Housing starts dropped 8.2 percent in October, the largest monthly decline in three years, the government reported yesterday. Analysts blamed higher interest rates for the drop, not the Oct. 19 stock market collapse.

Analysts said they expect the housing market to improve slightly this month and in December, primarily because the stock market's decline last month has brought down interest rates. Mortgage rates recently have declined more than 1 percentage point, to 10 or 10 1/2 percent, at many lenders around the country.

"Builders may have pulled in their horns" and gone to the sidelines, said Warren Lasko, executive director of the Mortgage Bankers Association of America. "But they will be back in November because {interest} rates are really down."

The Commerce Department reported that housing starts in October fell to an annual rate of 1.51 million units, a reversal from September, when starts rose 4 percent to 1.65 million units. Single-family construction dropped 7 percent last month to an annual rate of 1.1 million units, after a 6.8 percent rise in September. Construction of multifamily homes fell 11.3 percent to an annual rate of 410,000 units, compared with a 3 percent drop in September.

Housing starts in the Midwest dropped 19.3 percent to 238,000 units, the worst showing in the country.

Housing starts in the the South -- which includes the District, Virginia and Maryland -- dropped 11 percent to 615,000 units. In the West, starts fell 1 percent to 414,000. The Northeast was the only region to show an increase in starts, a 1 percent rise to 246,000 units.

In the first 10 months of the year, housing starts totaled 1.41 million units, down from 1.57 million for the same period last year.

Between March and June, housing starts were on a steady decline during a period when interest rates began rising from 8 and 9 percent to 11 and 12 percent. During the summer, starts rose slightly and jumped sharply in September.

But housing specialists said rising interest rates forced some home buyers out of the housing market.

When the stock market collapsed, some prospective buyers lost assets they had planned to use for down payments, and others postponed their plans to see which direction rates would take.

Some builders also took a wait-and-see attitude until the interest rates began to fall. Concerns about the federal budget deficit and the growing trade deficit may have contributed to uncertainty in buyers and builders, analysts said.

"Builders felt they were going to have a very cold winter before the rates started going down," said Robert Villanueva, director of forecasting for the National Association of Home Builders. "But over the next few months, it's a very cheery picture."

However, many housing economists are predicting lower housing starts in 1988.

John A. Tuccillo, chief economist for the National Association of Realtors, said he expects starts to drop to 1.52 million units next year, down from a projected 1.6 million for 1987 and 1.805 million in 1986. U.S. Housing Markets, a Michigan-based newsletter, expects housing starts to drop at least 9 percent in 1988.