Consider the following shipment data that represent cubic trend pattern mixed with some randomness:

Period	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Shipment	42	69	100	115	132	141	154	171	180	204	228	247	291	337	391

Apply a single 3-period moving average, a single 5-period moving average, a single 7-period moving average, a double 3 x 3 moving average, and a double 5 x 5 moving average. For the missing data at the beginning or the end of the sample, just get the average of what is available. Which type of moving average seems most appropriate to you in identifying the cubic pattern of the data? (40 points)

Hint: Double 3 x 3 moving average is the average of the 3-period moving average for the previous period, current period, and the next period. Likewise, for the double 5 x 5 moving average where you use the average of the 5-period moving average for the two previous periods, current period, and the next two periods.

Using the shipment data in question 2 above, calculate the moving average forecast, MA (3) and MA (5) for possible periods. Calculate MAPE and WAPE for both cases. (20 points)

Show that a 3 x 5 MA is equivalent to a 7-term weighted moving average with weights of 0.067, 0.133, 0.200, 0.200, 0.200, 0.133, and 0.067. (20 points)

Please submit your answers in a Word document. Please also attach the corresponding Excel spreadsheets showing your work.