setPpr function

Point Process

Constructor of a Point Process Regression Model

setPPR(yuima, counting.var = "N", gFun, Kernel,
  var.dx = "s", var.dt = "s", lambda.var = "lambda",
  lower.var = "0", upper.var = "t", nrow = 1, ncol = 1)

Arguments

• yuima: an object of yuima.model-class that describes the mathematical features of counting and covariates processes Y[t]=(X[t],N[t]).
• counting.var: a label denoting the name of the counting process.
• gFun: a vector string that is the mathematical expression of the vector function g(t,Y[t-],theta) in the intensity process.
• Kernel: a matrix string that is the kernel kappa(t-s,Y[s],theta) in the definition of the intensity process.
• var.dx: a string denoting the integration variable in the intensity process.
• var.dt: a string denoting the integration time variable in the intensity process.
• lambda.var: name of the intensity process.
• lower.var: Lower bound of the support for the integral in the definition of the intensity process.
• upper.var: Upper bound of the support for the integral in the definition of the intensity process.
• nrow: number of rows in the kernel.
• ncol: number of columns in the kernel.

Returns

An object of yuima.PPR

References

Insert Here References

Author(s)

The YUIMA Project Team

Contacts: Lorenzo Mercuri lorenzo.mercuri@unimi.it

Note

There may be missing information in the model description. Please contribute with suggestions and fixings.

Examples

## Not run:

## Hawkes process with power law kernel

# I. Law Definition:
my.rHwk2 <- function(n){
  as.matrix(rep(1,n))
  }
Law.Hwk2 <- setLaw(rng = my.rHwk2, dim = 1)

# II. Definition of the counting process N_t
mod.Hwk2 <- setModel(drift = c("0"), diffusion = matrix("0",1,1),
  jump.coeff = matrix(c("1"),1,1), measure = list(df = Law.Hwk2),
  measure.type = "code", solve.variable = c("N"),
  xinit=c("0"))

# III. Definition of g() and kappa()
g.Hwk2 <- "mu"
Kern.Hwk2 <- "alpha/(1+(t-s))^beta"

# IV. Construction of an yuima.PPR object
PPR.Hwk2 <- setPPR(yuima = mod.Hwk2, gFun=g.Hwk2,
  Kernel = as.matrix(Kern.Hwk2),var.dx = "N")
## End(Not run)