How to use distribution graphs in rugarch package in R

Question

I have a time series of returns like this:

ret <- rnorm(50, -0.8 , 0.8)

I fit a GARCH model with rugarch package:

library(rugarch)
      comtspec <- ugarchspec(mean.model=list(
                  armaOrder=c(1,0)), distribution="std",
                  variance.model=list(model="eGARCH"))

      fit <- ugarchfit(spec=comtspec, ret)
      
      hisPDF <- ugarchdistribution(fit, n.sim = 200, n.start = 1, m.sim = 20,  
                recursive = TRUE, recursive.length = 6000,
                recursive.window = 1000,
                solver = "solnp")

And I plot the section number 1 output (Parameter Density Plots) from the results:

  plot(hisPDF)

This gives me a graph like this:

I want to use the density function in the plot (The red circle for example) as a function to integrate and find the moments etc. but I don't know how. Can anyone help me with this>

Answer 1

All the coefficients from the simulation are stored in:

coefs <- hisPDF@dist[[1]]$simcoef

The autoregressive coefficient(ar) is the 2nd column:

ar <- coefs[,2]  

Now if you want to create the density plot as the package do, you need:

d <- density(ar1)
plot(d)

However, if you want the summary statistics from the distribution, you do not need to integrate the density, you just need to

 summary(ar1)
Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.17477 -0.13441 -0.08838 -0.07304 -0.03163  0.05786 

Note that the values will be different because you are using a random generator for simulation without specifying a random.seed.