Hotter-than-expected inflation readings have some Fed officials describing the path down to their 2% inflation target as "bumpy."

New data due out Thursday morning will determine whether that picture is about to get bumpier.

Economists expect the Fed's preferred inflation measure — the "core" Personal Consumption Expenditures (PCE) Index that excludes volatile food and energy prices — will clock in at 2.8% for the month of January on a year-over-year basis.

That would be a hair lower than the 2.9% year-over-year increase registered in December. But the month-over-month increase expected by economists is 0.4%, up from the 0.2% seen in December.

That could stoke fears that inflation is not moving down quickly enough. It could also bring the six-month and three-month annualized inflation numbers back above the Fed’s 2% target, according to Bank of America.

The new PCE reading is important for investors as they try to determine how quickly the central bank will begin loosening its monetary policy following the most aggressive campaign to cool inflation since the 1980s.

Markets began the year betting on six cuts starting in March, only to revert to three cuts starting in June following cautious commentary from Fed Chair Jerome Powell and a bevy of other Fed officials, along with higher-than-expected readings on inflation.

Read more: What the Fed rate decision means for bank accounts, CDs, loans, and credit cards

The Consumer Price Index (CPI) in January was hotter than economists expected, as was the Producer Price Index (PPI), which tracks the prices businesses pay to manufacture products and services.

Because there is a correlation between PPI and PCE, "there is a risk" that PCE "does come out higher" when the number is released this Thursday, according to Wilmer Stith, bond portfolio manager for Wilmington Trust.

If the PCE number is indeed high and US jobs numbers continue to outperform expectations, it’s possible the Fed could decide to keep rates higher for longer, Stith added.

"I don't think they're going to raise rates," he said. "[But] maybe the Fed walks it back a little bit to two cuts instead of three."

Several Fed officials last week cited the recent inflation data as evidence that the path down to 2% is going to be "bumpy," with both Fed vice chair Philip Jefferson and Fed vice chair for supervision Michael Barr using that exact word.

Fed governor Chris Waller raised the question of whether the January data was a more serious "pothole," emphasizing the central bank should take its time when it comes to rate cuts.