nonpar_trawlest {ambit} | R Documentation |
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
In the case when lag=n, the n-1 dimensional vector
is returned.
Value
ahat Returns the lag-dimensional vector
Here,
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