Investors have become very dependent on the Federal Reserve, but once macroeconomic issues improve, the central bank will become much less important to the stock market, said Bob Doll, chief equity strategist at Nuveen Asset Management.
He also thinks the Fed may move toward the exit of its bond-buying program perhaps a little sooner than expected.
"Watch GDP, watch weekly unemployment claims, watch monthly jobs numbers and most importantly watch earnings. And if they're OK, the Fed will continue to recede in importance," Doll said Thursday on CNBC's " Street Signs ."
The dependence on "every word that came out of the Fed's mouth" was understandable, he added, since "we were in unchartered waters."
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However, on Wednesday the Fed released the minutes from its last meeting, which showed some central bank officials want a "relatively prompt" rate hike. Despite that news, U.S. stocks mostly climbed higher.
"As long as inflation is contained, a better economy, coupled with marginally and slowly rising rates is not bad news at all for the stock market," he said.
-By CNBC's Michelle Fox