The steady pace of home price growth stretched into January, according to the latest Home Price Index from CoreLogic.

CoreLogic reported Tuesday that home prices rose 6.9% year over year in January. On a monthly basis, prices were 0.7% higher than in December.

"With lean for-sale inventories and low rental vacancy rates, many markets have seen housing prices outpace inflation," said Frank Nothaft, chief economist for CoreLogic.

Prices aren't just going up in the home-buying market, though. CoreLogic also said its Single-Family Rental Index was up 2.7%, again outstripping inflation.

CoreLogic predicts that price appreciation will continue in the year ahead, thanks to factors such as the economic recovery, low housing supply and mortgage rates that remain low by historical standards. But the prices won't pick up as much as they have in the past: CoreLogic is only predicting 4.8% year-over-year growth for January 2018.

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