yuima (version 1.0.81)

Diagnostic.Cogarch: Function for checking the statistical properties of the COGARCH(p,q) model

Description

The function check the statistical properties of the COGARCH(p,q) model. We verify if the process has a strict positive stationary variance model.

Usage

Diagnostic.Cogarch(yuima.cogarch, param = list(), matrixS = NULL, mu = 1, display = TRUE)

Arguments

yuima.cogarch

an object of class yuima.cogarch, yuima or a class cogarch.gmm-class

param

a list containing the values of the parameters

matrixS

a Square matrix.

mu

first moment of the Levy measure.

display

a logical variable, if TRUE the function displays the result in the console.

Value

• The functon returns a List with entries:
• meanVarianceProc
  Unconditional Stationary mean of the variance process.
• meanStateVariable
  Unconditional Stationary mean of the state process.
• stationary
  If TRUE, the COGARCH(p,q) has stationary variance.
• positivity
  If TRUE, the variance process is strictly positive.

Examples

# Definition of the COGARCH(1,1) process driven by a Variance Gamma nois:
param.VG <- list(a1 = 0.038,  b1 =  0.053,
                  a0 = 0.04/0.053,lambda = 1, alpha = sqrt(2), beta = 0, mu = 0, 
                  x01 = 50.33)

cog.VG <- setCogarch(p = 1, q = 1, work = FALSE,
                      measure=list("rngamma(z, lambda, alpha, beta, mu)"),
                      measure.type = "code", 
                      Cogarch.var = "y",
                      V.var = "v", Latent.var="x",
                      XinExpr=TRUE)

# Verify the stationarity and the positivity of th variance process

test <- Diagnostic.Cogarch(cog.VG,param=param.VG)
show(test)

# Simulate a sample path

set.seed(210)

Term=800
num=24000

samp.VG <- setSampling(Terminal=Term, n=num)

sim.VG <- simulate(cog.VG,
                    true.parameter=param.VG,
                    sampling=samp.VG,
                    method="euler")
plot(sim.VG)

# Estimate the model

res.VG <- gmm(sim.VG, start = param.VG, Est.Incr = "IncrPar")

summary(res.VG)

#  Check if the estimated COGARCH(1,1) has a positive and stationary variance

test1<-Diagnostic.Cogarch(res.VG)
show(test1)

# Simulate a COGARCH sample path using the estimated COGARCH(1,1) 
# and the recovered increments of underlying Variance Gamma Noise

esttraj<-simulate(res.VG)
plot(esttraj)