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# Load necessary library
library(stats)

# Define non-seasonal MA coefficients (example values)
ma_coeffs <- c(0.5, 0.3) 

# Define seasonal MA coefficients (example values)
seasonal_ma_coeffs <- c(0.4, 0.2) 

# Set seasonal period
seasonal_period <- 12

# Set number of simulations
n_simulations <- 200 

# For reproducibility
set.seed(123) 

# Simulate SARIMA(0,0,2)(0,0,2)[12] model
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 = "Simulated SARIMA(0,0,2)(0,0,2)[12] Time Series",
     xlab = "Time", ylab = "Value", type = "l")

# Plot ACF and PACF for the simulated data (no differencing applied as d=0, D=0)
par(mfrow = c(2, 1)) # Arrange plots
acf(sarima_sim, main = "ACF of Simulated SARIMA (No Differencing)")
pacf(sarima_sim, main = "PACF of Simulated SARIMA (No Differencing)")
par(mfrow = c(1, 1)) # Reset plot layout

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