WASHINGTON (AP) — U.S. home prices rose in most major cities in October compared with a year ago, pushed up by rising sales and a decline in the supply of available homes. Higher prices show the housing market is improving even as it moves into the more dormant fall and winter sales period.

The Standard & Poor’s/Case-Shiller national home price index released Wednesday increased 4.3 percent in October compared with a year ago. That’s the largest year-over-year increase in two and a half years, when a homebuyer tax credit temporarily boosted sales.

Prices rose in October from a year ago in 18 of 20 cities. Phoenix led all cities with a 21.7 percent gain, followed Detroit, where prices increased 10 percent. Prices declined in Chicago and New York.

Home prices fell in 12 of 20 cities in October compared with September. Monthly prices are not seasonally adjusted, so the decreases reflect the end of the peak buying season.

Still, the broader trend is encouraging. October marked the fifth straight month of year-over-year gains, after nearly two years of declines. Prices rose in mid-2010 in the final months before the tax credit expired. They had fallen sharply in 2008 and 2009.

The improvement in housing is adding to economic growth and most analysts expect that to continue in 2013.

But automatic tax increases and spending cuts that are set to take effect next week could drag down growth. The White House and Congress have so far failed to reach agreement on a way to avoid the “fiscal cliff.” President Barack Obama and congressional lawmakers will return to Washington on Thursday to resume talks.

“We expect home price appreciation to continue for the foreseeable future, because inventories are lean amid rising sales,” said Joseph LaVorgna, chief U.S. economist at Deutsche Bank. “This assumes that a resolution to the ‘fiscal cliff’ is found … otherwise, the recent positive trend in housing would most certainly be in jeopardy along with the rest of the current economic expansion.”

Prices nationwide have recovered to about the same level as in the fall of 2003, according to the Case-Shiller index.