c4est {ambit}

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_{\Delta_n}, \ldots, X_{(n-1)\Delta_n} is given by

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

where

RQ_n:=\frac{1}{\sqrt{2 n\Delta_{n}}} \sum_{k=0}^{n-2}(X_{(k+1)\Delta_n}-X_{k\Delta_n})^4,

and

\hat a(0)=\frac{1}{2\Delta_{n}n} \sum_{k=0}^{n-2}(X_{(k+1)\Delta_n}-X_{k\Delta_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)