Simulasi Model SARIMA

By : Camelia Cahya Masyithah | 5003231024

ARIMA (3,1,0)(0,1,3)^12

\[ y_t = y_{t-1} + y_{t-12} - y_{t-13} + \phi_1 z_{t-1} + \phi_2 z_{t-2} + \phi_3 z_{t-3} + a_t - \Theta_1 a_{t-12} - \Theta_2 a_{t-24} - \Theta_3 a_{t-36} \\ dimana, \\ z_{t-1} = y_{t-1} - y_{t-2} - y_{t-13} + y_{t-14} \\ z_{t-2} = y_{t-2} - y_{t-3} - y_{t-14} + y_{t-15} \\ z_{t-3} = y_{t-3} - y_{t-4} - y_{t-15} + y_{t-16} \]

library(tseries)

## Warning: package 'tseries' was built under R version 4.4.3

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

library(forecast)

## Warning: package 'forecast' was built under R version 4.4.3

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.4.3

set.seed(123)
at <- rnorm(1000, mean = 0, sd = 2)
phi1 <- 0.5
phi2 <- -0.3
phi3 <- 0.2
theta1 <- 0.4
theta2 <- -0.2
theta3 <- 0.3

n <- length(at)
y <- numeric(n)

for (t in 37:n) {
  wt <- (phi1 * (y[t-1] - y[t-2] - y[t-13] + y[t-14]) +
         phi2 * (y[t-2] - y[t-3] - y[t-14] + y[t-15]) +
         phi3 * (y[t-3] - y[t-4] - y[t-15] + y[t-16]) +
         at[t] - 
         theta1 * at[t-12] - 
         theta2 * at[t-24] - 
         theta3 * at[t-36])
  y[t] <- y[t-1] + y[t-12] - y[t-13] + wt
}

y <- y[-(1:100)]
ts.plot(y, main="Plot Sebelum Differencing")

par(mfrow=c(1,2))
acf(y, main="ACF Sebelum Differencing")
pacf(y, main="PACF Sebelum Differencing")

#par(mfrow=c(1,2))
ts.plot(diff(y,1), main="Plot Setelah Differencing Non-Seasonal")

acf(diff(y,1), lag.max = 50, main="ACF Setelah Differencing Non-Seasonal")

pacf(diff(y,1), lag.max = 50, main="PACF Setelah Differencing Non-Seasonal")

diff_seasonal <- diff(diff(y,1), lag = 12)
ts.plot(diff_seasonal)

#par(mfrow = c(1,2))
acf(diff_seasonal, lag.max = 50, main="ACF Setelah Differencing Seasonal")

pacf(diff_seasonal, lag.max = 50, main="PACF Setelah Differencing Seasonal")