Stocks closed mixed on Friday as the S&P 500 (^GSPC) officially entered correction territory to cap off a tough week for markets.

The S&P 500 closed down about 0.5% despite notching gains earlier in the session, while the Dow Jones Industrial Average (^DJI) dropped about 1.2%, or more than 350 points.

The Nasdaq Composite (^IXIC) held on to gains, closing up about 0.4%, as earnings from Amazon (AMZN) and Intel (INTC) eased some concerns around Big Tech. The index entered into a correction earlier this week amid a sell-off fueled by mixed earnings from megacap techs.

On Friday, the Federal Reserve's preferred inflation metric showed prices over the prior month jumped by the most since May while annual price increases continued to cool in September, sharpening the prospects for the central bank to keep interest rates "higher for longer."

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

The "Core" Personal Consumption Expenditures (PCE) Index, which excludes the volatile food and energy categories, showed prices rose 0.3% in September and 3.7% from the prior year, data released by the Commerce Department on Thursday showed. The 0.3% increase in core PCE was driven by categories like cars, prescription drugs, and travel.

On a headline basis, which includes all categories, PCE rose 3.4% over last year and 0.4% month over month. September's annual rise in "core" PCE was the smallest since May 2021 and marks the third straight month prices have increased at a slower annual rate.

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