As the above chart shows, housing prices according to both the Case Shiller index and the Radar Logic index are up about 10% in the past year. The Case Shiller index is now at a post-recession high. Prices have been relatively flat for the past four years, and on the margin they are showing rather impressive strength.
The chart above shows the Case Shiller home price index adjusted for inflation. Real home prices according to this index have yet to post net gains since the recession, but they are down fully 37% from their 2006 highs. If the prices of houses was a bubble, it has certainly burst. Four years of consolidation is enough to warrant the supposition that housing prices are more likely to rise than decline in the years to come.
As the chart above shows, housing prices and rents are coming back into line, after prices shot up to unreasonably high levels. Owner's Equivalent Rent is an important component of the CPI, and is used instead of housing prices; that served to insulate the CPI from the housing price runup in the early 2000s, and from the housing price collapse that followed.
Lots of evidence here to support the notion that housing prices have fallen enough to equilibrate demand and supply. When coupled with the fact that new home construction has almost doubled in the past two years, the housing market recovery appears to be well underway.