Extrapolation and prediction

In this post, I will try to estimate the future direction of the Case-Shiller home price index to see when the bottom occurs and to determine what the total decline will be. The plots below show the results of this. In the top plot, we have plotted the real Case-Shiller 10-city index, that is corrected for inflation. The 20-city would perhaps be more representative of the nation but only the 10-city index has the full history back to 1987 so we use that. The natural assumption would be to assume that the REAL index falls back to the previous trough which occurred about 1997 and that the fall will take about as much time as it took to build up. History shows that house price bubbles generally fall fairly symmetrically so this is probably a fairly good estimator for the future direction of the real index over the next few years until the next trough. It took about 9 years to go from trough to peak and will probably take about 9 years to go from peak to trough.

I have fit the peak profile to a particular analytic form and use this to extrapolated the curve forward. This curve (in green) reaches the previous trough value in 2015.

Now we can use this to make predictions for the nominal index which is what most people care about. All we have to do is pick a future inflation rate. I have chosen 2.0%. Small changes from this do not make a big difference in the results. However actual deflation or high inflation rates obviously would change them substantially.

This is shown in the second plot. The red line shows the CPI; the actual CPI in the past and my 2.0% extrapolation. I have defined it to be 100 at year 2000 just like the index to put them on the same plot. The green curve shows my extrapolated model including inflation. The next trough in the nominal index occurs about 2013. The fall from the peak value is about 47%.



I have applied the same modeling to the individual cities in the Case Shiller index. Here are the results below.

City	Trough year	Decline from peak
Phoenix	2011.7	51%
Los Angeles	2013.5	59%
San Diego	2013.5	56%
San Francisco	2013.0	53%
Washington DC	2013.4	46%
Miami	2012.3	53%
Tampa	2012.1	45%
Chicago	2011.7	26%
Boston	2015.0	40%
Las Vegas	2010.7	44%
New York City	2015.0	43%
San Francisco	2013.0	53%
10 city composite	2013.2	47%