Creating values from a normal inverse gaussian (NIG) distribution

Maxim · October 1, 2020, 2:13pm

I have a vector of empirical observations 'a' containing about 16000 values.

Maxim-ml/Data/blob/master/mydata.txt

c(0.000219340245067201, -0.000337214578067346, -0.000343879521105706, 
5.24083263844233e-05, 0.000347135805631282, 0.000248815671433533, 
-0.000193154158898423, 2.94666053335391e-05, 0.000196421849288697, 
-0.000124396024725471, -0.000173525565170252, 0.000150608820067788, 
0.000170226139289298, 0.000104740146339211, 4.2547550986427e-05, 
-6.21854927995713e-05, 0.000130912328200949, -6.21812190022553e-05, 
2.61820371605381e-05, 0.00013417218238132, -4.25404502468751e-05, 
0.000170150943930025, 0.000232274739529359, 0.000497082918432312, 
-9.80889013195707e-05, -0.000395722927168052, -7.19664505801632e-05, 
0.000104676761527145, 0.000137371623162963, -0.0001897086342737, 
0.000801110480004752, 0.000588162271316861, 0.000555169128569233, 
-0.00027101465767565, 0.000404862270734441, -6.52892805028671e-05, 
-8.16175954927445e-05, -1.30594334812884e-05, 1.63242652035933e-05, 
1.30592203007041e-05, -4.24430895371586e-05, 0.000127323864745676, 
9.46662119041264e-05, -5.22285259272337e-05, -8.81418235163522e-05, 
0.000163219471792431, -0.000235044479984126, -0.000225302812831174, 
-4.89855900820402e-05, -0.000182900740931302, -0.000166599428393255, 
0.000163333039695956, 6.85919221847797e-05, 7.83850076011561e-05, 
-0.000163309033311521, -1.95988763316279e-05, -0.000231949207430304, 
0, 0.00014048270533884, 0.000261310670476078, -4.57244384151068e-05,

This file has been truncated. show original

The empirical histogram looks like the following:

I'm trying to test, whether the normal inverse gaussian (NIG) fits the empirical data or not. First, I estimate the distribution parameters on the data:

SP500NIG<-fit.NIGuv(a, silent = TRUE)

Then I try to generate values from the NIG distribution with the parameters above. I do the following:

library(fBasics)

SP_NIG_sim<-rnig(length(a),mu=SP500NIG@mu,delta=SP500NIG@sigma,alpha = SP500NIG@alpha.bar,beta=SP500NIG@gamma)

And get the corresponding theoretical histogram, which doesn't look like the empirical one:

Where is the mistake in my code? How to generate values from the NIG distribution with the estimated parameters, which will more or less coincide with the empirical data?

Thank you for your help.

system · October 22, 2020, 2:14pm

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