Jul$-20151585\mathrm{.}7$

Aug$-20151586\mathrm{.}3$

Sep$-20151541\mathrm{.}9$

Oct$-20151591\mathrm{.}9$

Nov$-20151590\mathrm{.}0$

Dec$-20151592\mathrm{.}5$

Jan$-20161610\mathrm{.}3$

Feb$-20161591\mathrm{.}6$

Mar$-20161584\mathrm{.}6$

Apr$-20161580\mathrm{.}8$

May$-20161567\mathrm{.}4$

Jun$-20161582\mathrm{.}1$

Jul$-20161537\mathrm{.}2$

Aug$-20161541\mathrm{.}6$

Sep$-20161537\mathrm{.}8$

Oct$-20161536\mathrm{.}8$

Nov$-20161524\mathrm{.}3$

Dec$-20161550\mathrm{.}1$

Jan$-20171554\mathrm{.}7$

Feb$-20171542\mathrm{.}9$

Mar$-20171545\mathrm{.}1$

Apr$-20171604\mathrm{.}2$

May$-20171550\mathrm{.}6$

Jun$-20171548\mathrm{.}7$

Jul$-20171541\mathrm{.}7$

Aug$-20171519\mathrm{.}8$

Sep$-20171557\mathrm{.}1$

Oct$-20171566\mathrm{.}8$

Nov$-20171536\mathrm{.}8$

Dec$-20171553\mathrm{.}1$

Jan$-20181544\mathrm{.}7$

Feb$-20181547\mathrm{.}5$

Mar$-20181548\mathrm{.}6$

Apr$-20181542\mathrm{.}1$

May$-20181588\mathrm{.}6$

Jun$-20181577\mathrm{.}2$

Jul$-20181540\mathrm{.}7$

Aug$-20181554\mathrm{.}6$

Sep$-20181560\mathrm{.}0$

Oct$-20181565\mathrm{.}6$

Nov$-20181537\mathrm{.}1$

Dec$-20181567\mathrm{.}6$

Jan$-20191540\mathrm{.}1$

Feb$-20191566\mathrm{.}3$

Mar$-20191535\mathrm{.}7$

Apr$-20191565\mathrm{.}8$

May$-20191575\mathrm{.}7$

Jun$-20191570\mathrm{.}0$

Jul$-20191548\mathrm{.}9$

Aug$-20191575\mathrm{.}1$

Sep$-20191576\mathrm{.}2$

Oct$-20191571\mathrm{.}7$

Nov$-20191580\mathrm{.}8$

Dec$-20191590\mathrm{.}7$

Jan$-20201566\mathrm{.}5$

Feb$-20201587\mathrm{.}1$

Mar$-20201426\mathrm{.}1$

Apr$-20201241\mathrm{.}6$

May$-20201751\mathrm{.}8$

Jun$-20201574\mathrm{.}8$

Jul$-20201630\mathrm{.}6$

Aug$-20201470\mathrm{.}1$

Sep$-20201466\mathrm{.}6$

Oct$-20201590\mathrm{.}5$

Nov$-20201809\mathrm{.}0$

Dec$-20201701\mathrm{.}0$

Jan$-20211678\mathrm{.}0$

Feb$-20211672\mathrm{.}8$

Mar$-20211786\mathrm{.}1$

Apr$-20211713\mathrm{.}6$

May$-20211673\mathrm{.}0$

Jun$-20211566\mathrm{.}2$

Jul$-20211395\mathrm{.}6$

Aug$-20211221\mathrm{.}2$

Sep$-20211234\mathrm{.}5$

Oct$-20211525\mathrm{.}4$

Nov$-20211800\mathrm{.}2$

Dec$-20211582\mathrm{.}7$

Jan$-20221629\mathrm{.}3$

Feb$-20221752\mathrm{.}4$

Mar$-20221801\mathrm{.}2$

Apr$-20221800\mathrm{.}1$

May$-20221843\mathrm{.}7$

Jun$-20221851\mathrm{.}2$

Jul$-20221870\mathrm{.}1$

Aug$-20221893\mathrm{.}2$

Sep$-20221887\mathrm{.}9$

Oct$-20221895\mathrm{.}8$

Nov$-20221908\mathrm{.}3$

Dec$-20221772\mathrm{.}8$

Jan$-20231901\mathrm{.}5$

Feb$-20231882\mathrm{.}1$

Mar$-20231896\mathrm{.}2$

Apr$-20231915\mathrm{.}5$

May$-20231904\mathrm{.}8$

Jun$-20231814\mathrm{.}1$

Jul$-20231874\mathrm{.}0$

Aug$-20231879\mathrm{.}9$

Sep$-20231913\mathrm{.}6$

Oct$-20231895\mathrm{.}9$

Nov$-20231971\mathrm{.}5$

Dec$-20231844\mathrm{.}6$

Jan$-20241878\mathrm{.}5$

Feb$-20241924\mathrm{.}4$

Mar$-20241889\mathrm{.}1$

Apr$-20241888\mathrm{.}0$

May$-20241872\mathrm{.}5$

Jun$-20241890\mathrm{.}8$

Forecast the out$-$of$-$sample values for every month in the period July $2023$ June $2024($both months

inclusive$)$ using only one appropriate exponential smoothing model $($either simple

exponential smoothing or Holt exponential smoothing models that you think is most

appropriate given the data$).$ Your starting value for any parameters should be $0\mathrm{.}5.$

Before you begin Exercise $1,$ let$$s check that you have the right data! The average

should be $1617!$

For Simple Exponential Smoothing $$ for the seed of the level use the first observation,

Y$1.$

$$ For Holt$$s Exponential Smoothing $$ for the seed of the level use the first observation,

Y$1.$ For the seed of the trend $$ take the difference of the first two observations $($Y$2$ Y$1)$

Once you identify and develop an appropriate exponential smoothing model with the starting values for parameter$($s$)=0\mathrm{.}5,$

Critically think for a way to optimise alpha and beta $($if there is no beta, you can input $0$ for

question $7)$ via the MSE, and report the following values after your optimisation:

$6.$ Alpha.

$7.$ Beta.

$8.$ The MAPE.

$9.$ The within$-$sample forecast for Januar