SARIMA_Model_Simulation

Seasonal ARIMA(0,0,0)(3,0,31^(12) Model

\[ y_t = \Phi_1 y_{t-12} + \Phi_2 y_{t-24} + \Phi_3 y_{t-36} + a_t + \Theta_1 a_{t-12} + \Theta_2 a_{t-24} + \Theta_3 a_{t-36} \]

#Jumlah observasi
n <- 1000

#White noise
a <- rnorm(n, mean = 0, sd = 1)

#Koefisien Seasonal AR (Φ) dan MA (Θ)
Phi <- c(0.5, -0.3, 0.2)     #AR musiman orde 3
Theta <- c(0.4, 0.2, -0.1)   #MA musiman orde 3

#Inisialisasi y
y <- numeric(n)
y[1:36] <- 0  

#Loop simulasi model SARIMA
for (t in 37:n) {
  y[t] <- 
    Phi[1] * y[t - 12] +
    Phi[2] * y[t - 24] +
    Phi[3] * y[t - 36] +
    a[t] +
    Theta[1] * a[t - 12] +
    Theta[2] * a[t - 24] +
    Theta[3] * a[t - 36]
}

#Membuang 100 nilai awal agar lebih stabil
y <- y[-(1:100)]

#Plot deret waktu
ts.plot(y)

#Plot ACF dan PACF
par(mfrow = c(1, 2))
acf(y, main = "ACF (Autocorrelation Function)")
pacf(y, main = "PACF (Partial Autocorrelation Function)")