An article in yesterday's Business section, relying on a wire service report, erroneously reported that General Motors Corp. stock's closing price Monday, 82 3/4, was a record. It was GM's highest close in nearly 20 years, but its highest, 112 5/8, was on Oct. 27, 1965.

Stock prices soared yesterday in heavy trading, although analysts said there was no specific explanation for the Inauguration Day rally.

The Dow Jones average of 30 industrial stocks, the most widely followed index of stock market performance, soared 34.01 points to close at 1,261.37. It was the biggest one-day gain in the Dow average since Dec. 18 and its highest close in more than a year. The Dow closed at 1,266.02 on Jan. 19, 1984.

Jerry Hinkle, chief trader at the brokerage firm Sanford C. Bernstein & Co., said the stock market took off "like a banshee" yesterday, but said he could detect no catalyst for the performance.

Brokers said there was no single news event that triggered the buying spree and that there was nothing remarkable in President Reagan's inaugural speech, delivered after his public oath-taking in the Capitol Rotunda.

Hinkle attributed the surge to optimism over the economy, inflation and interest rates.

Most analysts think that economic growth will regain some of the momentum it lost in the last half of 1984, but that the economy will grow at a "sustainable" pace -- fast enough to continue to create jobs but not so fast that it will create new inflationary pressures.

Stock prices rose steadily from the opening bell to almost the close -- when analysts said there was some selling to realize profits.

The stock price surge was widespread, although the types of big blue-chip industrial companies that make up the Dow index did better than the overall New York Stock Exchange index. The 34.01-point rise in the Dow index was a 2.8 percent gain, while the NYSE index climbed 2.1 percent -- from 99.04 to 101.12. Trading was heavy, with 146.83 million shares changing on the New York exchange yesterday, compared with 104.7 million on Friday.

More than 1,320 NYSE stocks closed higher, while only 372 closed lower. According to NYSE data, 230 stocks reached new highs, while only four stocks were at record lows.

General Motors Corp., the world's largest automobile producer closed at an all-time high of $82.75 a share, up $2.375 from its Friday close. International Business Machines closed at $128.25, up $4.125 from Friday.

The American Stock Exchange market value index climbed 4.60 points to 215.69 -- a 2.2 percent rise. Stocks that gained in price outnumbered those that lost ground by 461 to 151 on the Amex. More than 11.3 million shares were traded yesterday, compared with slightly more than 9 million on Friday.

Yesterday's blistering stock performance defied a condition technical analysts call "overbought." When the market is overbought, stock prices have risen too long without a normal, sometimes temporary decline -- in which the lure of taking profits entices enough investors to sell to trigger a drop in prices for a few days.

In addition, analysts said, the way trading has developed in recent months, prices have generally stopped rising when the Dow average reached 1,250. But yesterday, Sanford C. Bernstein's Hinkle said, there was no "resistance" at all. The Dow moved through 1,250 without faltering.

Robert Stovall, senior vice president of the securities firm Dean Witter Reynolds, said the sharp climb in the Dow average represents a catchup of the big industrial stocks with the performance of the rest of the stock market.

Standard & Poor's 500-stock composite index gained 3.91 points to 175.23, while S&P's index of 400 industrials rose 4.88 points to 196.13.

The Nasdaq composite index for the over-the-counter market picked up 3.36 points to 266.41.