NEW YORK, JAN. 7 -- Stock prices bounced up in late trading today, recovering from some early selling to post their fourth straight advance in 1988.

The Dow Jones average of 30 industrials, down more than 20 points in early trading, closed with a 14.09 gain at 2051.89. That extended its rise in the new year to 113.06 points.

Advancing issues outnumbered declines by about 3 to 2 on the New York Stock Exchange. Big Board volume totaled 175.36 million shares, up from 169.73 million Wednesday.

Analysts said the dollar's fluctuations continued to set the mood for stock traders.

The dollar started the day by rising in the Far East, extending its three-day advance. But after a wave of concerted intervention by major central banks to support the dollar in those three days, skepticism about the banks' strategy took hold later today in European trading, pushing the dollar lower.

The dollar rebounded later in New York. Dealers attributed the gain to a statement by Federal Reserve Board Vice Chairman Manuel Johnson that the recent intervention by central banks should be interpreted as a warning to speculators that betting against the dollar at these low levels is very risky.

The dollar finished in New York trading at 129.45 yen, up slightly from 129.00 yen late Wednesday, and at 1.6550 marks, up from 1.6440.

Stocks encountered some selling early in the session as the dollar pulled back a bit against leading foreign currencies. As the dollar resumed its rally, stock prices rebounded.

"Basically, the stock market is riding the tail of the dollar," said Newton Zinder at Shearson Lehman Bro. Inc.

With its performance this week, the market has stirred some memories of the way it began 1987 with a record run of 13 consecutive up days for the Dow Jones industrial average. Over that span the average climbed 208.52 points and broke 2000 for the first time.

The mood is considerably less exuberant this year, with memories of the drop in October still fresh.

Still, the recent gains have provided support for followers of the so-called "January effect" -- derived from studies showing a historical tendency for the market to rally in the first month of the year, with smaller stocks in particular attracting buyers.

Gainers among the blue chips in today's trading included International Business Machines, up 1/2 at 123 3/8; General Electric, up 1/4 at 47 1/4; General Motors, up 2 at 66 1/4; American Telephone & Telegraph, up 1 at 29 1/4, and Merck, up 2 1/4 at 166 3/4.

The NYSE's composite index of all its listed common stocks added 1.07 to 145.89.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 200.33 million shares.

Standard & Poor's index of 400 industrials rose 2.44 to 302.74, and S&P's 500-stock composite index was up 2.18 at 261.07.