Home prices in the United States rose for the 32nd consecutive month in October, but the increases have slowed for high-end properties and hastened at the lower end. Compared with October of 2013, home prices rose 6.1%, including the sales of distressed properties. Month over month, October home prices rose by 0.5%. In September, prices rose 5.6% year-over-year and slipped 0.1% month-over-month.

In 28 states and the District of Columbia, home prices are at or within 10% of their peak. Home prices remain 12.4% below the peak set in April 2006. The data were released Tuesday by research firm CoreLogic.

Including sales of distressed properties, the five states posting the largest year-over-year price increases were Michigan (up 10.5%), South Dakota (10.4%), Montana (9.1%), Texas (8.7%) and Colorado (8.6%).

Excluding sales of distressed properties, the five states posting the biggest price increases over the past 12 months were South Dakota (up 10.4%), Massachusetts (9.7%), Maine (8.4%), Texas (8.1%) and Michigan (8%).

The five states with the largest peak-to-current declines, including distressed transactions, were Nevada (down 36.1%), Florida (down 33.5%), Arizona (down 29.0%), Rhode Island (down 28.3%) and Maryland (down 21.9%).

CoreLogic’s CEO said:

The gradual recovery of the housing market continues to be propelled by improving employment, more buyer and seller confidence, continued low rates and, in certain parts of the country, investor demand. The continued actual and projected rise in home prices confirms that fact. Based on our projections, home prices in over half the country will have reached or surpassed levels last seen at the height of the housing bubble sometime in mid-2015.

CoreLogic has forecast that home prices, including distressed sales, will rise 0.2% in November, compared with October, and by 5.1% in the 12 months between October 2014 and October 2015. Both estimates include distressed sales.

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