2 . ( Forecasting an ARNA ( 2 2 ) process ) Consider the ARNA ( 2 2 ) process with iid errors PARK 413/4 $ 23 / t - 2 A jet - 1 + 0 2 Et - 2 ( a ) Verify that the optimal I - step- ahead forecast made at time I I + 1 , I = PUT + 4 2 4 1 - 1 + BET + BRET ( b ) Verify that the optimal 2 - step-ahead forecast made at time I is 3 1 + 2 I = 4 IT + LI + BOUT + BRET and express it purely in terms of elements of the time- I information set ( C ) Verify that the optimal 3 - step-ahead forecast made at time I is 3 1 + 3 I = BIBI + 2 I + 42BIT LI and express it purely in terms of elements of the time - I information set ( d ) Show that for any forecast horizon h greater than or equal to 3 3 Ith I = 4 13/ Ith - 1 1 + 42 3 I th - 2 I 3 . ( Empirical question - optional ) Reproduce all the figures and tables in part 4 of Chapters Flem " Application : Forecasting Housing Starts " ( Please refer to Page 104 , Elements of forecast lication : by Francis x Diebold . ) 4 . ( Empirical Question - optional ) Please reproduce the Figure 102 103 10 4 10 , 10.6 and Table 10. 1 10.3 in Chapter 10 in Elements of Forecasting by Francis X Diebold