# fit_Exptrawl: Fits an exponential trawl function to equidistant time series... In trawl: Estimation and Simulation of Trawl Processes

## Description

Fits an exponential trawl function to equidistant time series data

## Usage

 `1` ```fit_Exptrawl(x, Delta = 1, 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 `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 parameter λ > 0 as follows:

g(x) = e^{λ x}, \mbox{ for } x ≤ 0.

The Lebesgue measure of the corresponding trawl set is given by 1/λ.

## Value

lambda: the memory parameter λ in the exponential trawl

LM: the Lebesgue measure of the trawl set associated with the exponential trawl, i.e. 1/λ.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```#Simulate a univariate trawl process and fit the exponential trawl function set.seed(1) t <- 1000 Delta <- 1 v <- 250 lambda <- 0.25 #Simulate a univariate trawl process with exponential trawl function and #Poisson marginal law trawl <- sim_UnivariateTrawl(t,Delta,burnin=50,marginal =c("Poi"),trawl ="Exp",v=v, lambda1=lambda) #Fit the exponential trawl function to the simulated data fittrawlfct <- fit_Exptrawl(trawl,Delta, plotacf=TRUE,lags=500) #Print the results print(paste("lambda: estimated:", fittrawlfct\$lambda, ", theoretical:", lambda)) ```

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