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|
|New York City||2015.0||43%|
|10 city composite||2013.2||47%|