nonpar_trawlest: Nonparametric estimation of the trawl function

In ambit: Simulation and Estimation of Ambit Processes

Nonparametric estimation of the trawl function

Description

This function implements the nonparametric trawl estimation proposed in Sauri and Veraart (2022).

Usage

nonpar_trawlest(data, Delta, lag = 100)

Arguments

data	Data to be used in the trawl function estimation.
Delta	Width of the grid on which we observe the data
lag	The lag until which the trawl function should be estimated

Details

Estimation of the trawl function using the methodology proposed in Sauri and Veraart (2022). Suppose the data is observed on the grid 0, Delta, 2Delta, ..., (n-1)Delta. Given the path contained in data, the function returns the lag-dimensional vector

(\hat a(0), \hat a(Δ), …, \hat a((lag-1) Δ)).

In the case when lag=n, the n-1 dimensional vector

(\hat a(0), \hat a(Δ), …, \hat a((n-2) Δ))

is returned.

Value

ahat Returns the lag-dimensional vector (\hat a(0), \hat a(Δ), …, \hat a((lag-1) Δ)). Here, \hat a(0) is estimated based on the realised variance estimator.

a0_alt Returns the alternative estimator of a(0) using the same methodology as the one used for t>0. Note that this is not the recommended estimator to use, but can be used for comparison purposes.

Examples

##Simulate a trawl process
##Determine the sampling grid
my_n <- 5000
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(1726)
#Simulate the trawl process
Poi_data<-ambit::sim_weighted_trawl(my_n, my_delta, "Exp", my_lambda, "Poi", my_v)$path

#Estimate the trawl function
my_lag <- 100+1
PoiEx_trawl <- nonpar_trawlest(Poi_data, my_delta, lag=my_lag)$a_hat

#Plot the estimated trawl function and superimpose the true one
l_seq <- seq(from = 0,to = (my_lag-1), by = 1)
esttrawlfct.data <- base::data.frame(l=l_seq[1:31],
                               value=PoiEx_trawl[1:31])
p1 <- ggplot2::ggplot(esttrawlfct.data, ggplot2::aes(x=l,y=value))+
  ggplot2::geom_point(size=3)+
  ggplot2::geom_function(fun = function(x) acf_Exp(x*my_delta,my_lambda), colour="red", size=1.5)+
  ggplot2::xlab("l")+
  ggplot2::ylab(latex2exp::TeX("$\\hat{a}(\\cdot)$ for Poisson trawl process"))
p1

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