boxplot(AirPassengers~cycle(AirPassengers, xlab=”Date”, ylab = “Passenger Numbers (1000’s)”, main = “Monthly air passengers boxplot from 1949-1960”))
From the above plot, you can see that the number of ticket sales goes higher in June, July, and August as compared to the other months of the years.
- Build the ARIMA Model Using auto.arima() Function
mymodel <- auto.arima(AirPassengers)
- Plot the Residuals
- Forecast the Values for the Next 10 Years
myforecast <- forecast(mymodel, level=c(95), h=10*12)
- Validate the Model by Selecting Lag Values
Box.test(mymodel$resid, lag=5, type=”Ljung-Box”)
Box.test(mymodel$resid, lag=10, type=”Ljung-Box”)
Box.test(mymodel$resid, lag=15, type=”Ljung-Box”)
Looking at the lower p values, we can say that our model is relatively accurate, and we can conclude that from the ARIMA model, that the parameters (2, 1, 1) adequately fit the data.