Estimating non-parametric density of t-statistics for gamma of each realization (in R)

[Anonymous No.15834175]

Its a pretty straight-forward question, I have an ARIMA model with 160 observations and I've run it 200 times, each time has generated a t-statistic for γ (gamma) , how do I estimate non-parametrically each t-statistic's density? How dwould I go about plotting it?Just in case, here is my current code in R:

set.seed(123456)

num_realizations <- 200

# Number of observations in each realization

num_obs <- 160

# Parameters of the ARIMA(2,1,0) model

delta1 <- 1.1

delta2 <- -0.28

Phi1 <- 2.1

Phi2 <- -1.38

Phi3 <- 0.28

# Generating independent realizations

realizations <- matrix(0, nrow = num_obs, ncol = num_realizations)

for (realization in 1:num_realizations) {

# Generate white noise with average 0 and standard deviation 1

epsilon <- rnorm(num_obs)

# Initialize observations X

x <- numeric(num_obs)

# Setting up initial conditions

x[1] <- 0

x[2] <- 0

# Generating observations x using the ARIMA model

for (t in 3:num_obs) {

x[t] <- delta1 * x[t - 1] + delta2 * x[t - 2] + (Phi1 + Phi2 + Phi3 - 1) * x[t - 1] + epsilon[t]

}

realizations[, realization] <- x

}

[Anonymous No.15834290]

bump

[Anonymous No.15834370]

>>15834175
>How dwould I go about plotting it?
Bro, it's just a histogram