Mr. Ng is a trader in the commodity market. He has followed the corn price for a few years and would like to use an ARIMA model for forecasting. The time series plot of the price (in cents) per bushel of corn for 120 consecutive months is shown in Figure 2-1. The autocorrelation plot of the corn price is shown in Figure 2-2. After some transformation, the sample autocorrelation function and sample partial autocorrelation function of the transformed data are shown in Figure 2-3 and Figure 2-4.

400 350 - 300 - Price 250 - 200 - 150 - 100 - 12 24 36 48 60 72 84 96 108 120 Month Figure 2-1: Time series plot of the corn price 1.0 - 0.8 - 0.6 - 0.4 - 0.2- Autocorrelation 0.0 TTT -0.2 - -0.4 -0.6 - -0.8 - -1.0 - N - 10 12 14 16 18 20 22 24 26 28 30 Lag Figure 2-2: Autocorrelation function for the corn price1.0 - 0.8- 0.6 0.4- Autocorrelation 0.0 -0.2- -0.4- -0.6 - -0.8 -1.0- 30 35 U - 10 15 20 25 Lag Figure 2-3: Autocorrelation function for the transformed data 1.0 0.8 0.5 0.4 0.2 Partial Autocorrelation 0.0 -0.2 -0.4- -0.6 -0.8- -1.0- 10 15 20 25 30 35 Lag Figure 2-4: Partial autocorrelation function for the transformed data