Exercise $1-$ Application $(10$ marks$)$

This exercise involves numerical responses to be submitted via a quiz tool on iLearn

For the purposes of this report, only consider the data from February $2014$ to January $2023$ as the sample of data that is available to you $-$ that is$,$ ignore any recent observations. This means that the first actual observation in your Excel file is from February $2014$ and your last actual observation in your Excel file is from January$-2023.$

For the Seasonally$-$adjusted data for the Total Type of Building $($Series ID: A$422173$X$)$ available in Table $30$: Value of building approved $-$ New South Wales: Forecast the out$-$ofsample values for every month in the period February $2023-$January $2024($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 $0\mathrm{.}5.$ Please see the notes on page $5$ of this document $-$ regarding seeds.

Before you begin Exercise $1,$ let's check that you have the right data! The average should be $3218853!$

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

The within$-$sample forecast for July $2022.$

The out$-$of$-$sample forecast for May $2023.$

The out$-$of$-$sample forecast for January $2024.$

The MAPE.

The MAE.

Critically think for a way to optimise alpha and beta $($if there is no beta, you can input $\text{'}0\text{'}$ 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 July $2022.$

$10.$ The out$-$of$-$sample forecast for January $2024.$

$6$