President Donald Trump's growing criticisms of the Federal Reserve will not sway the U.S. central bank from its gradual path of rate hikes, analysts say.

Trump has slammed the Fed for three straight days, arguing that its rate increases could put economic growth at risk. He sharpened that criticism Oct. 10, saying the Fed "has gone crazy" and later telling Fox News that the central bank is "going wild" and "going loco."

The comments came amid a steep drop in the equities markets, with the Dow Jones Industrial Average falling about 3% on Oct. 10 and continuing its decline Oct. 11. Trump told reporters at the White House that the stock market moves were a "correction that I think is caused by the Fed and interest rates," according to CNBC.

But Fed officials will likely continue along their path of raising interest rates to more normal levels in the coming months.

Kansas City Fed President Esther George, for example, said in an Oct. 11 speech that the Fed's "gradual normalization of policy seems appropriate to me," given that the central bank has largely achieved its goal of ensuring full employment and stable prices. The Fed is expected to raise its benchmark federal funds rate in December and has signaled it would continue hiking rates in 2019.

A day earlier, two Fed officials said they were not overly worried about the stock market selloff. Atlanta Fed President Raphael Bostic said he "won't let a stock market move on its own reshape my view of the economy," while Chicago Fed President Charles Evans said financial stability conditions remain "reasonably moderate," according to Bloomberg News.

Some analysts agree that the Fed is likely to blame for the current stock market woes.

Ryan Sweet, director of real-time economics at Moody's Analytics, said it is not because the Fed is tightening policy too much, as Trump has argued. Rather, it is because the Fed is weaning markets off the forward guidance that has given investors a clearer idea of where the Fed thinks interest rates should be in the future. Yields on 10-year Treasurys have increased significantly in recent days amid the shift in the Fed's language.

"This process was necessary but wasn't going to go perfectly," Sweet wrote in a note to clients. "Still, the economic implications of the recent drop in equity prices are minimal for now, and one could argue that it's more therapeutic than harmful."

Trump is "clearly setting the Fed up to be the scapegoat if the economy weakens," Sweet said, though he also noted that the Fed's gradual rate hikes appear to be giving it a better shot at making sure the economy grows at a sustainable pace.

The president also said Oct. 11 that he would not fire Fed Chairman Jerome Powell but is "just disappointed" in his pick to lead the central bank.

Oliver Ireland, a former Fed lawyer who now works at the law firm Morrison & Foerster, said there is a process that lets the president fire a Fed chief and other Fed governors "for cause."

Though legal scholars may debate the definition of the phrase, the general working assumption among Fed officials is that "disagreement over policy isn't cause," Ireland said. That gives Fed officials the ability to make monetary policy decisions without contemplating retaliation from the president.

"[The Fed] will do what it thinks it ought to do," Ireland said.