* Jobless claims lowest in almost 15 years
* Alibaba shares tumble after results, Yahoo follows
* Indexes up: Dow 1.19 pct, S&P 0.91 pct, Nasdaq 0.91 pct (Updates with market moves, comments)
By Sinead Carew
NEW YORK, Jan 29 (Reuters) - U.S. stocks were up in a volatile session on Thursday, helped by firmer oil prices, even as mixed corporate news and confusion over U.S. monetary policy left investors anxious about which way to turn.
The S&P 500 index was up 0.9 percent in the afternoon after a decline of as much as 0.6 percent earlier in the session and oil futures turned positive on a day when strong job market data contrasted with disappointing reports from Alibaba and Qualcomm.
The market has been advancing and retreating within a range of 200 to 300 points for some time as traders grapple with good and bad earnings reports, a strong dollar and weak oil prices and uncertainty about when U.S. interest rates will rise, said Dennis Dick, head of markets structure at Bright Trading LLC.
"It's technical bounces is what it is. There's a lot technical trading going on," he said. "When the fundamentals are confusing and the macro is confusing, you have to lean on the technicals."
Harman International shares rose 22 percent to $123.52, making it the biggest gainer in the S&P on Thursday after it beat profit and revenue expectations.
Coach Inc shares rose 6 percent to $38.81 after the handbag maker posted a better-than-expected quarterly profit. McDonald's added 5 percent to $93.23 after it said Chief Executive Don Thompson would leave at the end of February.
But shares in Chinese internet giant Alibaba Group dropped 9 percent to $89.67 after revenue missed expectations, which also pushed down shares in part-owner Yahoo.
Qualcomm fell 10 percent to $63.84, after trimming its 2015 outlook and warning that its newest chip will not be in a major customer's phone.
"We're looking at the big household names that put out disappointing numbers this week and we're putting undue influence on that," said Art Hogan, chief market strategist at Wunderlich Securities in New York.
The Dow Jones industrial average rose 204.57 points, or 1.19 percent, to 17,395.94, the S&P 500 gained 18.12 points, or 0.91 percent, to 2,020.28 and the Nasdaq Composite added 42.30 points, or 0.91 percent, to 4,680.30.
Supporting stocks, data showed weekly applications for unemployment insurance fell to their lowest in almost 15 years, adding to bullish signals on the labor market.
Investors also continued to digest Wednesday's Federal Reserve statement, which reiterated confidence in the U.S. economy but referred to international developments, making some investors worry that rates could rise later than expected.
The energy sector turned slightly higher with U.S. crude oil turning around to settle up 8 cents at $44.53. The sector had fallen almost 2 percent earlier.
Advancing issues outnumbered declining ones on the NYSE by 1,837 to 1,216, for a 1.51-to-1 ratio; on the Nasdaq, 1,650 issues rose and 1,046 fell for a 1.58-to-1 ratio.
The S&P 500 was posting 13 new 52-week highs and 26 lows; the Nasdaq Composite was recording 32 new highs and 100 lows. (Additional reporting by Rodrigo Campos; Editing by Bernadette Baum and Nick Zieminski)