fit_DExptrawl {trawl}

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

Description

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

Usage

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\leq w \leq 1 and \lambda_1,\lambda_2 > 0 as follows:

g(x) = we^{\lambda_1 x}+(1-w)e^{\lambda_2 x}, \mbox{ for } x \le 0.

The Lebesgue measure of the corresponding trawl set is given by w/\lambda_1+(1-w)/\lambda_2.

Value

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

lambda1: the first memory parameter (denoted by \lambda_1 above)

lambda2: the second memory parameter (denoted by \lambda_2 above)

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