NEW YORK, JAN. 4 -- Inspired by a rallying dollar, the stock market greeted 1988 with a burst of enthusiasm today as prices surged broadly in robust trading.

The Dow Jones industrial average of 30 leading stocks advanced 76.42 points to close at 2015.25, posting the fourth-largest one-day point gain on record.

Many traders and analysts attributed the market's strength to firmness in the dollar caused by unusually strong intervention by U.S. and foreign central bankers. They also said that stock prices were buoyed by technical factors such as the impact on investors of the start of a new tax year. A moderate amount of computer-assisted program trading also played a role, they said.

The day's rally began promptly at the opening bell and advanced virtually without interruption until the close. About 182 million shares changed hands at the New York Stock Exchange, a large number by historical standards but moderate compared with the frenzied trading that sometimes has occurred since the Oct. 19 market collapse.

"I think it's a great way to start the new year and the first installment on a pattern that will prevail for the year as a whole," predicted Joseph J. McAlinden, director of research at the large Wall Street firm of Dillon, Read & Co., reflecting a seemingly widespread optimism about the day's market performance.

McAlinden added that he expects the historically weak level of the dollar to fuel exports by American companies in the first months of 1988, boosting corporate earnings and supporting a steady stock market advance.

"The market {late last year} was forecasting a recession that won't occur, at least not in 1988," said Donna Hostetler, director of research at Crowell, Weedon & Co., a Los Angeles-based brokerage. "The consensus now seems to be that we're going to get by without a recession."

Other analysts were more cautious about today's rally. Some noted parallels between the day's advance and similar rallies during the first days of January in previous years. These analysts said that a surge in prices at the beginning of a new year reflects active "recovery" buying by investors who sold stocks late in December in order to obtain tax losses.

Several professional investors acknowledged today that they were buying stocks in the day-long rally because they had sold stocks heavily in December for tax reasons. "I know it's a factor because I'm doing it," one professional investor said.

Another factor in January stock market rallies is that allocation of new money for investment at major institutions often occurs at the beginning of the calendar year. The availability of new money often leads to broad stock buying.

"There has sometimes been reinvestment demand in past Januarys -- different kinds of investors get new monies to reinvest at the beginning of the year," said Richard McCabe, a market analyst at Merrill Lynch & Co. "But I think the more important mechanical factor is that there's often a lot of selling done in December for bookkeeping reasons, and then you get the reverse" in early January.

Several traders said that a rally in stock prices, if sustained for several days, could unleash an unexpected market surge because many institutional investors have huge amounts of cash on hand with which to buy stocks. Those cash inventories were accumulated in the aftermath of Oct. 19, when fear and uncertainty gripped market participants large and small.

The Dreyfus Fund, for example, a $2.4 billion mutual fund, has about 30 percent of its assets in cash -- or about $720 million, an unusually high amount, according to a fund spokesman.

The market's updraft today carried every major index higher. The Standard & Poor's 500 stock index rose 8.86 to 255.95, and the broad NYSE composite index surged 4.67 to close at 142.90.