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Let's practice time-series forecasting of new home sales. Click here

(https://www.census.gov/construction/nrs/historical_data/index.html) to see the newest data in the first table: Houses Sold - Seasonal Factors, Total (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2009, so delete the earlier observations, and use the data through April 2019. Keep only the US data, both the seasonally unadjusted monthly (column B) and the seasonally adjusted annual (column G). Make a new column of seasonally adjusted monthly by dividing the annual data by 12. Make a column called "t" where t will go from 1 (Jan. 2009) to 124 (Apr. 2019); make a t^2 column too (since, if you look at the data, you can see sales are slightly U-shaped; hence the quadratic). Also make a column "D" that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with connectors) of both







a.) Do you think making a seasonal adjustment will be useful, given what you observe at this point?









*****Run four regressions:

  1. seasonally unadjusted monthly as the dependent, and t
  2. t and t
  3. 2
  4. t2 as the independents,
  5. seasonally unadjusted monthly as the dependent, and t
  6. t, t
  7. 2
  8. t2, and D
  9. D as the independents,
  10. seasonally adjusted monthly as the dependent, and t
  11. t and t
  12. 2
  13. t2 as the independents, and
  14. seasonally adjusted monthly as the dependent, and t
  15. t, t
  16. 2
  17. t2, and D
  18. D as the independents.

In interpreting your p-values, remember that, say, 1.0E-08 is 1.0×10

−8

1.0×10−8, which is 0.00000001




b.) In comparing the regression results between models 1 and 2 (the unadjusted sales), it is notable that including the extra variable D

D in model 2








c.) In comparing the regression results between models 2 and 3, it is notable that




d.) The regression results for model 4 are notable because

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