a non-negative integer that indicates the number of the autoregressive coefficients.
q
a non-negative integer that indicates the number of the moving average coefficients.
loc.par
location coefficient. The default value loc.par=NULL implies that c0=0.
scale.par
scale coefficient. The default value scale.par=NULL implies that sigma=1.
ar.par
a character-string that is the label of the autoregressive coefficients. The default Value is ar.par="a".
ma.par
a character-string that is the label of the moving average coefficients. The default Value is ma.par="b".
Carma.var
a character-string that is the label of the observed process. Defaults to "v".
Latent.var
a character-string that is the label of the unobserved process. Defaults to "x".
lin.par
a character-string that is the label of the linear coefficients. If lin.par=NULL, the default, the 'setCarma' builds the CARMA(p, q) model defined as in Brockwell (2000).
XinExpr
a logical variable. The default value XinExpr=FALSE implies that the starting condition for Latent.var is zero. If XinExpr=TRUE, each component of Latent.var has a parameter as a initial value.
Cogarch
a logical variable. The default value Cogarch=FALSE implies that the parameters are specified according to Brockwell (2000).
...
Arguments to be passed to 'setCarma', such as the slots of yuima.model-class
measure
Levy measure of jump variables.
measure.type
type specification for Levy measure.
xinit
a vector of expressions identyfying the starting conditions for CARMA model.
Details
Please refer to the vignettes and the examples or to the yuimadocs package.
An object of yuima.carma-class contains:
info:
It is an object
of carma.info-class which is a list of arguments that identifies the carma(p,q) model
and the same slots in an object of yuima.model-class .
Value
model
an object of yuima.carma-class.
Note
There may be missing information in the model description.
Please contribute with suggestions and fixings.
Author(s)
The YUIMA Project Team
References
Brockwell, P. (2000)
Continuous-time ARMA processes, Stochastic Processes: Theory and Methods. Handbook of Statistics, 19, (C. R. Rao and D. N. Shandhag, eds.) 249-276. North-Holland, Amsterdam.
Examples
# Ex 1. (Continuous ARMA process driven by a Brownian Motion)
# To describe the state-space representation of a CARMA(p=3,q=1) model:
# Vt=c0+alpha0*X0t+alpha1*X1t
# dX0t = X1t*dt
# dX1t = X2t*dt
# dX2t = (-beta3*X0t-beta2*X1t-beta1*X2t)dt+dWt
# we set
mod1<-setCarma(p=3,
q=1,
loc.par="c0")
# Look at the model structure by
str(mod1)
# Ex 2. (General setCarma model driven by a Brownian Motion)
# To describe the model defined as:
# Vt=c0+alpha0*X0t+alpha1*X1t
# dX0t = X1t*dt
# dX1t = X2t*dt
# dX2t = (-beta3*X0t-beta2*X1t-beta1*X2t)dt+(c0+alpha0*X0t)dWt
# we set
mod2 <- setCarma(p=3,
q=1,
loc.par="c0",
ma.par="alpha",
ar.par="beta",
lin.par="alpha")
# Look at the model structure by
str(mod2)
# Ex 3. (Continuous Arma model driven by a Levy process)
# To specify the CARMA(p=3,q=1) model driven by a Compound Poisson process defined as:
# Vt=c0+alpha0*X0t+alpha1*X1t
# dX0t = X1t*dt
# dX1t = X2t*dt
# dX2t = (-beta3*X0t-beta2*X1t-beta1*X2t)dt+dzt
# we set the Levy measure as in setModel
mod3 <- setCarma(p=3,
q=1,
loc.par="c0",
measure=list(intensity="1",df=list("dnorm(z, 0, 1)")),
measure.type="CP")
# Look at the model structure by
str(mod3)
# Ex 4. (General setCarma model driven by a Levy process)
# Vt=c0+alpha0*X0t+alpha1*X1t
# dX0t = X1t*dt
# dX1t = X2t*dt
# dX2t = (-beta3*X1t-beta2*X2t-beta1*X3t)dt+(c0+alpha0*X0t)dzt
mod4 <- setCarma(p=3,
q=1,
loc.par="c0",
ma.par="alpha",
ar.par="beta",
lin.par="alpha",
measure=list(intensity="1",df=list("dnorm(z, 0, 1)")),
measure.type="CP")
# Look at the model structure by
str(mod4)