setCogarch | R Documentation |
setCogarch
describes the Cogarch(p,q) model introduced in Brockwell et al. (2006):
dGt = sqrt(Vt)dZt
Vt = a0 + (a1 Yt(1) + ... + a(p) Yt(p))
dYt(1) = Yt(2) dt
...
dYt(q-1) = Yt(q) dt
dYt(q) = (-b(q) Yt(1) - ... - b(1) Yt(q))dt + (a0 + (a1 Yt(1) + ... + a(p) Yt(p))d[ZtZt]^{q}
setCogarch(p, q, ar.par = "b", ma.par = "a", loc.par = "a0", Cogarch.var = "g", V.var = "v", Latent.var = "y", jump.variable = "z", time.variable = "t", measure = NULL, measure.type = NULL, XinExpr = FALSE, startCogarch = 0, work = FALSE, ...)
p |
a non negative integer that is the number of the moving average coefficients of the Variance process. |
q |
a non-negative integer that indicates the number of the autoregressive coefficients of the Variance process. |
ar.par |
a character-string that is the label of the autoregressive coefficients. |
ma.par |
a character-string that is the label of the autoregressive coefficients. |
loc.par |
the location coefficient. |
Cogarch.var |
a character-string that is the label of the observed cogarch process. |
V.var |
a character-string that is the label of the latent variance process. |
Latent.var |
a character-string that is the label of the latent process in the state space representation for the variance process. |
jump.variable |
the jump variable. |
time.variable |
the time variable. |
measure |
Levy measure of jump variables. |
measure.type |
type specification for Levy measure. |
XinExpr |
a vector of |
startCogarch |
Start condition for the Cogarch process |
work |
Internal Variable. In the final release this input will be removed. |
... |
Arguments to be passed to |
We remark that yuima
describes a Cogarch(p,q) model using the formulation proposed in Brockwell et al. (2006). This representation has the Cogarch(1,1) model introduced in Kluppelberg et al. (2004) as a special case. Indeed, by choosing beta = a0 b1, eta = b1
and phi = a1
, we obtain the Cogarch(1,1) model proposed in Kluppelberg et al. (2004) defined as the solution of the SDEs:
dGt = sqrt(Vt)dZt
dVt = (beta - eta Vt) dt + phi Vt d[ZtZt]^{q}
Please refer to the vignettes and the examples.
An object of yuima.cogarch-class
contains:
info
:It is an object
of cogarch.info-class
which is a list of arguments that identifies the Cogarch(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., Chadraa, E. and Lindner, A. (2006) Continuous-time GARCH processes, The Annals of Applied Probability, 16, 790-826.
Kluppelberg, C., Lindner, A., and Maller, R. (2004) A continuous-time GARCH process driven by a Levy process: Stationarity and second-order behaviour, Journal of Applied Probability, 41, 601-622.
Stefano M. Iacus, Lorenzo Mercuri, Edit Rroji (2017) COGARCH(p,q): Simulation and Inference with the yuima Package, Journal of Statistical Software, 80(4), 1-49.
# Ex 1. (Continuous time GARCH process driven by a compound poisson process) prova<-setCogarch(p=1,q=3,work=FALSE, measure=list(intensity="1", df=list("dnorm(z, 0, 1)")), measure.type="CP", Cogarch.var="y", V.var="v", Latent.var="x")
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