samp0<-setSampling(Terminal=100,n=250)
+set.seed(123)
+sim0<-simulate(mod0,
+ true.parameter=true.parm0,
+ sampling=samp0)
+
+system.time(
+carmaopt0 <- qmle(sim0, start=list(a1=1.39631,a2=0.05029,
+ b0=1,
+ sigma=0.23))
+)
+
+summary(carmaopt0)
+
+# carma(p=2,q=1) driven by a brownian motion without location parameter
+
+mod1<-setCarma(p=2,
+ q=1)
+
+true.parm1 <-list(a1=1.39631,
+ a2=0.05029,
+ b0=1,
+ b1=2)
+
+samp1<-setSampling(Terminal=100,n=250)
+set.seed(123)
+sim1<-simulate(mod1,
+ true.parameter=true.parm1,
+ sampling=samp1)
+
+system.time(
+ carmaopt1 <- qmle(sim1, start=list(a1=1.39631,a2=0.05029,
+ b0=1,b1=2),joint=TRUE)
+)
+
+summary(carmaopt1)
+
+# carma(p=2,q=1) driven by a compound poisson process where the jump size is normally distributed.
+
+mod2<-setCarma(p=2,
+ q=1,
+ measure=list(intensity="1",df=list("dnorm(z, 0, 1)")),
+ measure.type="CP")
+
+true.parm2 <-list(a1=1.39631,
+ a2=0.05029,
+ b0=1,
+ b1=2)
+
+samp2<-setSampling(Terminal=100,n=250)
+set.seed(123)
+sim2<-simulate(mod2,
+ true.parameter=true.parm2,
+ sampling=samp2)
+
+system.time(
+ carmaopt2 <- qmle(sim2, start=list(a1=1.39631,a2=0.05029,
+ b0=1,b1=2),joint=TRUE)
+)
+
+summary(carmaopt2)
+
+# carma(p=2,q=1) driven by a normal inverse gaussian process
+mod3<-setCarma(p=2,q=1,
+ measure=list(df=list("rNIG(z, alpha, beta, delta1, mu)")),
+ measure.type="code")
+#
+
+# True param
+true.param3<-list(a1=1.39631,
+ a2=0.05029,
+ b0=1,
+ b1=2,
+ alpha=1,
+ beta=0,
+ delta1=1,
+ mu=0)
+
+samp3<-setSampling(Terminal=100,n=200)
+set.seed(123)
+
+sim3<-simulate(mod3,
+ true.parameter=true.param3,
+ sampling=samp3)
+
+
+carmaopt3<-qmle(sim3,start=true.param3)
+
+summary(carmaopt3)
+
+# Simulation and Estimation of COGARCH(1,1) with CP driven noise
+
+# Model parameters
+eta<-0.053
+b1 <- eta
+beta <- 0.04
+a0 <- beta/b1
+phi<- 0.038
+a1 <- phi
+
+
+# Definition
+
+cog11<-setCogarch(p = 1,q = 1,
+ measure = list(intensity = "1",
+ df = list("dnorm(z, 0, 1)")),
+ measure.type = "CP",
+ XinExpr=TRUE)
+
+# Parameter
+paramCP11 <- list(a1 = a1, b1 = b1,
+ a0 = a0, y01 = 50.31)
+# Sampling scheme
+samp11 <- setSampling(0, 3200, n=64000)
+
+# Simulation
+set.seed(125)
+
+SimTime11 <- system.time(
+ sim11 <- simulate(object = cog11,
+ true.parameter = paramCP11,
+ sampling = samp11,
+ method="mixed")
+)
+
+plot(sim11)
+
+# Estimation
+
+timeComp11<-system.time(
+ res11 <- qmle(yuima = sim11,
+ start = paramCP11,
+ grideq = TRUE,
+ method = "Nelder-Mead")
+)
+
+timeComp11
+
+unlist(paramCP11)
+
+coef(res11)
+
+# COGARCH(2,2) model driven by CP
+
+cog22 <- setCogarch(p = 2,q = 2,
+ measure = list(intensity = "1",
+ df = list("dnorm(z, 0, 1)")),
+ measure.type = "CP",
+ XinExpr=TRUE)
+
+# Parameter
+
+paramCP22 <- list(a1 = 0.04, a2 = 0.001,
+ b1 = 0.705, b2 = 0.1, a0 = 0.1, y01 = (1 + 2 / 3),
+ y02=0)
+
+# Use diagnostic.cog for checking the stat and positivity
+
+check22 <- Diagnostic.Cogarch(cog22, param = paramCP22)
+
+# Sampling scheme
+
+samp22 <- setSampling(0, 3600, n = 64000)
+
+# Simulation
+
+set.seed(125)
+SimTime22 <- system.time(
+ sim22 <- simulate(object = cog22,
+ true.parameter = paramCP22,
+ sampling = samp22,
+ method = "Mixed")
+)
+
+plot(sim22)
+
+timeComp22 <- system.time(
+ res22 <- qmle(yuima = sim22,
+ start = paramCP22,
+ grideq=TRUE,
+ method = "Nelder-Mead")
+)
+
+timeComp22
+
+unlist(paramCP22)
+
+coef(res22)
+
+}
+}
+
+
+% Add one or more standard keywords, see file 'KEYWORDS' in the
+% R documentation directory.
+\keyword{ts}
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