Here are updates with the January 2014 Case-Shiller housing data.
I have speculated that when rents and home prices rise or fall together, this might be cyclical behavior; but when rents and home prices are moving in opposite directions, this might be behavior related to the effect of low real and nominal interest rates on home prices.
I am using annualized monthly changes of weighted moving averages in order to retain the ability to see recent changes while minimizing the monthly noise in these series. Home prices and rent are both continuing to increase. However, home prices have stopped accelerating since mid-2013, roughly coincident with rising interest rates.
Current behavior suggests cyclical recovery, although the lack of acceleration in home prices suggests that the recovery phase may be maturing.
I expect both the continued low interest rate environment and the low level of housing starts to continue to push both of these levels up. This is partly dependent on expansion of bank balance sheets as the Fed winds down QE3. As the bottom graph shows, this expansion appears to be tentatively gaining traction.