Several Federal Reserve officials signaled encouragement from a new reading on inflation showing signs that inflation may be moderating, though they stressed that doesn’t mean it’s time to start easing up on the central bank's rate-hiking campaign.

Dallas Fed President Lorie Logan on Thursday called October’s consumer price index data “a welcome relief” but said “there is still a long way to go.” Cleveland Fed President Loretta Mester said October’s CPI report suggests some easing in inflation. San Francisco Fed President Mary Daly called the CPI number "good news," and Philadelphia President Patrick Harker suggested the pace of rate hikes could soon slow.

CPI clocked in still quite hot in October but cooled from previous months. The inflation gauge, excluding volatile food and energy prices (the so-called core reading), rose 0.4% month over month, coming in below expectations of 0.5% and lower than the 0.6% rise seen in both September and August. On an annual basis, core CPI rose 6.3%, compared with 6.6% in September, 6.3% in August and 5.9% in July. The Fed prefers to strip out food and energy prices since they can be so volatile.

“A positive sign is that the three-month changes in underlying inflation measures are lower now than they were in June, although they remain high,” Mester said in a speech Thursday at Princeton University. “On the other hand, services inflation, which tends to be sticky, has not yet shown signs of slowing.”

Mester says she expects inflation to begin to “slow meaningfully” next year and the following year, reaching the Fed’s 2% inflation goal in 2025 – as the Fed’s rate hikes filter through.

The Fed raised interested rates by 75 basis points last week for the fourth straight meeting. Now, Mester says the Fed’s focus is shifting from how quickly the central bank can raise rates to a level that’s “restrictive” — and to determine the appropriate level of restrictiveness that will continue to bring down inflation.

“Given the current level of inflation, its broad-based nature, and its persistence, I believe monetary policy will need to become more restrictive and remain restrictive for a while in order to put inflation on a sustainable downward path to 2%,” Mester said.

Mester said exactly how much higher rates need to rise and how long rates need to remain elevated depends on how much inflation — and inflation expectations — are moving down. That, she says, is contingent on how much demand slows, supply challenges resolve, and price pressures ease.

Daly echoed Mester's sentiments to focus on becoming more restrictive, suggesting a federal funds rate that ends up higher than the 4.6% forecast in September. The federal funds rate currently sits between 3.75% and 4%.