The U.S. Department of Commerce publishes data on industrial machinery and equipment. Shown here are the shipments (in $ billions) of industrial machinery and equipment from the first quarter of year 1 through the fourth quarter of year 6. Use these data to determine the seasonal indexes for the data through time-series decomposition methods. Use the four-quarter centered moving average in the computations.
Industrial Machinery and
Time Period ........ Equipment Shipments
1st quarter (year 1) ...... 54.019
2nd quarter ....... 56.495
3rd quarter ....... 50.169
4th quarter ........ 52.891
1st quarter (year 2) .... 51.915
2nd quarter ........ 55.101
3rd quarter ....... 53.419
4th quarter ....... 57.236
1st quarter (year 3) .... 57.063
2nd quarter ....... 62.488
3rd quarter ........ 60.373
4th quarter ....... 63.334
1st quarter (year 4) .... 62.723
2nd quarter ........ 68.380
3rd quarter ....... 63.256
4th quarter ........ 66.446
1st quarter (year 5) ..... 65.445
2nd quarter ....... 68.380
3rd quarter ....... 63.256
4th quarter ....... 66.446
1st quarter (year 5) .... 65.445
2nd quarter ....... 68.011
3rd quarter ....... 63.245
4th quarter ........ 66.872
1st quarter (year 6) .... 59.714
2nd quarter ....... 63.590
3rd quarter ....... 58.088
4th quarter ........ 61.443