Bootstrap for stochastic processes

Simulation

Simulation d’un AR(p)

AR_sim = function(p,phis,epsilon){
  #phis is a vector of size p in the order phi1, phi2,...
  n = length(epsilon)
  if (length(phis)!=p) {
    print("le vecteur de param??tres n'a pas la bonne dimension ")}
  X = rep(0,(n))
  for(j in (p+1):(n)){
    X[j] = phis%*%X[(j-p):(j-1)] +  epsilon[j]
  }
  return(X[(p+1):(n)])
}

n=200
epsilon = rexp(n)-1
phis=c(-0.6)
p=1
ar1 = AR_sim(p,phis,epsilon)
length(ar1)

[1] 199

Simulation d’un MA(q)

MA_sim = function(q,psis,epsilon){
  n = length(epsilon)
  #psis is a vector of size q in the order psi1, psi2,...
  if (length(psis)!=q) {
    print("le vecteur de param??tres n'a pas la bonne dimension")}
  X = rep(0,n)
  for(j in (q+1):(n)){
    X[j] =  epsilon[j] + psis%*%epsilon[(j-q):(j-1)]
  }
  return(X[(q+1):(n)])
}

n=200
epsilon = rexp(n)-1
psis=c(0.5)
q=1
ma1 = MA_sim(q,psis,epsilon)