The U.S. Department of Commerce publishes data on industrial machinery and equip

Question

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 and the seasonal indexes below to deseasonalize the data.

Give the answer for quarter 1 year 5. (Rounded to three decimal places.)

1st Quarter (year 5)=

Time Period Industrial Machinery and
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 68.011 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

Explanation / Answer

deseasonalized data = 67.20535041

Quarter Actual Demand y years average Seasonal Factor Deseasonalized Demand y_d 1st quarter (year 1) 54.019 53.3935 1.011714909 0.973806395 55.47201198 2nd quarter 56.495 53.3935 1.058087595 1.03775226 54.43977542 3rd quarter 50.169 53.3935 0.939608754 0.9668003 51.89179192 4th quarter 52.891 53.3935 0.990588742 1.021641045 51.77062949 1st quarter (year 2) 51.915 54.41775 0.954008573 0.973806395 53.31141824 2nd quarter 55.101 54.41775 1.012555646 1.03775226 53.09648758 3rd quarter 53.419 54.41775 0.981646613 0.9668003 55.25339617 4th quarter 57.236 54.41775 1.051789168 1.021641045 56.02359096 1st quarter (year 3) 57.063 60.8145 0.938312409 0.973806395 58.59788999 2nd quarter 62.488 60.8145 1.027518108 1.03775226 60.21475682 3rd quarter 60.373 60.8145 0.992740218 0.9668003 62.44619493 4th quarter 63.334 60.8145 1.041429264 1.021641045 61.99241928 1st quarter (year 4) 62.723 65.20125 0.961990759 0.973806395 64.41013361 2nd quarter 68.38 65.20125 1.0487529 1.03775226 65.89241249 3rd quarter 63.256 65.20125 0.970165449 0.9668003 65.42819649 4th quarter 66.446 65.20125 1.019090892 1.021641045 65.03849894 1st quarter (year 5) 65.445 65.89325 0.993197331 0.973806395 67.20535041 2nd quarter 68.011 65.89325 1.032139104 1.03775226 65.53683629 3rd quarter 63.245 65.89325 0.959809996 0.9668003 65.41681875 4th quarter 66.872 65.89325 1.01485357 1.021641045 65.45547514 1st quarter (year 6) 59.714 60.70875 0.983614388 0.973806395 61.32019703 2nd quarter 63.59 60.70875 1.04746021 1.03775226 61.2766673 3rd quarter 58.088 60.70875 0.95683077 0.9668003 60.08272856 4th quarter 61.443 60.70875 1.012094632 1.021641045 60.14147564

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