Q $2)$ Your objective is to apply and compare different time series forecasting techniques including moving averages, weighted moving averages and exponential smoothing. You will also evaluate the accuracy of these methods using the Mean Absolute Deviation $($MAD$).$ Use the attached excel file and put your results in it $($You will find the data in the second page of the excel file$).$

a$.$ Calculate the $3$ month moving average for the provided data

$(10$ p$.)$

b$.$ Calculate the $3$ month weighted moving average for the provided data $($give weights as $3-2-1$ from the current to oldest$)$

$(10$ p$.)$

c$.$ Apply exponential smoothing with two smoothing constant: $0\mathrm{.}2($Take the first month's forecast as $14\mathrm{.}00)$

d$.$ Apply exponential smoothing with two smoothing constant: $0\mathrm{.}5,2($Take the first month's forecast as $14\mathrm{.}00)$

$(10$ p$.)$

e$.$ Calculate the mean absolute deviation $($MAD$)$ for each method.

$(10$ p$.)$

f$.$ Compare the MAD values and determine the acuracy of each forecasting method. Provide a brief analysis of which method provided the most accurate forecast and why $(15$ p$.)$