$($a$)$ Using the data below in Table $1$ fit an exponential smoothing model with the

assumption that the smoothing parameter is $=0\mathrm{.}3.$ Next, generate the

four$-$step ahead $(2012$Q$4)$ forecast. $(10$ marks$)$

Table $1$: Observed data

$($b$)$ Imagine using the data in Table $1$ and we estimate an $AR(2)$ model which results

in

$y_t=0\mathrm{.}001+0\mathrm{.}6y_{t-1}+0\mathrm{.}1y_{t-2}+lo{n}_t,lo{n}_{t}N(0,{}^2),$

Using the iterative forecasting method, generate the four$-$step ahead $(2012$Q$4)$

forecast. If the actual realisation for $2012$Q$4$ is $0\mathrm{.}35,$ which of the two models,

$AR(2)$ or the exponential smoothing method, gives the best four$-$step ahead

forecast? $(10$ marks$)$