Illustration 7.3 (p. 262-4) describes time-series forecasting of new home sales,
ID: 3858045 • Letter: I
Question
Illustration 7.3 (p. 262-4) describes time-series forecasting of new home sales, but you can see that the data is old. Click here (https://www.census.gov/construction/nrs/historical_data/index.html) and download the first table: Houses Sold – Seasonal Factors, Total (Excel file is sold_cust.xls). Look at the monthly data on the “Reg Sold” tab.
Only keep the dates beginning in January 2008, so delete the earlier observations, and use the data through May 2017. 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” similar to the book’s column 4 on page 262 (t will go from 1 to 113 through May 2017); make a t2 column too (since, if you look at the data, you can see sales dropping until about mid-2011 then rising again; hence the quadratic). Also make a column “D” that is a dummy variable equal to one during the spring and summer months, similar to the book’s column 5.
Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with connectors) of both. 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 and t2 as the independents, 2) seasonally unadjusted monthly as the dependent, and t, t2, and D as the independents, 3) seasonally adjusted monthly as the dependent, and t and t2 as the independents, and 4) seasonally adjusted monthly as the dependent, and t, t2, and D as the independents. Discuss your findings, and determine which of the four models is the best for forecasting new home sales. In interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001. State the equation that would be used to forecast sales.
Explanation / Answer
1 ans ) the coefficient estimates for t and t2 change dramatically, even though the models are very comparable (unadjusted with a seasonal dummy is pretty close to seasonally adjusted).
2 ans) adding a redundant seasonal dummy to already seasonally-adjusted data results in the D variable being insignificant, as expected, and the model's explanatory power is essentially the same as models 2 and 3.