Emanuel said he still expects volatile swings, and he doesn't believe the correction that began in late January is over just yet. The Fed meeting could resolve some issues, such as whether the futures market is correct in pricing in just three rate hikes, rather than a fourth as some economists now expect.
Other issues have also concerned the markets, including the tariffs President Donald Trump imposed on steel and aluminum this past week. But the market shook off some of its concerns when he exempted Canada and Mexico for now.
"How does the trade friction unfold? That story is not going away. For us it's an open question," Emanuel said. "… But what we would say is it's very encouraging when you look at the tape. The rally appears to be broadening out into the more cyclical sectors, like financial, energy, materials and industrials," he said.
Emanuel said the ISM manufacturing data in the past week was a sign the bull market can continue to run on, based on history. ISM rose to 60.8 for February, well above the 50 level that signals expansion.
After the ISM crosses 60, as it also did last September, the stock market on average has not peaked for 28 months, according to data going back to 1954. Emanuel also said on average there was no recession for 41 months.
With few earnings in the coming week, investor focus will turn to economic data. The most important are the inflation reports — particularly the consumer price index Tuesday but also producer prices Wednesday. That data should provide the most clues about inflation ahead of the Fed's March 20 and 21 meeting. There is also retail sales for February on Wednesday.
"After having a week full of contradictory Fed speak, we'll be glued to the inflation data because this is a Fed that feels like it wants to raise rates more than consensus. The good news was the jobs report. The February numbers put aside runaway inflation fears," said Art Hogan, chief market strategist at B. Riley FBR.
Stocks soared Friday after February's jobs report showed that hiring was surprisingly strong, with 313,000 jobs added, but wage growth remained tepid,which was a positive since it means there's no inflationary pressure to push the Fed to raise interest rates any faster than currently expected.
Stocks had sold off in February as interest rates spiked on concerns inflation would push the Fed faster than the three interest rate hikes it currently forecasts for this year. The Fed is expected to raise interest rates on March 21, and it will also release new interest rate and economic forecasts that day. That could be when the market is put to the test.
"This is an untested Fed. … Optically, it looks more hawkish than it did last year," said Hogan.
The Nasdaq jumped 1.8 percent Friday, regaining its all-time high to close at a new record of 7,560. The Dow, just under 5 percent away from its all-time high, gained 1.8 percent Friday and 3.3 percent for the week, to 25,335. The S&P 500 gained 3.5 percent for the week to 2,786, and is 3 percent below its all-time high.