Wall Street economists are warming to the idea that the Fed may raise interest rates four or more times next year, moving faster than its current forecast.

The Fed has been forecasting three interest rate hikes for 2018, but the it will move even twice because of the sluggish pace of inflation — and until the second half of the year — the sluggish pace of growth. But growth has picked up to the point where there is potential for a three-quarter run of 3 percent growth, something that last happened in 2005.

"I think four times is likely given the juice from the tax cuts," said Mark Zandi, chief economist at Moody's Analytics. "That'll push unemployment below 4 percent and put a lot of pressure on the Fed to normalize rates much more quickly."

The Fed's policymaking committee raised the benchmark short-term federal funds rate by a quarter percentage point to a range of 1.25 to 1.5 percent in December. The Fed raised rates three times this year and five times since it took the rate to zero during the financial crisis.

Stock strategists, meanwhile, say an unexpectedly aggressive Fed could be one of the biggest headwinds for stocks in the coming year if the economy does not also keep up its growth pace. Economists surveyed in the CNBC/Moody's Analytics rapid update see an average 2.7 percent average growth for the fourth quarter, and Zandi said growth could continue in the high 2 percent range next year.

"It's not that the Fed could get too aggressive. It's that the market didn't price it in," said Diane Swonk, CEO of DS Economics. "The market has gone beyond anything that is ." She said the stock market has been riding high on a boost from the tax bill, which cuts corporate taxes to 21 percent from 35 percent.

John Briggs, head of strategy at NatWest Markets, said he is expecting four hikes in 2018 because of a continued strong economy and labor market, but the market is lagging with just three hikes expected for 2018. "The market will need evidence inflation is improving again to get to price in four," he said, adding that the Fed could change its outlook for interest rates at its March meeting.

The March meeting would be the first chaired by Jerome Powell, incoming Fed chair, who replaces Janet Yellen when her term ends in early February. While Powell's views are seen as somewhat similar to those of Yellen, the overall Federal Reserve board could seem a bit more hawkish than the current group.

"It depends on who actually gets nominated, but someone like [Trump appointee Marvin] Goodfriend, he's an inflation targeter, so if [inflation] is still low, he'll be on the other side," said Swonk. "It's hard to pin him down as a hawk or a dove."

Powell has been a Fed governor, but he is not an economist. "He'll be relying more on the staffers for an outlook on inflation," she said.

Other new members include Randal Quarles, who joined the board in October as vice chair for supervision. The Richmond Fed also recently appointed Thomas Barkin as president.

Economists agree that the Fed succeeded in meeting the employment goal of its dual mandate but inflation remains a wild card.

Briggs said he expects inflation to reach the Fed's 2 percent target by the end of 2018. "That supports the gradual removal of accommodation and the Fed returning to neutral policy rates," he noted.

But Joseph LaVorgna, chief economist for the Americas at Natixis, does not agree the Fed could speed up rate hikes, and he sees just two rate hikes next year.

"They're not going to go four times," said LaVorgna. "One reason is there's no inflation, and secondly, I don't think there's going to be inflation because most of the growth next year is going to be business spending."

LaVorgna said he is watching the release of Wednesday's FOMC meeting minutes because of Yellen's recent comments about inflation. "She spoke out about how there might be noncyclical factors suppressing inflation. Yellen, now that she's leaving, is being more open about what she thinks about the world," he said.