Applications for mortgages to buy a home or refinance both fell for a second week, marking a swift reversal of what had been a hopeful sign of a revival in the US housing market.

The Mortgage Bankers Association’s index of home-purchase applications declined 1.2% in the week ended Oct. 3, while a gauge of refinancing fell 7.7%. Both dropped back to levels seen in early September, when mortgage rates were on their way to a one-year low.