The biggest yearly gains were in Colorado, Texas, New York, Nevada and Michigan. Just three states saw prices fall compared with 12 months earlier: Maryland, Vermont and Connecticut.
The state data also reflects the steadier nature of the increases. Prices rose 7.1 percent in Nevada, after jumping more than 20 percent early last year.
"As the year progresses, we expect upward pressure as low inventories and more first-time buyers drive up home prices," Anand Nallathambi, CEO of CoreLogic, said.
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Nationwide, home prices are still 13.4 percent below the peak reached in April 2006, before the housing bust. There are 27 states that are at or within 10 percent of their peaks, CoreLogic said.
Sales of existing homes slipped 3.1 percent last year to 4.9 million. But this year, economists expect sales will get a boost from lower mortgage rates, healthy hiring, and lower down payment requirements from mortgage giants Fannie Mae and Freddie Mac.
The pickup may take a few months to appear. Signed contracts to buy homes slid in December, according to the National Association of Realtors. Signed contracts usually result in final sales one-to-two months later.
Still, other recent data on housing suggests that sales and construction are on the upswing. While sales of existing homes fell in 2014, they picked up in December, increasing 2.4 percent from the previous month to a seasonally adjusted annual pace of 5.04 million. Many economists forecast sales will rise to about 5.2 million this year.
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Mortgage rates have fallen for four straight weeks and the average rate on a 30-year fixed mortgage is just 3.63 percent. That makes it easier for would-be buyers to purchase a home. It has also prompted a spike of refinancing applications that could enable many Americans to lower their monthly mortgage payments, freeing up cash to spend or save.
Home construction, meanwhile, jumped 4.4 percent last month to an annual rate of 1.09 million. Builders began construction on 1.01 million new houses and apartments in 2014, the most in nine years and 8.8 percent more than in 2013.