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# Decomposition of time series

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The Costello Music Company has been in business for 5 years, selling electric organs. Below are the quarterly sales by year, with annual totals.

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total
1 4 2 1 5 12
2 6 4 4 14 28
3 10 3 5 16 34
4 12 9 7 22 50
5 18 10 13 35 76

A.) Compute the trend in sales, use that to estimate sales in each quarter, and compute the mean absolute deviation between actual and estimated sales.

B.) Compute the quarterly seasonal indexes.

C.) Use the quarterly seasonal indexes to deseasonalize the data.

D.) Compute the trend in deseasonalized sales per quarter and use that to estimate sales in each quarter.

E.) Reseasonalize the estimate in the previous step.

F.)Calculate the mean absolute deviation between actual and estimated sales.

G.) Compare the trend and error of the simple trend model from a. to that of the seasonally adjusted model from F.

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#### Solution Summary

The solution gives the details of decomposition of time series data into four components. Mean absolute deviation between actual and estimated sales are also given.

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