Mortgage rates showed little movement to start the year, according to the latest data released by Freddie Mac.

The 30-year fixed-rate average fell slightly to 3.34 percent with an average 0.7 point decline. It was down from 3.35 percent a week ago and 3.91 percent a year ago. The 30-year fixed rate has averaged less than 3.5 percent the past 15 weeks. The all-time low was 3.31 percent set Nov. 21.

The 15-year fixed-rate average dropped to 2.64 percent with an average 0.7 point. It was down from 2.65 percent a week ago and 3.23 percent a year ago. The 15-year fixed-rate average has remained below the five-year adjustable rate mortgage average since Oct. 4.

Hybrid adjustable-rate mortgages climbed slightly. The five-year ARM went up to 2.71 percent with an average 0.6 point. It was 2.70 percent a week ago.

The one-year ARM rose to 2.57 percent with an average 0.4 point, up from last week when it was 2.56 percent.

“Mortgage rates started the year near record lows which should continue to aid the ongoing housing recovery,” Frank E. Nothaft, Freddie Mac vice president and chief economist, said in a statement. “New home sales rose in November to a two-year high and were up 15.3 percent from the previous November. Similarly, pending sales on existing homes increased for the third month in November to the strongest pace since April 2010.”

Meanwhile, because of the holidays, mortgage applications fell off sharply during the final two weeks of the year, according to the Mortgage Bankers Association.

The Market Composite Index, a measure of loan application volume, was down 21.6 percent from the week ending Dec. 14. The Refinance Index plummeted 23.3 percent, while the Purchase Index decreased 14.8 percent.

The refinance share of mortgage activity dropped to 82 percent of total applications.