ABC Company has accumulated the following historical sales data with some missing information

as shown below:

Dec. Jan. Feb. Mar. Apr. May Jun.

Actual $($in thousands$)320360350$

Forecast $($in thousands$)380350340$

Use exponential smoothing with

$0\mathrm{.}5$

to answer the following questions.

$($i$)$ Find the sales forecast for March and June. $4$ marks

$($ii$)$ Find the actual values for March and April. $5$ marks

$($iii$)$ It has been found that the actual sales in December was wrongly entered as $320$ instead of

$384.$ Find the forecast for June. $7$ marks

$($iv$)$ Suppose the company uses a $5$ month moving average technique to forecast sales, what is

the new forecast for June? $5$ marks

$($b$)$ Consider the following time series data.

Time $($

x

$)1234567891011$

Arrivals $($

y

$)9\mathrm{.}9411\mathrm{.}2511\mathrm{.}9810\mathrm{.}918\mathrm{.}8310\mathrm{.}408\mathrm{.}9010\mathrm{.}2611\mathrm{.}6413\mathrm{.}8015\mathrm{.}10$

$($i$)$ Find next year$$s forecast using time series linear regression. $15$ marks

$($ii$)$ Compare a $3$ point moving average forecast and an exponential smoothing forecast with

$0\mathrm{.}7$

$.$ Using MSE over the past $8$ periods, find which one provides better forecasts.

$12$ marks

$($iii$)$ What is the forecast for next year using the MSE in part $($ii$)$