SARIMA

Model SARIMA \((0,0,0)(0,0,4)^{12}\)

\[ Z_t = a_t + \Theta_1 a_{t-12} + \Theta_2 a_{t-24} + \Theta_3 a_{t-36} + \Theta_4 a_{t-48} \]

set.seed(123)
at     <- rnorm(1000, mean = 0, sd = 2)
THETA1 <- 0.65
THETA2 <- 0.45
THETA3 <- 0.3
THETA4 <- 0.7

n <- length(at)
z <- numeric(n)
for (t in 49:n) {
  z[t] <- at[t]+THETA1*at[t-12]+THETA2*at[t-24]+THETA3*at[t-36]+THETA4*at[t-48]
}
#Menghapus data z ke-1 hingga ke-48 karena tidak diketahui nilainya
z <- z[-(1:48)]

ts.plot(z, main = "Simulated Seasonal Time Series")

par(mfrow = c(1, 2))
acf(z, lag.max = 48, main = "ACF of z")
pacf(z, lag.max = 48, main = "PACF of z")