As January goes, so goes the rest of the year. That's been a stock market axiom for decades.

Just as political savants, oracles and farmers have looked at Maine, entrails or woolly caterpillars to predict the future, stock market analysts have assembled a coterie of indicators that purport to predict the course of stock prices.

The so-called January barometer, devised years ago by market analyst Yale Hirsch, has had an uncanny knack for divining the course of the Standard & Poor's index of 500 important stocks. If stock prices rise in January, they will be higher on Dec. 31 than they were on Jan. 1. Similarly, if the S&P index declines in January, it will be lower on New Year's Eve than on the previous New Year's day.

Unfortunately for investors, the January barometer was correct in 1981. The S&P index declined 4.8 percent in January 1981. For the year it was off 9.7 percent.

In 28 of the past 32 years, the January barometer has been right, failing only to predict a bull market in 1966 and bear markets in 1956, 1968 and 1978.

However, as E. F. Hutton's Newton Zinder points out, if a bleak January barometer last year sent believers to the sidelines, they "got hooked in February and March." While the January barometer may tell investors something about the next December, it carries scant clues for the months in between.

Last year, as it turned out, stock prices on average reached their peaks in late April. Investors who cashed in their chips in February lost some profits. Of course, they were better off than someone who bought in April, then sold in September when stock prices hit their lows for the year.

Some investors are so anxious that they cannot wait until Jan. 31 to find out about Dec. 31. They can rely on the First Five Session indicator. It's less reliable than waiting for the full month to unfold, but the five-session indicator usually predicts what will happen during the full month of January.

Again last year, the five-day barometer did the trick. The S&P index declined 2 percent during the first five trading days of 1981. Five-day afficianados cannot be very heartened so far this year. Although only three sessions are under the market's belt, the S&P index is well below its Dec. 31 level.

For investors whose interest is more shortsighted, Lee H. Idleman of Dean Witter Reynolds has developed the Presidential Approval Ratio. According to Dean Witter's research director, the level of public approval "of the president's performance correlates very well with the performance of the stock market."

Last April, for example, when President Reagan carried a 66 percent approval ratio in the AP/NBC News poll, the stock market was near its peak and the Dow Jones industrial average was above the magic 1,000 level. In December, however, when the president's popularity had dipped 20 percentage points, the Dow had fallen nearly as much, about 15 percent.

It used to be that the performance of General Motors stock was a good prognosticator, but no more. Now GM stock tends to hit highs when the rest of the market does and to decline when other stocks do. In the parlance of the economist, the GM indicator is no longer leading, it is coincident.

The Seventh Avenue indicator has fallen into disuse as well. In less tortured times, market forecasters could look to the fashion world. If women's hemlines rose so did stock prices; longer skirt lengths presaged a declining market. Today, as mini skirts coexist with knickers, brokers canceled their subscriptions to Vogue and Harper's Bazaar.

The Hirsch Organization, which publishes the Stock Trader's Almanac, argues that no other indicator can match its January barometer. "What other indicator sports an 87 percent batting average?" it asks.

Why, the most accurate indicator of them all: The Super Bowl indicator. Created by Dean Witter's chief analyst Robert Stovall, it's been wrong only once since the old American Football League and the National Football League began their January tilt back in 1967. That's a 93 percent average on anybody's calculator.

If a team that has its roots in the old NFL wins the Super Bowl (regardless of whether the merged league puts the team in the American or National Conferences), stock prices rise. If an old AFL team wins, it's bad news for stock traders.

Last year, when the Oakland Raiders knocked off the Philadelphia Eagles, knowing investors had sell orders on their brokers' desks the next morning.

This year Wall Street insiders are rooting for San Francisco or Dallas to win Super Bowl XVI. A Cincinnati or San Diego victory would be bad news for stock prices.