an object of class yuima.data-class contains the observations available at uniformly spaced time. If data=NULL, the default, the 'CarmaNoise' uses the data in an object of yuima.data-class.
NoNeg.Noise
Estimate a non-negative Levy-Driven Carma process. By default NoNeg.Noise=FALSE.
Value
incr.Levy
a numeric object contains the estimated increments.
Note
The function qmle uses the function CarmaNoise for estimation of underlying Levy in the carma model.
Author(s)
The YUIMA Project Team
References
Brockwell, P., Davis, A. R. and Yang. Y. (2011)
Estimation for Non-Negative Levy-Driven CARMA Process, Journal of Business And Economic Statistics, 29 - 2, 250-259.
Examples
## Not run:
#Ex.1: Carma(p=3, q=0) process driven by a brownian motion.
mod0<-setCarma(p=3,q=0)
# We fix the autoregressive and moving average parameters
# to ensure the existence of a second order stationary solution for the process.
true.parm0 <-list(a1=4,a2=4.75,a3=1.5,b0=1)
# We simulate a trajectory of the Carma model.
numb.sim<-1000
samp0<-setSampling(Terminal=100,n=numb.sim)
set.seed(100)
incr.W<-matrix(rnorm(n=numb.sim,mean=0,sd=sqrt(100/numb.sim)),1,numb.sim)
sim0<-simulate(mod0,
true.parameter=true.parm0,
sampling=samp0, increment.W=incr.W)
#Applying the CarmaNoise
system.time(
inc.Levy0<-CarmaNoise(sim0,true.parm0)
)
# We compare the orginal with the estimated noise increments
par(mfrow=c(1,2))
plot(t(incr.W)[1:998],type="l", ylab="",xlab="time")
title(main="True Brownian Motion",font.main="1")
plot(inc.Levy0,type="l", main="Filtered Brownian Motion",font.main="1",ylab="",xlab="time")
# Ex.2: carma(2,1) driven by a compound poisson
# where jump size is normally distributed and
# the lambda is equal to 1.
mod1<-setCarma(p=2,
q=1,
measure=list(intensity="Lamb",df=list("dnorm(z, 0, 1)")),
measure.type="CP")
true.parm1 <-list(a1=1.39631, a2=0.05029,
b0=1,b1=2,
Lamb=1)
# We generate a sample path.
samp1<-setSampling(Terminal=100,n=200)
set.seed(123)
sim1<-simulate(mod1,
true.parameter=true.parm1,
sampling=samp1)
# We estimate the parameter using qmle.
carmaopt1 <- qmle(sim1, start=true.parm1)
summary(carmaopt1)
# Internally qmle uses CarmaNoise. The result is in
plot(carmaopt1)
# Ex.3: Carma(p=2,q=1) with scale and location parameters
# driven by a Compound Poisson
# with jump size normally distributed.
mod2<-setCarma(p=2,
q=1,
loc.par="mu",
scale.par="sig",
measure=list(intensity="Lamb",df=list("dnorm(z, 0, 1)")),
measure.type="CP")
true.parm2 <-list(a1=1.39631,
a2=0.05029,
b0=1,
b1=2,
Lamb=1,
mu=0.5,
sig=0.23)
# We simulate the sample path
set.seed(123)
sim2<-simulate(mod2,
true.parameter=true.parm2,
sampling=samp1)
# We estimate the Carma and we plot the underlying noise.
carmaopt2 <- qmle(sim2, start=true.parm2)
summary(carmaopt2)
# Increments estimated by CarmaNoise
plot(carmaopt2)
## End(Not run)