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# Time Series: seasonality, trend-seasonal model

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Question 1 (30 pts.): The Excel file attendance.xls contains the daily attendance data at a theme park for a period of four weeks in summer. The park manager wants to use these data to make forecasts for the following summer week.

a) Make a time-series plot of the data. Is there a trend? Is there seasonality in the data? What is the seasonality period? (5 pts.)
b) Fit a trend-seasonal model to the data and make forecasts for the 7 days of the next week. Do the forecasts appear reasonable? (5 pts.)
c) Fit only a seasonal model to the data and make forecasts for the next week. Do the forecasts appear reasonable? Which model would you choose? Answer based on the reasonableness of the forecasts and the MAPE values for the two models. (8 pts.)
d) Interpret the seasonal indexes for Saturday and Sunday from part (c) in words. Also explain what the deseasonalized (seasonally adjusted) series means. In particular, explain why in Week 2, although the Saturday attendance (12,714) was higher than the Sunday attendance (11,977), actually the theme park did better on Sunday than on Saturday. (12 pts.)

Week Day Attendance
1 Mon. 4392
1 Tue. 4428
1 Wed. 5143
1 Thu. 6510
1 Fri. 7175
1 Sat. 13796
1 Sun. 11791
2 Mon. 4440
2 Tue. 5072
2 Wed. 5553
2 Thu. 6250
2 Fri. 7119
2 Sat. 12714
2 Sun. 11977
3 Mon. 4523
3 Tue. 5021
3 Wed. 5530
3 Thu. 6279
3 Fri. 7105
3 Sat. 13116
3 Sun. 11982
4 Mon. 3594
4 Tue. 4364
4 Wed. 5732
4 Thu. 6648
4 Fri. 7795
4 Sat. 12937
4 Sun. 11425