# c4est: Estimating the fourth cumulant of the trawl process In ambit: Simulation and Estimation of Ambit Processes

 c4est R Documentation

## Estimating the fourth cumulant of the trawl process

### Description

This function estimates the fourth cumulant of the trawl process.

### Usage

c4est(data, Delta)


### Arguments

 data The data set used to estimate the fourth cumulant Delta The width Delta of the observation grid

### Details

According to Sauri and Veraart (2022), estimator based on X_0, X_{Δ_n}, …, X_{(n-1)Δ_n} is given by

\hat c_4(L')=RQ_n/\hat a(0),

where

RQ_n:=\frac{1}{√{2 nΔ_{n}}} ∑_{k=0}^{n-2}(X_{(k+1)Δ_n}-X_{kΔ_n})^4,

and

\hat a(0)=\frac{1}{2Δ_{n}n} ∑_{k=0}^{n-2}(X_{(k+1)Δ_n}-X_{kΔ_n})^{2}.

### Value

The function returns the estimated fourth cumulant of the Levy seed: \hat c_4(L').

### Examples

##Simulate a trawl process
##Determine the sampling grid
my_n <- 1000
my_delta <- 0.1
my_t <- my_n*my_delta

###Choose the model parameter
#Exponential trawl function:
my_lambda <- 2
#Poisson marginal distribution trawl
my_v <- 1

#Set the seed
set.seed(123)
#Simulate the trawl process
Poi_data<-ambit::sim_weighted_trawl(my_n, my_delta, "Exp", my_lambda, "Poi", my_v)\$path

#Estimate the fourth cumulant of the trawl process
c4est(Poi_data, my_delta)


ambit documentation built on Aug. 19, 2022, 5:19 p.m.