By Lucia Mutikani

WASHINGTON (Reuters) - New U.S. single-family home sales unexpectedly rose in September, pointing to sustained demand for housing even as data for the prior three months were revised lower.

Other reports on Wednesday suggested a stronger pickup in economic growth in the third quarter than is currently anticipated. The goods trade deficit narrowed sharply, while both wholesale and retail inventories increased in September.

"A lot of the pieces of the puzzle have come back together in a positive direction, with a pickup in the export of goods to the rest of the world and new home sales," said Chris Rupkey, chief economist at MUFG Union Bank in New York.

The Commerce Department said new home sales increased 3.1 percent to a seasonally adjusted annual rate of 593,000 units last month, pulling them close to a nine-year high touched in July. However, the pace for the prior three months was revised down by a total of 85,000 units from previous estimates.

New home sales, which are derived from building permits, are volatile on a month-to-month basis and subject to large revisions. Sales increased 29.8 percent from a year ago.

Economists had forecast single-family home sales, which account for about 9.8 percent of overall home sales, falling to a rate of 600,000 units last month.

"The housing market may not be booming but it is clearly moving forward at a steady pace," said Joel Naroff, chief economist at Naroff Economic Advisors in Holland, Pennsylvania. "But the big problem is still the lack of inventory. Builders are cautious and tend to do very little speculative construction."

Despite the downward revisions, new home sales rose in the third quarter compared to the April-June period. Residential construction, however, likely remained a mild drag on gross domestic product for a second straight quarter.

According to a Reuters survey of economists, GDP probably increased at a 2.5 percent rate in the third quarter, quickening from the second-quarter's tepid 1.4 percent pace.

But advance data on Wednesday showing the goods trade deficit falling 5.2 percent to $56.1 billion in September amid strong exports suggested that third-quarter GDP growth could exceed expectations.

In addition, wholesale inventories increased 0.2 percent in September and retail inventories rose 0.3 percent.

"Based on this morning's data, we now believe the boost from trade could be closer to a full percentage point, almost twice what we had expected," said Michelle Girard, chief economist at RBS in Stamford, Connecticut.

"Even assuming some offset in farm inventories, and possibly business investment, we now look for real GDP growth in the third quarter to have advanced by 3.3 percent."

The government will publish its advance GDP growth estimate for the third quarter on Friday.

HOME BUILDING LAGGING

The broader PHLX housing index <.HGX>, which includes builders, building products and mortgage companies, was little changed in early afternoon trading. Shares in the nation's largest homebuilder, D.R. Horton Inc <DHI.N>, were slightly lower. Lennar Corp <LEN.N> rose 0.48 percent, while Toll Brothers <TOL.N> was flat.

Despite rising demand for housing, home building has been lagging, with builders complaining about land and labor shortages. Demand is being driven by rising wages as the labor market nears full employment, as well as by low mortgage rates.

"New home sales are still running ahead of single-family housing starts when inventories of new and existing homes for sale are already very lean," said Ted Wieseman, an economist at Morgan Stanley in New York.

"This should support much better future homebuilding activity if homebuilders can overcome what they've described as supply-side constraints on activity from shortages of qualified labor and lots."

Separately, the Mortgage Bankers Association said applications for home loans for last week fell to their lowest level since January.

Last month, new single-family homes sales rose in the Northeast, the Midwest and South. They fell in the West.

The inventory of new homes on the market dipped 0.4 percent to 235,000 units. At September's sales pace it would take 4.8 months to clear the supply of houses on the market, down from 4.9 months in August.

(Reporting by Lucia Mutikani; Editing by Paul Simao)