$2.(12$ 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. $*$ 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 $27\mathrm{.}0830.$ Part $2$: Out$-$of$-$sample comparison Second, we will perform an out$-$of$-$sample comparison of DES and TES, based on the forecasts for $16-$Aug$-2019$ to $31-$pug$-2019.$ This is our hold$-$out data so we are going to treat it as the future. This means the learning phase ends on $15-$Aug$-2019$ and the prediction phase starts on $16-$Aug$-2019.3.(8$ pts$.)$ Implement the DES method to obtain the k$-$day$-$ahead forecasts for $16-$Aug$-2019$ to $31-$Aug$-2019.$ Use the same values of LS and TS that you found in Question $1.$ The difference is that now you must stop updating the level and trend after $15-$Aug$-2019.$ Report the following: $(7$ pts$.)$ DES Forecasts for $16-$Aug$-2019$ to $31-$Aug$-2019,(1$ pt$.)$ The RMSE of DES method for $16-$Aug$-2019$ to $31-$Aug$-2019.4.(8$ pts$.)$ Implement the TES method to obtain the k$-$day$-$ahead forecasts for $16-$Aug$-2019$ to $31-$ Aug$-2019.$ As before, assume a weekly seasonal pattern, with p $=7,$ and use the same values of LS$,$ TS$,$ and SS that you found in Question $2.$ The difference is that now you must stop updating the level, trend, and seasonal indices after $15-$Aug$-2019.$ Report the following: $(7$ pts$.)$ TES Forecasts for $16-$Aug$-2019$ to $31-$Aug$-2019.(1$ pt$.)$ The RMSE of TES method for $16-$Aug$-2019$ to $31-$Aug$-2019.5.($for practice, will not be marked$)$ Which method do you choose?