President Donald Trump's attempt to fire Federal Reserve Governor Lisa Cook is unlikely to affect the U.S. central bank's path toward cutting interest rates next month, but it creates new uncertainties about what happens after that meeting amid the unprecedented attack on the Fed's independence.

"The combination of stronger core and softer headline readings has left some traders struggling for direction," said Daniela Sabin Hathorn, senior market analyst at Capital.com. "There is a reason to be both bullish and bearish depending on which CPI reading you wish to focus on.