It's been an autumn rally to make heads spin.

Wall Street said goodbye to a lackluster summer on Sept. 20. Since then, stock prices have soared.

Declining interest rates touched off the climb in stock prices. But the rally has been abetted by the intangible herd instincts that analysts find so impossible to project, but so easy to identify in hindsight.

"Clearly the stock market has been moving in lock step with interest rates and it has been doing so in the face of choppy corporate earnings and a herky-jerky economy," according to James Balog, vice chairman of the big securities firm Drexel Burnham Lambert Inc.

Declining interest rates almost always boost stock prices. Lower rates make the expected return on investments in stocks more attractive and they also reduce the costs of borrowing to buy stocks.

Investors who were slow to catch on to the interest rate rally have been fueling the boom recently.

Firms that manage portfolios for pension funds and other so-called institutional investors are making a mad rush to buy stocks before the end of the year -- when they report to their clients on their holdings. "They're trying to become fully invested in stocks, to make it look like they were smart all quarter long," said Balog.

The mad rush peaked Wednesday and Thursday. The Dow Jones industrial average -- the most carefully watched although hardly the most representative stock market barometer -- jumped 25 points on Wednesday to close at 1484.40. It was a heavy trading day in which 180.4 million stocks listed on the New York Stock Exchange changed hands.

The frenzy increased on Thursday. The Dow average jumped another 16 points during the first three hours of trading. Shortly after 1 p.m., it crossed the 1,500 barrier for the first time in history.

Lunch injected an element of sobriety. The Dow average began to sag and finished the day down 1.49 at 1482.91. But trading was at one of its highest levels in history.

On the New York Stock Exchange, 181 million shares were bought and sold. Another 30 million NYSE-listed stocks were traded on other exchanges and over-the-counter that day.

The Dow average dropped another 5.73 points Friday to 1,477.18. Trading was more moderate, but still heavy, as about 146 million shares changed hands.

The deterioration in stock prices on Thursday and Friday was a prelude to the end of the boom, according to some analysts.

But many predict that after a pause, the rally will resume.

"We've gone through 1,400, then close to 1,500 rather easily," said Victor Melone, chief executive officer of Manufacturers Hanover Investment Corp.

"The fact that it's down for a day or two isn't even worth analyzing. The market is catching its breath. You'll hear a lot of technical mum- bo jumbo that doesn't mean any- thing more than its catching its breath," Malone said.

Jerry Hinkle, the chief trader for the brokerage firm Sanford C. Bernstein & Co., said that the next jump in stock prices will be propelled by an improving economy that will boost corporate earnings.

Hinkle said his firm had projected the autumn rally, but had expected the rally to come from a strong rebound in the U.S. economy, not a decline in interest rates.

Now, he said, the improvement in the economy he thought would appear in the early fall appears to be occurring.

Although faster economic growth is likely to put some upward pressure on interest rates, rates are not likely to rise enough to retard the stock market rally.

It was a steep decline in interest rates in the summer of 1982 that touched off the bull market that continues today. The Dow aver- age has climbed 90 percent since then.

Drexel Burnham's Balog, however, is among the analysts who say the long-run steam is gone from the rally, although there may be some short-run punch left.

There are generally two areas that spark and maintain stock market rallies: falling interest rates and rising corporate profits.

Most analysts agree with Balog that interest rates are unlikely to fall much farther.

But there are two schools of thought on the future of the economy and its impact on stock prices.

Experts like Melone and Hinkle foresee an improvement in the overall economy.

"I'm not looking for an explosion," said Melone. "The economy will grow at a 4 percent annual rate compared with a 2 percent rate."

He said that will be fast enough to boost corporate profits without putting pressure on interest rates.

Balog, on the other hand, said he does not anticipate the economic growth that other analysts foresee. The declining dollar eventually will help export-oriented industries, he said. But the initial effect will be inflationary as import prices rise, he said. Already some Japanese automobile and semiconductor manufacturers have raised their U.S. prices because of the falling value of the dollar.

Balog conceded that the high-tech industries could provide the source of renewed economic growth. But, he said, more traditional sources of economic growth -- the capital goods industries and the consumer -- are unlikely to provide much impetus to economic growth in 1986.

The consumer already is overburdened with debt and is unlikely to boost spending substantially. Most industries already have more production capacity than they need and are unlikely to order up more machine tools and build more plants.

But there is one potential source of stock market buying that has not yet been heard from: the individual investor. Although individuals have been buying mutual funds -- which pool investor money to buy stocks -- they have not been buying individual stocks in large quantities.

"Individual investors are generally late to rallies. If they join this one, then it may have some time to go," said a Washington broker.