By Lucia Mutikani

WASHINGTON (Reuters) - Groundbreaking for U.S. single-family homes raced to the highest level in more than 6-1/2 years in December and permits surged, in a hopeful sign for the sluggish housing market recovery.

Housing has lagged an acceleration in economic growth, but Wednesday's report hinted at a pick-up in activity. That should help to further strengthen the U.S. economy's fundamentals as it confronts headwinds from slowing global growth.

"The last piece of the economic puzzle is starting to come together now as housing construction is coming back. The housing market is continuing to heal," said Chris Rupkey, chief financial economist at MUFG Union Bank in New York.

The Commerce Department said on Wednesday that single-family housing starts, the largest part of the market, jumped 7.2 percent to a seasonally adjusted annual pace of 728,000-units - the highest level since March 2008.

That offset a 0.8 percent fall in groundbreaking for the volatile multi-family homes segment, lifting overall housing starts 4.4 percent to a 1.09 million-unit rate last month. Wall Street had forecast starts rising to a 1.04 million-unit pace.

Homebuilder shares were trading higher on the data, helping the housing index to outperform the broader U.S. stock market. DR Horton, the largest homebuilder, rose 0.65 percent, while Lennar Corp gained 1.03 percent and Pulte Group was up 0.19 percent.

IMPROVEMENT EYED

A separate report from the Mortgage Bankers Association showed applications for loans to buy homes fell 3 percent last week after a 24 percent surge in the week ending Jan. 9.

Tepid wage growth has constrained housing, sidelining first-time buyers from the market and forcing many young adults, most of whom are saddled with college debts, to stay at home with their parents or share lodgings with relatives and friends.

The resulting weak household formation, in particular, has hurt residential construction. Household formation is currently running at about 500,000 a year, far below the more than 1-million mark that would signal a robust housing market.

But with wage growth expected to pick up, the 30-year mortgage rate down more than 80 basis points from early 2014 and moves by the government to ease credit conditions, housing is seen gaining momentum this year and expected to help soften the blow from slowing global economic growth.

"This should allow for many more individuals to enter the market. We expect much of the improvement to occur in sales at the lower end of the market, which has been lagging the overall housing recovery," said David Nice, an economist at Mesirow Financial in Chicago.

For all of 2014, groundbreaking increased 8.8 percent to 1.01 million units, the highest since 2007. Single-family housing starts in 2014 were also the highest in seven years.

While overall permits for future home building fell 1.9 percent in December, they were dragged down by an 11.8 percent plunge in the multi-family segment.

Single-family permits rose 4.5 percent to their highest level since January 2008, with permits in the populous South hitting their highest level since February 2008.

(Reporting by Lucia Mutikani; Editing by Paul Simao)