Seasonal ARIMA Simulation

Ini adalah simulasi model Seasonal ARIMA (SARIMA) dengan orde ARIMA(0,0,2)(0,0,2)^12. Simulasi ini akan menunjukkan bagaimana data yang dihasilkan dari model tersebut beserta karakteristik ACF dan PACF-nya.

Deskripsi Model: ARIMA(0,0,2)(0,0,2)[12]

  • Non-seasonal part (0,0,2):
    • p = 0 (No AutoRegressive terms)
    • d = 0 (No non-seasonal differencing)
    • q = 2 (Moving Average of order 2)
  • Seasonal part (0,0,2)[12]:
    • P = 0 (No Seasonal AutoRegressive terms)
    • D = 0 (No seasonal differencing)
    • Q = 2 (Seasonal Moving Average of order 2)
    • s = 12 (Seasonal period is 12)

Load necessary library

```R library(stats) # Paket dasar R yang mengandung fungsi arima.sim, acf, pacf

ma_coeffs <- c(0.5, 0.3) seasonal_ma_coeffs <- c(0.4, 0.2) seasonal_period <- 12 n_simulations <- 200 set.seed(123) sarima_sim <- arima.sim(n = n_simulations, model = list(ma = ma_coeffs, seasonal = list(order = c(0, 0, 2), sma = seasonal_ma_coeffs, period = seasonal_period)))

Plot the simulated time series

plot(sarima_sim, main = “Simulasi Deret Waktu SARIMA(0,0,2)(0,0,2)[12]”, xlab = “Waktu”, ylab = “Nilai”, type = “l”, col = “blue”) grid()

Plot ACF and PACF for the simulated data

par(mfrow = c(2, 1)) # Arrange plots acf(sarima_sim, main = “ACF dari Simulasi SARIMA (Tanpa Differencing)”, lag.max = 3seasonal_period) pacf(sarima_sim, main = “PACF dari Simulasi SARIMA (Tanpa Differencing)”, lag.max = 3seasonal_period) par(mfrow = c(1, 1)) # Reset plot layout