sim_weighted_trawl_gen {ambit}

Simulation of a weighted trawl process with generic trawl function

Description

This function simulates a weighted trawl process for a generic trawl function and various choices the marginal distribution. The specific trawl function to be used can be supplied directly by the user.

Usage

sim_weighted_trawl_gen(
  n,
  Delta,
  trawlfct_gen,
  distr,
  distr_par,
  kernelfct = NULL
)

Arguments

n

number of grid points to be simulated (excluding the starting value)

Delta

grid-width

trawlfct_gen

the trawl function a used in the simulation

distr

marginal distribution. Choose from "Gamma" (Gamma), "Gauss" (Gaussian), "Cauchy" (Cauchy), "NIG" (Normal Inverse Gaussian), Poi" (Poisson), "NegBin" (Negative Binomial)

distr_par

parameters of the marginal distribution: (Gamma: shape, scale; Gauss: mu, sigma (i.e. the second parameter is the standard deviation, not the variance); Cauchy: l, s; NIG: alpha, beta, delta, mu; Poi: v, NegBin: m, theta)

kernelfct

the kernel function p used in the ambit process

Details

This functions simulates a sample path from a weighted trawl process given by

Y_t =\int_{(-\infty,t]\times (-\infty, \infty)} p(t-s)I_{(0,a(t-s))}(x)L(dx,ds),

for t \ge 0, and returns Y_0, Y_{\Delta}, \ldots, Y_{n\Delta}. The user needs to ensure that trawlfct_gen is a monotonic function.

Value

path Simulated path

slice_sizes slice sizes used

S_matrix Matrix of all slices

kernelweights kernel weights used

Examples

#Simulation of a Gaussian trawl process with exponential trawl function
n<-2000
Delta<-0.1

trawlfct_par <-0.5
distr<-"Gauss"
distr_par<-c(0,1) #mean 0, std 1
set.seed(233)

a <- function(x){exp(-trawlfct_par*x)}
path <- sim_weighted_trawl_gen(n, Delta, a,
                           distr, distr_par)$path
#Plot the path
library(ggplot2)
df <- data.frame(time = seq(0,n,1), value=path)
p <- ggplot(df, aes(x=time, y=path))+
  geom_line()+
  xlab("l")+
  ylab("Trawl process")
p