fit_DExptrawl: Fits the trawl function consisting of the weighted sum of two...

Description Usage Arguments Details Value Examples

View source: R/FitTrawlFunctions.R

Description

Fits the trawl function consisting of the weighted sum of two exponential functions

Usage

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fit_DExptrawl(x, Delta = 1, GMMlag = 5, plotacf = FALSE,
  lags = 100)

Arguments

x

vector of equidistant time series data

Delta

interval length of the time grid used in the time series, the default is 1

GMMlag

lag length used in the GMM estimation, the default is 5

plotacf

binary variable specifying whether or not the empirical and fitted autocorrelation function should be plotted

lags

number of lags to be used in the plot of the autocorrelation function

Details

The trawl function is parametrised by the three parameters 0≤q w ≤q 1 and λ_1,λ_2 > 0 as follows:

g(x) = we^{λ_1 x}+(1-w)e^{λ_2 x}, \mbox{ for } x ≤ 0.

The Lebesgue measure of the corresponding trawl set is given by w/λ_1+(1-w)/λ_2.

Value

w: the weight parameter (restricted to be in [0,0.5] for identifiability reasons)

lambda1: the first memory parameter (denoted by λ_1 above)

lambda2: the second memory parameter (denoted by λ_2 above)

LM: The Lebesgue measure of the trawl set associated with the double exponential trawl

Examples

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#Simulate a univariate trawl process and fit the double exponential trawl
#function
set.seed(1)
t <- 1000
Delta <- 1
v <- 250
w <- 0.1
lambda1 <- 0.1
lambda2 <- 1
#Simulate a univariate trawl process with double exponential trawl function
#and Poisson marginal law
trawl <- sim_UnivariateTrawl(t,Delta,burnin=50,marginal =c("Poi"),trawl
="DExp",v=v, w=w,lambda1=lambda1,lambda2=lambda2)
#Fit the double exponential trawl function to the simulated data
fittrawlfct <- fit_DExptrawl(trawl,Delta, plotacf=TRUE,lags=500)
#Print the results
print(paste("w: estimated:", fittrawlfct$w, ", theoretical:", w))
print(paste("lambda1: estimated:", fittrawlfct$lambda1, ", theoretical:",
lambda1))
print(paste("lambda2: estimated:", fittrawlfct$lambda2, ", theoretical:",
lambda2))

trawl documentation built on Aug. 16, 2018, 5:04 p.m.