# fit_LMtrawl: Fits a long memory trawl function to equidistant univariate... In trawl: Estimation and Simulation of Trawl Processes

## Description

Fits a long memory trawl function to equidistant univariate time series data

## Usage

 `1` ```fit_LMtrawl(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 two parameters H> 1 and α > 0 as follows:

g(x) = (1-x/α)^{-H},\mbox{ for } x ≤ 0.

The Lebesgue measure of the corresponding trawl set is given by α/(1-H).

## Value

alpha: parameter in the long memory trawl

H: parameter in the long memory trawl

LM: The Lebesgue measure of the trawl set associated with the long memory trawl

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```#Simulate a univariate trawl process and fit the long memory trawl function set.seed(1) t <- 1000 Delta <- 1 v <- 250 alpha <- 0.01 H <- 1.3 #Simulate a univariate trawl process with LM trawl function and Poisson #marginal law trawl <- sim_UnivariateTrawl(t,Delta,burnin=50,marginal =c("Poi"),trawl ="LM",v=v, alpha=alpha, H=H) #Fit the LM trawl function to the simulated data fittrawlfct <- fit_LMtrawl(trawl,Delta, plotacf=TRUE,lags=500) #Print the results print(paste("alpha: estimated:", fittrawlfct\$alpha, ", theoretical:", alpha)) print(paste("H: estimated:", fittrawlfct\$H, ", theoretical:", H)) ```

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