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 below data to determine the seasonal index of quarter 4 for the data through time-series decomposition methods. Use the four-quarter centered moving average in the computations.

(Round your answer to 2 decimal place.)


Q4 index =

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

Q4 index = 1.021641045

= 1.02

Quarter Actual Demand y years average Seasonal Factor I 54.019 53.3935 1.011714909 0.973806395 II 56.495 53.3935 1.058087595 1.03775226 III 50.169 53.3935 0.939608754 0.9668003 IV 52.891 53.3935 0.990588742 1.021641045 I 51.915 54.41775 0.954008573 0.973806395 II 55.101 54.41775 1.012555646 1.03775226 III 53.419 54.41775 0.981646613 0.9668003 IV 57.236 54.41775 1.051789168 1.021641045 I 57.063 60.8145 0.938312409 0.973806395 II 62.488 60.8145 1.027518108 1.03775226 III 60.373 60.8145 0.992740218 0.9668003 IV 63.334 60.8145 1.041429264 1.021641045 I 62.723 65.20125 0.961990759 0.973806395 II 68.38 65.20125 1.0487529 1.03775226 III 63.256 65.20125 0.970165449 0.9668003 IV 66.446 65.20125 1.019090892 1.021641045 I 65.445 65.89325 0.993197331 0.973806395 II 68.011 65.89325 1.032139104 1.03775226 III 63.245 65.89325 0.959809996 0.9668003 IV 66.872 65.89325 1.01485357 1.021641045 I 59.714 60.70875 0.983614388 0.973806395 II 63.59 60.70875 1.04746021 1.03775226 III 58.088 60.70875 0.95683077 0.9668003 IV 61.443 60.70875 1.012094632 1.021641045

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