graphics.off();
objects();
remove(list=objects());
options(scipen=20);
sink(file = "output.txt", append = FALSE, type = "output", split = TRUE);

i = 1;
st=101;
end = 20000;
z = 0;
eps   = 0;
r   = 0;
sigma2 = 0;

# SET UP MODEL PARAMETERS
mu    =  0.;
omega =  0.01;
alpha = .01;
beta  = .95;
uncond = omega/( 1.0- alpha - beta ); 

print("Simulating GARCH(1,1) time-series:");
print("population size is:");
print(end);

# SIMULATE GARCH(1,1) DATA

while(i<=end){

z = rnorm(1, 0, 1); # draw X~N(0,1)

if(i==1){
  sigma2[i] = uncond;
}else{
  sigma2[i] = omega + alpha*(eps[i-1]^2) + beta*sigma2[i-1];
}
  
eps[i] = sigma2[i]^(0.5) * z;
r[i] = mu + eps[i]; 
  
#print(i);  
i = i + 1;
} 

# GENERATE SAMPLE STATISTICS

print("Mean of 'r' and 'sigma2':");
print(mean(r[st:end]));
print(mean(sigma2[st:end]));

print("Variance of 'r' and 'sigma2':");
print(var(r[st:end]));
print(var(sigma2[st:end]));

# sets plot to display 4 graphs at once
par(mfcol=c(2,2))

plot(r[st:end]);
hist(r[st:end]);
plot(sigma2[st:end]);
hist(sigma2[st:end]);

print(summary(r[st:end]));

print("Quantiles 0.01,0.05,0.1,.5,.9,.95,.99");
print( quantile(r[st:end], probs = c(0.01,0.05,0.1,.5,.9,.95,.99)));


sink(file = NULL);