Forecasting Using Time Series Techniques a$)(2$ points$)$ What forecasting technique$($s$)$ would be best suited to forecast the sales? Why? Split the data into two: $2013-16($for forecast model building or calibration$)$ and $2017-18($for forecast model validation or testing$)$ b$)(25$ points$)$ Use data for years $201316$ for building the forecast models $-$ Moving Average of $2$ data points $-$ Linear Regression $-$ Decomposition technique $-$ Single Exponential Smoothing i$.$ Generate forecasts using alpha $=0\mathrm{.}25-$ Double Exponential Smoothing i$.$ Generate forecasts using alpha $=0\mathrm{.}25,$ beta $=0\mathrm{.}15-$ Triple Exponential Smoothing i$.$ Generate forecasts using alpha $=0\mathrm{.}25,$ beta $=0\mathrm{.}15$ gamma $=0\mathrm{.}35$ c$)(8$ points$)$ Forecast for years $2013-16$ as well as $2017-18$ d$)(5$ points$)$ Plot actual data versus forecasts in graphs e$)(5$ points$)$ Test the accuracy of the model for years separately for $2013-16$ and $2017-18,$ using the mean$-$squared error $($MSE$)$ and mean$-$absolute deviation $($MAD$)$ metrics. $-$ How does the accuracy compare for the $2013-16$ model building periods versus $2017-18($model validation$)$ periods? Explain why? $-$ Which forecasting technique is performing better? Why? f$)(2$ points$)$ Why did we split the data into two parts for this analysis? What would happen if we did not split? Discuss the pros and cons of splitting the data into two as calibration and validation data? g$)(3$ points$)$ For the exponential smoothing, imagine you were not given alpha, beta and gamma parameters. What would you do to complete the analysis? How would you make sure that your recommendations are robust? Setup an optimization problem using MS Excel's Solver to identify the best alpha, beta and gamma parameters that minimizes MSE. Compare the forecast performance of the optimal single, double, and triple exponential smoothing models to the non$-$optimal ones. Solve using MS Excel and clearly label solutions for each part above and include interpretations in text boxes next to each solution.