arimasim

\[ Y_t = \phi_1 Y_{t-12} + \phi_2 Y_{t-24} + \phi_3 Y_{t-36} + \phi_4 Y_{t-48} + \varepsilon_t + \theta_1 \varepsilon_{t-12} + \theta_2 \varepsilon_{t-24} + \theta_3 \varepsilon_{t-36} + \theta_4 \varepsilon_{t-48} \]

theta <- c(0.6, 0.4, 0.2, 0.1)  
theta_arma <- c(rep(0, 11), theta[1],  # Θ1 di lag 12
                rep(0, 11), theta[2],  # Θ2 di lag 24
                rep(0, 11), theta[3],  # Θ3 di lag 36
                rep(0, 11), theta[4])  # Θ4 di lag 48

acf_ <- ARMAacf(ar = 0, ma = theta_arma, lag.max = 60)
pacf_ <- ARMAacf(ar = 0, ma = theta_arma, lag.max = 60, pacf = TRUE)

set.seed(123)
X <- arima.sim(model = list(ma = theta_arma), n = 500)

plot(X, type = "l", col = "blue", 
     main = "Simulasi SARIMA(0,0,0)(4,0,4)[12]",
     xlab = "Time", ylab = "Value")

par(mfrow = c(1, 2))

# ACF 
plot(0:60, acf_, type = "h", xlab = "Lag", ylab = "ACF", 
     ylim = c(-0.2, 1), main = "ACF", lwd = 2, col = "red")
abline(h = 0, lty = 2)

# PACF 
plot(1:60, pacf_, type = "h", xlab = "Lag", ylab = "PACF", 
     ylim = c(-0.2, 0.5), main = "PACF", lwd = 2, col = "orange")
abline(h = 0, lty = 2)