The last report on home prices in 2013 reinforced that the housing recovery is here to stay.

Home prices rose 13.6 percent in October across the nation, the highest gain in seven years, according to the Standard & Poor’s Case-Shiller index released Tuesday morning. That was in line with analysts’ expectations and a continuation of the double-digit growth that home values have enjoyed this year.

Cities that posted the highest rate of growth compared with a year ago included Las Vegas (27 percent), San Francisco (24.6 percent), and Los Angeles (22.1 percent). Washington-area home values were 7.4 percent higher than a year ago.

Historically-low mortgage rates spurred homebuyers to flock to the market in 2013, but they were met by an inventory crunch. This combination of pent-up demand and limited new construction pushed home prices higher all year.

The housing market has been a driver of growth in the economic recovery through most of 2013. Rising home prices have lifted some of the hardest-hit regions out of the depths of the financial crisis, and economists expect more gains in 2014, although at a slower pace.

“Housing appears to be on a positive track as we turn the corner,” Lindsey Piegza, chief economist at the investment banking and brokerage firm Sterne, Agee & Leach, wrote in a research note. “Going forward, job creation and income growth will further propel new homebuyers into the market place for 2014.”

On a monthly basis, prices rose at a slightly slower pace than September, by 0.2 percent.