# fit_DExptrawl: Fits the trawl function consisting of the weighted sum of two... In trawl: Estimation and Simulation of Trawl Processes

## Description

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

## Usage

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```#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.