JPMorgan Chase ($36.07 0%) analysts expect national home prices to rebound 12% over the next four years.

“We believe that, nationally, home prices have hit a bottom, and we continue to project a gradual recovery path for the next few years,” according to a report from the banking analysts this week.

Most price indices began turning upward this year — see one from Clear Capital, another from Lender Processing Services and the latest CoreLogic report. And the Standard & Poor’s Case-Shiller index, which lags behind the others, showed slowing declines earlier in the year.

A recent Zillow ($42.11 0%) survey showed economists expect an average 0.4% decline in prices through the end of 2012 followed annual by gains of 3% through 2016.

Chase analysts said they expect the more pessimistic view in the short term (another 2% decline this year) followed by a more optimistic recovery to prices in the survey as shown in the chart below. (Click to expand.)

The uncertainty revolves around the artificially low supply of homes on the market, due mostly to a slowed foreclosure process. Sales of the distressed homes will happen and when they do, prices in nearby areas suffer.

Chase estimates a supply of roughly 4.8 million possible homes in the shadow inventory, which includes those backing loans delinquent for 90 days or more. Cure rates and other variables trim the number, though. Assuming 75% of the delinquencies and 90% of the foreclosed homes are sold as distressed properties, the shadow inventory estimate drops to roughly 3.6 million, the analysts said.

Demand is creeping up after being negative (more looking to sell than buy) since 2007. Chase analysts expect more than 2.5 million problem loans to be resolved in 2012 through enhanced foreclosure prevention efforts, which would put “a major dent” in the shadow inventory.

“Of course, given the large supply and volume of continuing delinquencies, we expect it will take years to work through all the defaults, but significant progress is being made, which gives us reason to be more bullish on housing than we have been for years,” the analysts said.