rq {ambit}

Computing the scaled realised quarticity

Description

This function computes the scaled realised quarticity of a time series for a given width of the observation grid.

Usage

rq(data, Delta)

Arguments

data

The data set used to compute the scaled realised quarticity

Delta

The width Delta of the observation grid

Details

According to Sauri and Veraart (2022), the scaled realised quarticity for X_0, X_{\Delta_n}, \ldots, X_{(n-1)\Delta_n} is given by

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

Value

The function returns the scaled realised quarticity RQ_n.

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

#Compute the scaled realised quarticity
rq(Poi_data, my_delta)