The latest Consumer Price Index (CPI) report out Wednesday showed that housing costs accelerated in October, posing a lingering challenge to the Federal Reserve's inflation fight.

Data from the Bureau of Labor Statistics showed shelter costs, the largest component of CPI, ticked up 0.4% compared to the previous month in October. This was higher than September’s 0.2% increase and accounted for over half of October's overall monthly increase. On an annual basis, shelter costs rose 4.9% in October, matching September’s year-over-year gain of 4.9%.

"Falling inflation hit a snag in October, with the usual culprits — rising shelter and food costs — joined by higher used vehicles prices," Robert Frick, corporate economist with Navy Federal Credit Union, wrote in a note after the release. "Given food, transportation and shelter are the top three pain points for consumers, this report didn’t ease the burden of high prices."

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Economists have been long anticipating a slowdown in rent increases, which has been reflected in other data, but a widespread cooldown in rents hasn’t yet shown up in the CPI report. The discrepancy can be partly explained by how the BLS collects rent data every six months, which causes a lag.

"Shelter inflation seems to have become a bit noisier over the last two years following methodology shifts, meaning any single datapoint is harder to read too much into. Like broader inflation, shelter appears to be seeing slower progress as of late," Josh Jamner, investment strategy analyst at ClearBridge Investments, wrote after the release.

"However, the destination for shelter inflation over the next few months still seems to be lower given observed market prices and the well-known lags incorporated into the shelter CPI calculation.”

According to the BLS report, rents increased 0.3% in October from the previous month, unchanged from September’s 0.3% increase.

Owners' equivalent rent showed a slight acceleration, rising 0.4% for the month, up from September’s 0.3% gain. Owners' equivalent rent is the estimated rent a homeowner would pay if they were renting their own property.

Broadly, inflation rose 0.2% over the prior month in October, unchanged from the increase seen in September and in line with economists' estimates.

"Given the outsized importance of rental inflation, shelter costs need to resume more moderate increases in the coming months to keep inflation in line with the ultimate 2% goal," Nationwide chief economist Kathy Bostjancic wrote after the data release.