For the ARIMA(1, 1, 1) model (1 − ????????)???????? = (1 − ????????)????????, where ???????? = ∇????????:

(a) Write down the linearized form of the model.

(b) Set out how you would start off the calculation of the conditional nonlinear least-squares algorithm with start values ???? = 0.5 and ???? = 0.4 for a series whose first nine values are shown below.

???? ???????? ???? ????????

0 149 5 150 1 145 6 147 2 152 7 142 3 144 8 146 4 150