PREDICTIVE ANALYTICS BASED ON

TRADITIONAL FORECASTING METHODS

S$1$ Forecasting Charitable Donations at the Union Mission

Cash donations $($in thousands of dollars$)$ at the Union Mission for $20212023$ were as shown below.

Quarter Donations Quarter Donations Quarter Donations

Q$12021245$ Q$12022256$ Q$12023273$

Q$22021285$ Q$22022293$ Q$22023289$

Q$32021257$ Q$32022265$ Q$32023274$

Q$42021348$ Q$42022355$ Q$42023379$

a$.$ Ignoring seasonal effects, compare both the MAD and MSE values for the last value method, the averaging method, the moving average method $($based on the most recent $4$ quarters$),$ the exponential smoothing method $($with an initial estimate of $275$ and a smoothing constant of $=0\mathrm{.}2),$ and the exponential smoothing method with trend $($with initial estimates of $275$ for the average value, $2$ for the trend, along with smoothing constants of $=0\mathrm{.}2$ and $=0\mathrm{.}2)$ when they are applied retrospectively to the years $20212023.$

b$.$ Determine the seasonal factors for the four quarters.

c$.$ Repeat part a$,$ but now considering the seasonal effects.

d$.$ Using the forecasting method from part a or c with the lowest MAD value, make long$-$range forecasts for charitable donations in each of the quarters of $2022.$