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Principles of Data Science

Chapter 5

Principles of Data ScienceChapter 5

Chapter 5

Quantitative Problems

1.
Most likely, the period would be 52, as sales probably go through a cycle each year, and there are 52 weeks in the year.
2.
a.
There are peaks in the data at times 1, 5, and 9 as well as minimum points at times 4, 8, and 12, suggesting a period of 4 months.
b.
(728.6, 729.4, 728.6, 727.3, 727.1, 727.0, 726.0, 725.8)
There will be 8 terms in the centered SMA, as shown. These values form the trend-cycle component.
c.
(69.9, −225.3, 159.8, −1.5, 66.3, −228.0, 165.7, −3.8)
d.
(68.1, −226.65, 162.75, −2.65), repeating in blocks of 4
e.
(812.6, 953.85, 635.75, 506.75, 820.3, 952.45, 630.65, 501.65, 823.6, 948.65, 626.35, 504.25)
3.
a.
Since the missing data is due to different reporting policies on different days of the week, an SMA window of 7 days is most appropriate.
b.
See Solution Manual
4.
a.
Period = 3 from the ACF plot.
b.
See Solution Manual
5.
Forecasted value for 2024: 1.2124
6.
a.
MAE = 421.6 . RMSE = 313 , 168.55 = 559.6 . MAPE = 0.123 , or 12.3%. sMAPE = .0133 , or 13.3%.
b.
See Solution Manual
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