Bulls could keep the upper hand in the coming week, even with increasing warning signs that the market could be getting bubbly.
Highlights of the week will be Twitter's stock market debut, and important economic data—third-quarter gross domestic product and October's flukey jobs report, which should show the impact of the government shutdown.
Stocks in the past week were mixed, with the S&P 500 and Dow holding gains, but Nasdaq and Russell 2000 declining. The S&P 500 was up 0.1 percent at 1761, and the Dow 30 up 0.3 percent at 15,615. The Nasdaq lost 0.5 percent to 3,922, and the Russell 2000 was much harder hit, losing 2 percent to 1095.
Stock traders kept an eye on the bond market this past week, as yields on the long end gained after the Federal Reserve delivered a slightly less dovish statement than expected after its meeting Wednesday. The 10-year Treasury was yielding 2.62 percent late Friday, moving higher after hawkish Fed comments, including from Philadelphia Fed President Charles Plosser who told CNBC's Steve Liesman that the Fed's quantitative easing should be capped.
(Read More: Plosser: QE should be capped)
"I think the most important thing investors have to watch is the 10-year Treasury yield, which has created a range of 2.5 percent to 3," said Lindsey Group chief market strategist Peter Boockvar. "We dropped below 2.5 percent for a day or two and now we're right back up here again. If it gets back to 2.75 or north, people will have to ask if the Fed is losing control of the bond market."
Fed speakers are out in force again in the coming week, and Chairman Ben Bernanke participates in an International Monetary Fund panel on the financial crisis Friday with former Treasury Secretary Larry Summers and others. Summers had been in the running to be Bernanke's successor but he did not prove popular with the Senate, and Fed Vice Chair Janet Yellen was nominated instead.
The euro will also be closely watched in the week ahead. The European Central Bank meets Thursday, and there are expectations it could cut its refi rate by a quarter point. The euro already lost 2.3 percent against the dollar in the past week, and was also weaker against the yen.
Traders will also be watching the continued parade of third quarter earnings, with reports expected from media companies Time Warner, CBS and Disney, and a slew of energy companies, likeAnadarko, Marathon, and Chesapeake.
Markets are likely to be frustrated by economic data in the coming week as traders try to distill what impact the government shutdown had on the economy. The October jobs report is expected to show 125,000 nonfarm payrolls Friday, but economists concede their forecasts could be way off.
Barclays chief U.S. economist Dean Maki expects the unemployment rate to rise by 0.3 percent to 7.5 percent, and he is looking for 125,000 new jobs. Economists expect the impact of the shutdown to reverse in November so that report will also be difficult to read.
"That number is 25,000 below where we would otherwise put it because of the shutdown…We expect some private sector contractors to have experienced layoffs," Maki said.
(Read more: Bond market throws 'taper tantrum')
Fresh ISM Manufacturing data Friday was much better-than-expected, coming in at 56.4, the highest level since April, 2011. "The thing we're not seeing in the data is much effect from the government shutdown. We do think it will have some effect on GDP growth but it's the government line, not so much spreading to the rest of the economy," Maki said.
He also said ISM showed some improvement in export orders, a possible sign of recovery in Europe, he added.
Thursday's third-quarter GDP report is expected to show growth up 1.9 percent.
"We're looking for 2 percent GDP growth and that was pre-shutdown. That growth continued to be moderate through the third quarter," said Maki. The government was shut down for 16 days after Congress failed to pass a spending resolution by Oct. 1.
Pimco's Bill Gross and BlackRock's Larry Fink were on the same side this past week, both warning that the markets look a bit bubbly. But market analysts expected to see continued gains into the end of the year, even with the S&P 500 up 23.5 percent year-to-date.
Bob Doll, chief U.S. equity strategist at Nuveen Asset Management, said he sees stocks continuing to rise as long as the Fed continues to ease.
(Read More: This might be a scary sign for market - or not)
"They will start tapering when the economy permits them to taper. It's more about conditions than the time frame," he said. "As an equity investor, if the economy doesn't strengthen I'm going to have the Fed helping me along."
He said paring back the $85 billion bond purchase program should not hurt the market since the economy should be improving when the Fed takes that step. Expectations for when the Fed will slow its bond purchases have flip-flopped. Many Fed watchers had expected the central bank to move in March or later, but its statement this week now has some expecting a December timetable.
As for the stock market, "It's looking a little tired, time for a rest, but a rest in a bull market is probably sideways for a while," Doll said. "I'm not even sure we're going to get a pullback. The near-term and long-term direction of the market remains up. Pullbacks worth playing usually come from monetary tightening, rising oil prices or geopolitical events."
(Read More: Cramer's game plan: Market a Twitter next week)
Doll said the market can rise but it will not take off significantly until there is evidence of real earnings and revenue growth. "I think the driver in stocks has been more P/Es than it's been earnings, and P/Es have come up courtesy of crossing out some of the uncertainty and central banks," he said.
The S&P's price to earnings ratio has moved above the average 15.8 level, above 16, but Doll said that is not a concern yet. "To me, it's all about, tell me what corporate earnings are going to look like in 2014…but nobody knows the answer to that," he said.
A number of analysts have been warning that earnings expectations appear too high for 2014, and that could cause problems for the market at some point next year.
Doll said the Twitter initial public offering is important for the market. Twitter prices Wednesday and starts trading Thursday on the New York Stock Exchange. The offering is indicated to price between $17 and $20, and some analysts are already setting price targets way higher.
(Read More: Twitter's mysterious outside shareholder)
Twitter is taking a more conservative approach than social media rival Facebook when it came to market last year. Facebook's offering was surrounded by hype and its stock traded below its offer price for months.
"The market conditions are much more conducive for this IPO for sure, but the pricing is very different too. They're not trying to get every nickel out of this that they can," Doll said. "The management of Twitter is very aware of that. Leave some of it. Don't take it all. It will help you in the long run."
What to Watch
10 am Durable goods, factory orders
11:40 am Fed Gov. Jerome Powell
4 pm Boston Fed President Eric Rosengren
9 pm Dallas Fed President Richard Fisher
Earnings: DirecTV, Nissan, Delphi Automotive, Michael Kors, Liberty Media, Tesla Motors, AOL, CVS Caremark, Becton Dickinson, T-Mobile, Intercontinental Exchange, Host Hotels, HCA, Liberty Interactive, Zillow, Live Nation, Sturm Roger, 21st Century Fox, Och-Ziff, Red Robin Gourmet Burgers, Rowan Cos
10 am ISM non-manufacturing
Noon Richmond Fed President Jeffrey Lacker
Twitter IPO prices
Earnings: Toyota Motors, Ralph Lauren, Time Warner, Whole Foods, CBS, Icahn Enterprises, Chesapeake Energy, Activision Blizzard, Mondelez International, Prudential Financial, Transocean, ING U.S., Marsh and McLennan, Molson Coors, Humana, Hospira, Holly Frontier, Qualcomm, Vale, Solera, Carlyle Group, Duke Energy
7 am Mortgage applications
7:30 am Challenger layoffs
10 am Leading indicators (September)
10:30 am Oil inventories
Earnings: Disney, Priceline.com, Groupon, AMC Networks, Wendy's, Scripps Networks, International Game Tech, Arcelor Mittal, Apache, Beazer Homes, Nvidia, Sprouts Farmers Market, CareFusion, Great Plains Energy, Annie's
8:30 am Jobless claims, Real GDP Q3
8:30 am Productivity and costs
1:50 pm Fed Gov. Jeremy Stein
Earnings: Brookfield Asset Management, Nippon Telegraph, Leap Wireless, Aqua America, Covidien, Nippon Telegraph, Telefonica, Tesoro Logistics
8:30 am Employment report (October), personal income and spending (September)
9:55 am University of Michigan consumer sentiment
Noon Atlanta Fed President Dennis Lockhart
3:30 pm Fed Chairman Ben Bernanke on panel with Larry Summers, Stanley Fischer, Kenneth Rogoff at IMF conference
4 pm San Francisco Fed President John Williams
—By CNBC's Patti Domm. Follow here on Twitter @pattidomm.