Forecasting Monthly Data. Consider the following time series data:

Month $1234567$

Value $24132012192315$

a$.$ Construct a time series plot. What type of pattern exists in the data?

b$.$ Develop a three$-$week moving average for this time series. Compute MSE and a

forecast for week $8.$

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Problems $443$

c$.$ Use a $50\mathrm{.}2$ to compute the exponential smoothing values for the time series.

Compute MSE and a forecast for week $8.$

d$.$ Compare the three$-$week moving average forecast with the exponential smoothing forecast using a $50\mathrm{.}2.$ Which appears to provide the better forecast based on MSE?

e$.$ Use trial and error to find a value of the exponential smoothing coefficient a that

results in a smaller MSE than what you calculated for a $50\mathrm{.}2$