# 6.7 Exercises

- Show that a $3\times 5$ 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.
- The data below represent the monthly sales (in thousands) of product
A for a plastics manufacturer for years 1 through 5 (data set
`plastics`

).1 2 3 4 5 **Jan**742 741 896 951 1030 **Feb**697 700 793 861 1032 **Mar**776 774 885 938 1126 **Apr**898 932 1055 1109 1285 **May**1030 1099 1204 1274 1468 **Jun**1107 1223 1326 1422 1637 **Jul**1165 1290 1303 1486 1611 **Aug**1216 1349 1436 1555 1608 **Sep**1208 1341 1473 1604 1528 **Oct**1131 1296 1453 1600 1420 **Nov**971 1066 1170 1403 1119 **Dec**783 901 1023 1209 1013 - Plot the time series of sales of product A. Can you identify seasonal fluctuations and/or a trend?
- Use a classical multiplicative decomposition to calculate the trend-cycle and seasonal indices.
- Do the results support the graphical interpretation from part (a)?
- Compute and plot the seasonally adjusted data.
- Change one observation to be an outlier (e.g., add 500 to one observation), and recompute the seasonally adjusted data. What is the effect of the outlier?
- Does it make any difference if the outlier is near the end rather than in the middle of the time series?
- Use a random walk with drift to produce forecasts of the seasonally adjusted data.
- Reseasonalize the results to give forecasts on the original scale.

- Figure 6.13 shows the result of decomposing the number of persons in
the civilian labor force in Australia each month from February 1978
to August 1995.
- Write about 3–5 sentences describing the results of the seasonal adjustment. Pay particular attention to the scales of the graphs in making your interpretation.
- Is the recession of 1991/1992 visible in the estimated components?

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