The S&P 500 gained 0.88 percent Thursday to close at 2,013, ending above the psychologically key level of 2,000 for the first time since Aug. 20 and above its 50-day moving average for the first time since Aug. 18. The index is on pace for its best week since Oct. 24, 2014, when it gained 4.12 percent.
The Dow Jones industrial average gained more than 0.8 percent to close above 17,000, another notable level, for the first time since Aug. 19.
"I think the market psychology tomorrow will be driven by the same things (that they have been) for the last seven years. That's the Fed governors," said Michael Farr, president and CEO of Farr, Miller & Washington. "They've got to sound resolved. They've got to sound like they've got to do something and then they've got to do it."
The next Fed meeting is the last week of October.
The Fed minutes said policymakers don't expect to reach their 2 percent inflation goal before the end of 2018.
"Participants anticipated that recent global developments would likely put further downward pressure on inflation in the near term; compared with their previous forecasts, more now saw the risks to inflation as tilted to the downside," the September minutes said.
"But participants still expected that, as the labor market continued to improve and the transitory effects of declines in energy and non-oil import prices dissipated, inflation would rise gradually toward 2 percent over the medium term."
Michael Block, chief strategist at Rhino Trading Partners, said the positive market reaction Thursday was surprising given the sharp decline after the Fed decided not to raise rates at its September meeting.
"Someone needs to explain to me what's changed," he said, noting that the Fed is "doing a terrible job communicating."
Friday brings more Fed speakers: Fed Vice Chair William Dudley is slated to give an interview on CNBC at 11:00 a.m. ET, and Atlanta Fed's Dennis Lockhart and the Chicago Fed's Charles Evans are separately scheduled to speak during the day.
San Francisco Fed President John Williams told reporters after a scheduled speech late Thursday that the September jobs report did not change the narrative that the U.S. labor market is improving.
"Unfortunately, I expect more of this contradictory balderdash," Rhino Trading's Block noted on Williams' comments.
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Amid the Fed commentary, traders will watch the performance of recently oversold sectors.
Energy rallied nearly 2 percent Thursday for its eighth-straight day of gains, the longest streak since its nine consecutive days of gains in October 2009. For 2015, the sector is down about 13 percent and is the worst performer in the S&P 500.
Oil continued to gain, with crude settling up 3.4 percent, to $49.43 a barrel, its highest close since July 21. Prices will likely take another cue from the weekly oil rig count out Friday afternoon.
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Most analysts are skeptical that the recent gains in oil and energy-related stocks set the foundation for a sharp recovery in the near future.
"Energy is more of a recovery group for the short term," said James Meyer, chief investment officer at Tower Bridge Advisors. "The market's going to churn around a bit, searching for leadership."
"I think the market's getting back to the level, that channel we traded at all year until August. That's pretty heavy resistance," he said, noting stocks could give back some gains Friday after a solid week.
No major earnings are due Friday. JPMorgan kicks off the first big week of the earning season on Tuesday.
Alcoa reported quarterly results after the close Thursday, significantly missing Street expectations on both the top and bottom line. Sales also declined 11 percent from the previous year.
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U.S. import and export price indexes for September are scheduled for release at 8:30 a.m., ET. Wholesale trade for August is due at 10 a.m.