Given the five identified models and the corresponding values of the estimated autocorrelations of ???????? = ∇???? ???????? in the following table:

Identified Model

???????? ???? Estimated Autocorrelations

(1) 1 1 0 ????1 = 0.72

(2) 0 1 1 ????1 = −0.41

(3) 1 0 1 ????1 = 0.40, ????2 = 0.32

(4) 0 2 2 ????1 = 0.62, ????2 = 0.13

(5) 2 1 0 ????1 = 0.93, ????2 = 0.81

(a) Obtain preliminary estimates of the parameters analytically.

(b) Check these estimates using the charts and tables in Part Five of the book.

(c) Write down the identified models in backward shift operator notation with the preliminary estimates inserted.