$1.(12$ pts$.)$ Implement the DES method to calculate the one$-$day$-$ahead forecasts for $3-$April$-2019$

to $15-$Aug$-2019.$ Use solver to determine the values of LS and TS that minimize the withinsample

RMSE $($calculated based on the interval $8-$April$-2019$ to $15-$Aug$-2019),$ subject to the

constraint that LS and TS are between $0\mathrm{.}01$ and $0\mathrm{.}99.$ Report the following:

$(2$ pts$.$ feasibility, $1$ pt$.$ consistency, $2$ pts$.$ optimality$)$ Optimal values for LS$,$ TS$,$ and

the RMSE for $8-$April$-2019$ to $15-$Aug$-2019,$

$(7$ pts$.)$ Values of the level, trend, and one$-$day$-$ahead DES forecasts for $9-$Aug$-2019$

to $15-$Aug$-2019.$

v You can use the following information to confirm that you have set up your DES model

correctly: If you set LS $=$ TS $=0\mathrm{.}5,$ the value for level, trend, and DES forecast for $15-$Aug$2019$

should be $171\mathrm{.}56,2\mathrm{.}07,$ and $171\mathrm{.}13,$ respectively. And the within$-$sample RMSE should

be $24\mathrm{.}3030.$

$2.(12$ pts$.)$ Implement the TES method to calculate the one$-$day$-$ahead forecasts for $8-$April$-2019$

to $15-$Aug$-2019.$ Assume a weekly seasonal pattern, which means p $=7.$ Use solver to

determine the values of LS$,$ TS$,$ and SS that minimize the within$-$sample RMSE $($calculated based

on the interval $8-$April$-2019$ to $15-$Aug$-2019),$ subject to the constraint that LS$,$ TS$,$ and SS are

between $0\mathrm{.}01$ and $0\mathrm{.}99.$ Report the following:

$(2$ pts$.$ feasibility, $1$ pt$.$ consistency, $2$ pts$.$ optimality$)$ Optimal values for LS$,$ TS$,$ SS$,$

and the RMSE for $8-$April$-2019$ to $15-$Aug$-2019,$

$(7$ pts$.)$ Values of the level, trend, seasonality indices, one$-$day$-$ahead forecasts for $9-$

Aug$-2019$ to $15-$Aug$-2019.$

Hint: You may find the Weekday function useful for the TES forecast calculations.

v You can use the following information to confirm that you have set up your TES model

correctly: If you set LS $=$ TS $=$ SS $=0\mathrm{.}5,$ the value for level, trend, seasonality index and TES

forecast for $15-$Aug$-2019$ should be $168\mathrm{.}92,-0\mathrm{.}39,1\mathrm{.}01,$ and $169\mathrm{.}56,$ respectively. And the

within$-$sample RMSE should be $27\mathrm{.}0830.$