The energy sector was the hardest hit on the S&P 500, and Caterpillar, Chevron and Exxon Mobil all closed in the red.
The "perception is that oil has found a bottom, not that it won't still fluctuate," said Peter Cardillo, chief market economist at Rockwell Global Capital. He said oil should stay within a $45 to $55 range for now.
Read MoreOil whipsawed on supply glut
Wednesday's performance could indicate that nonenergy equities are set to perform well, some analysts said.
"U.S. companies that have just gone through the economic crisis have really cleaned up their act to become more profitable in the last two years," said Phil Quartuccio, CEO of Illustro Trading. "As an investor, I only see an upside."
Disney jumped as much as 8 percent on Wednesday to a new high following a blowout earnings report after the bell Tuesday. Consumer discretionary also led gains on the S&P.
Economic data out on Thursday include the Challenger Job-Cut report at 7:30 a.m., international trade figures at 8:30 a.m., weekly jobless claims at 8:30 a.m., productivity and costs at 8:30 a.m. and natural gas inventories at 10:30 a.m.
Outside of major beats or misses, the reports are secondary to Friday's highly anticipated nonfarm payrolls number and employment data.
A large number of companies will report on Thursday in the tail end of the earnings season, including Philip Morris before the bell and Twitter after the bell.
However, analysts said that earnings would likely make little impact as the bulk of companies have already reported and set the tone for this season.
"The feeling is lots of companies have come in below expectations," said Robert Pavlik, chief market strategist at Banyan Partners. We'll have "more of the same until we get out of this earnings season and we can focus on an improving economy."
And with the economy comes questions about signals the Federal Reserve may use to determine the timing of an interest rate hike.
The Cleveland Federal Reserve's president, Loretta Mester, a nonvoting member of the Fed, said on Wednesday that the U.S. economy is on course for a rate hike by June.
Roberts said the rate hike comments from Mester and other Fed speakers over the past two days were tests for market reaction ahead of an actual interest rate raise.
Read MoreBuffett: Fed rate hike not feasible
The U.S. 10-year yield continued to recover from Monday's lows but leveled off just under 1.80 percent. With those movements, analysts said they preferred equities as they weren't certain if the yield moves were from foreign inflows or a reflection of the U.S. economy.