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One thing Yellen could say that would worry markets

If Janet Yellen stops using weather as an excuse for a soggy economy, watch out.

Yellen testifies before the Senate Banking Committee on Thursday at 10 a.m. EST, in her second economic testimony before Congress this month. Her first was before the House Finance Committee on Feb. 11, and she said at the time that it's unclear why the employment reports were so weak, but weather could certainly be a factor.

She also made it clear the Fed would continue on a course to taper back its $65 billion-a-month bond-buying program, unless there was a notable change in the economy, so traders expect another cut of $10 billion when the Fed meets in March.

By then, the Fed will have plenty more data to review, including February jobs, but that report could be hit by weather as well.

"I'm sure she's going to be asked about that because in between her testimonies, we've only gotten more and more weather-depressed data, so it's become more of an issue," said Tom Simons, money market economist at Jefferies.

Even on Wednesday, mixed data showed the potential for more than just weather impact, with mortgage applications at a 20-year low, but new home sales better than expected.

Yellen is expected to stick to the same opening remarks she made before the House, but the questioning is certain to be different. There could also be more focus on banking regulation and "too big to fail" institutions. Senate Banking is chaired by Tim Johnson, D-S.D., and its members include Sens. Bob Corker, R-Tenn., and Elizabeth Warren, D-Mass.

But it's unlikely Yellen will leap to any conclusions about the weather impact.

Diane Swonk, chief economist at Mesirow Financial, said housing is one part of the economy that could come up in the question and answer session. It's also one area that the Fed has been credited with helping with its programs to keep interest rates low.

Swonk said she's personally concerned the batch of bad housing data are signaling a more structural problem than just weather effect.

Yellen, however, is unlikely to be definitive. "I think right now the Fed is playing it close to the vest. There's some movement away from 'it's just the weather alone' right now, but it's in her interest to just play it close to the vest and not be too different than two weeks ago," Swonk said.

"She will have to address the transitory nature of what we're seeing. I can't imagine she is going to try to move markets. Right now, they've got to stick to the story. They have a press conference in March. They have the ability to change the forecast, an ability to change their communications," Swonk said.

The Fed has said it will consider altering short-term rates when unemployment reaches 6.5 percent. It was at 6.6 percent in January, and the Fed also has a problem in that it communicated a specific rate that might soon be overtaken.

Fed officials have said that level is a target, not a trigger for action, but it remains a point of interest by the markets.

Swonk said there is talk the Fed could drop the idea of using a specific numerical target and move to "nuance."

(Read more: Kudlow: Janet Yellen's problem)

Simons also says Yellen will veer away from providing much more insight into what she thinks may be going on in the economy.

"I think part of that is that opinion is central to forming expectations for policy at this point. She is so careful about communications. She understands the weight the Fed chairman's words have all the time. She wouldn't want to do something that would unilaterally say something about policy," Simons said.

"She knows the signal to the market is much more important coming from her mouth. I expect if she's asked about the weather, she'll say something to the effect of 'We don't know, but our forecasts suggest things are going to get better.' "

Janet Yellen, chair of the Federal Reserve.
Getty Images
Janet Yellen, chair of the Federal Reserve.

Tony Crescenzi, senior portfolio manager at Pimco, said Yellen has said the improvements to the labor market were far from complete, a sign the Fed is still far from adjusting short-term rates.

"Given the view on the labor market that the recovery's far from complete, given the view on inflation that it won't even bet at target for years, one gets the very strong impression that the Fed will be very patient about removing its monetary accommodations. The tapering's not even on a preset course," said Crescenzi.

(Read more: Lower taxes if you want to create jobs: Rep Ryan)

"The minutes seem to suggest and public speeches suggest that the bar for changing the pace of tapering is very high. The statement from January made that clear as well. The statement had the upgrade in the assessment of economic growth despite the weak data and despite the market volatility in emerging markets," said Crescenzi.

When the Fed reviews data at its next meeting, it would certainly see a weaker picture than last time.

"The bond market is leaning a little more toward maybe it's not the weather idea but not much," Crescenzi said. The 10-year yield has stayed in a range of 2.5 percent to 3 percent for eight months. "It's been very tight. Right smack in the middle. The cloudiness over the outlook is what suppressed interest rate volatility because investors don't know which way it will go," he said.

(Read more: In Yellen's words, small hints will matter big-time)

Stocks were slightly higher Wednesday, with the S&P 500 bumping up against its all-time high.

"I think if listeners are expecting her to back off her tapering attack as a result of the economy, I would be very surprised if she would change her policy as a result of what's going on ... and I think the stock market is OK with it," said Jack Ablin, CIO of BMO Private Bank. Ablin said it appears the Fed wants to get past quantitative easing as quickly as possible.

"If you look at the inflation expectations around each quantitative easing announcement, the last one they did was actually accompanied by a reduction in inflation expectations so from their perspective ... QE3 really didn't work at least from what they're trying to accomplish. I think they'll try to get off the stage as fast as possible," Ablin said.

The stock market has digested the idea of Fed tapering and is taking it in stride even with expectations for higher interest rates.

(Watch: Why Yellen's testimony could be a 'non-event')

"I'm just keeping my fingers crossed that the weather warms up, and the economy will heat up and so will sales," said Ablin.

Besides Yellen's testimony, markets will be watching durable goods orders and jobless claims, both at 8:30 a.m. EST.

There are also earnings from Best Buy, Wendy's, AMC Networks, Windstream, Rowan, Ocwen and Mylan, before the bell. Gap, Monster Beverage, Salesforce.com, Decker's Outdoor, Sotheby's, Nimble Storage, Southwestern Energy, Sprouts Farmers Market and Splunk report after the market close.

—By CNBC's Patti Domm. Follow her on Twitter @pattidomm.

  • Patti Domm

    Patti Domm is CNBC Executive Editor, News, responsible for news coverage of the markets and economy.

  • A CNBC reporter since 1990, Bob Pisani covers Wall Street from the floor of the New York Stock Exchange.

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  • JeeYeon Park is a writer for CNBC.com. Follow her on Twitter: @JeeYeonParkCNBC

  • Rick Santelli joined CNBC Business News as an on-air editor in 1999, reporting live from the floor of the Chicago Board of Trade.

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