fit_DExptrawl function

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

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

Returns

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

Details

The trawl function is parametrised by the three parameters c("$0\\leq\n$", "$w \\leq 1$") and $\lambda_1,\lambda_2 > 0$ as follows:

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