BUSI 405 Research Paper

Figure 1
New One-Family Houses Sold (NHS), in thousands, in the U.S. January 1975 to present

Data Source: economagic.com

Figure 2 12-period plot of autocorrelation functions (ACF) for NHS

FIGURE 3 24-period plot of autocorrelation functions (ACF) for first differenced NHS

TABLE 1
MAPE (mean absolute percentage error) and RMSE (root-mean-squared error)
Models Historical period Holdout period Jan. 1975-Dec. 2010 Jan. 2011-Dec. 2011 MAPE RMSE RMSE/Mean* MAPE RMSE RMSE/Mean*
Winter’s exponential smoothing 6.65% 4.65 7.74% 5.92% 6.73 28.74%
Decomposition with exponential smoothing trend 5.45% 3.97 6.61% 4.63% 5.77 24.64%
ARIMA(1,0,0)(2,0,0) 7.23% 5.11 8.51% 8.02% 6.56 28.01%
*Mean of NHS for the historical period is 60.08 and for the holdout period is 23.42

The best model should be the one with the smallest error. Among these three time-series models, the decomposition with exponential smoothing trend has the smallest MAPE and RMSE for both historical period and holdout period. Therefore, we use this model and the data from January 2001 to October 2011 to perform the ex-ante point and interval forecasts for the next 14 months as shown in table 2 and figure 4.
TABLE 2
Point and interval (5% to 95%) forecasts of NHS from November 2011 to December 2012
Month Point forecast 5% 95%
November 20.99 14.70 27.28
December 19.90 13.61 26.19
January 21.95 15.66 28.24
February 24.84 18.55 31.13
March 29.20 22.91 35.49
April 28.38 22.09 34.67
May 27.77 21.48 34.06
June 27.04 20.75 33.33
July 25.81 19.52 32.10
August 26.21 19.92 32.50
September 23.94 17.65 30.32
October 23.75 17.46 30.04
November 20.98 14.69 27.27
December 19.87 13.58 26.16
FIGURE 4 Actual and forecast values of NHS

IS THE WORST OVER?
People would like to know whether the worst of this housing