WASHINGTON (MarketWatch) -- Encouraging data on the housing market in the past few weeks have some observers insisting that the worst is over. But others say the small improvements are merely statistical blips and that the market still has much further to fall. Depending on who's right, the economy could either bounce back from the current soft patch and reaccelerate next year, or it could continue to weaken, forcing the Federal Reserve to cut interest rates to stave off an abrupt economic chill or an outright recession. Arguing that real-estate woes have hit bottom, we have former Fed Chairman Alan Greenspan, who told an audience in Canada that "I suspect that we are coming to the end of this downtrend, as applications for new mortgages, the most important series, have flattened out." "I don't know, but I think the worst of this may well be over," Greenspan said. See full story. Greenspan's old sidekick, Fed Vice President Donald Kohn, concurred, saying, "starts may be much closer to their trough than to their peak." See full story. On the other side, we have current San Francisco Fed President Janet Yellen, who told an audience in California that "a significant buildup of home inventory implies that permits and starts may continue to fall, and the market may not recover for several years." See full story.The great debate The two former rivals and colleagues on the Fed board are joined by dozens of private-sector economists and academics, all arguing vociferously about where housing is heading and what it means for the economy. The recent housing data have been surprisingly good, bolstering the optimists' view that the market is at least beginning to flatten out. Just this week, the Realtors reported a decline in inventories of unsold homes, even as sales fell to a three-year low. See full story. The Commerce Department said sales of new homes rose for the second month in a row, sparked by huge price discounting by the builders. See full story. As reported earlier in the month, the home builders' confidence index rose slightly in October after plunging for eight straight months to a 15-year low in September. See full story. Housing optimists were also encouraged by the 6% increase in housing starts in September after they fell to a three-year low in August. See full story. Largely unnoticed in their glee was the 6% decrease in the less-volatile building permits data, the fastest pace of decline in seven years. And median home prices are falling at the fastest pace in decades. The monthly data are interesting but ultimately volatile and unreliable. What we want to know is where's the bottom? Is it true, as David Seiders, chief economist for the National Association of Home Builders, suggested, that the market "may be stabilizing"? Or as David Lereah, chief economist for the National Association of Realtors, put it a month ago: "We think the housing market has now hit bottom." The housing optimists are led by economists for two industry groups, so their views may be self-serving to some extent. But their ranks also include some of the more respected economists on Wall Street as well. "The housing market shows signs of stabilizing, said Dean Maki and Julia Coronado, economists for Barclays Capital, who, like Greenspan, point to the flattened out of mortgage applications as a key indicator. David Greenlaw, an economist for Morgan Stanley, is another optimist, relatively speaking. . "While we certainly do not think the housing market recession is over, a variety of incoming data increasingly suggest that the worst of it occurred in the third quarter -- and with little meaningful spillover into other sectors of the economy," Greenlaw said. While some economists saw a bottoming in last week's data, the far-more-common reaction was like this from MFR economist Joshua Shapiro: "It is clear there remains a deep-seated pessimism on the part of home builders." Or this from Ian Shepherdson, chief economist for High Frequency Economics: "It isn't over. It has barely begun.' Or this from Bart Malek of BMO Nesbitt Burns: "We have not yet seen the full fallout from the housing correction." Mortgage applications The rebound in mortgage application due to lower rates is a key element in the optimists' case.