Yale economist Robert Shiller, who predicted the recent housing bust as well as the Internet bust earlier this decade, says that a meaningful recovery seems to have occurred in the housing market — but that we shouldn’t expect it to continue at the current rate.

“It looks like a major turnaround,” Shiller, whose S&P Case-Shiller housing index has now risen for three straight months, told The Wall Street Journal. “We have some concern that it could be an aberration and temporary. But, at this point, it seems to be evident in just about every city in the U.S. That suggests it’s real. But it probably isn’t the beginning of a major boom, just because the economy is in such bad shape. … The most likely scenario is that it won’t continue at this high rate of increase, but that it will neither go down a lot, nor up a lot.”

That sideways move will likely last five years or so, Shiller says. He adds that major issues to watch will involve the coming expiration of government programs designed to stimulate the housing market — including the $8,000 first-time home-buyer credit and the Federal Reserve’s mortgage-backed security buying program. As those plans wind down, the question will be whether the housing market can continue to recover. “Part of the problem is that people are buying now rather than later,” he says. “When later comes, there could be a downturn in the market.”

Shiller also offers his thoughts on why an oversupply of houses could continue in the U.S., why the current “pretend-and-extend” economy isn’t conducive to the start of a new bubble despite extremely low interest rates, and why he’s not too worried about inflation right now.