setCarma | R Documentation |
'setCarma' describes the following model:
Vt = c0 + sigma (b0 Xt(0) + ... + b(q) Xt(q))
dXt(0) = Xt(1) dt
...
dXt(p-2) = Xt(p-1) dt
dXt(p-1) = (-a(p) Xt(0) - ... - a(1) Xt(p-1))dt + (gamma(0) + gamma(1) Xt(0) + ... + gamma(p) Xt(p-1))dZt
The continuous ARMA process using the state-space representation as in Brockwell (2000) is obtained by choosing:
gamma(0) = 1, gamma(1) = gamma(2) = ... = gamma(p) = 0.
Please refer to the vignettes and the examples or the yuima documentation for details.
setCarma(p,q,loc.par=NULL,scale.par=NULL,ar.par="a",ma.par="b", lin.par=NULL,Carma.var="v",Latent.var="x",XinExpr=FALSE, Cogarch=FALSE, ...)
p |
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 |
scale.par |
scale coefficient. The default value |
ar.par |
a character-string that is the label of the autoregressive coefficients. The default Value is |
ma.par |
a character-string that is the label of the moving average coefficients. The default Value is |
Carma.var |
a character-string that is the label of the observed process. Defaults to |
Latent.var |
a character-string that is the label of the unobserved process. Defaults to |
lin.par |
a character-string that is the label of the linear coefficients. If |
XinExpr |
a logical variable. The default value |
Cogarch |
a logical variable. The default value |
... |
Arguments to be passed to 'setCarma', such as the slots of
|
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
.
model |
an object of |
There may be missing information in the model description. Please contribute with suggestions and fixings.
The YUIMA Project Team
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.
# 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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.