SYDNEY (Reuters) - Asian shares were headed for the first weekly loss in five as the stunning rally in Chinese shares took a breather, although all eyes are on the details of the much-anticipated fiscal stimulus from Beijing this weekend.

Overnight, data showed core U.S. consumer inflation came in at 0.3% in September, slightly hotter than expected, which pointed to stalling progress in the Federal Reserve's fight against inflation. However, high weekly jobless claims figures kept bets that the Fed remains on track to cut interest rates in November.

MSCI's broadest index of Asia-Pacific shares outside Japan rose a subdued 0.3% but still set for a weekly loss of 1.7% after four straight weeks of gains. The Nikkei, however, gained 0.6%, bringing its weekly rise to 2.6%.

Wall Street futures were up 0.1%. Investors are watching the launch of Tesla's long-promised robotaxi late on Thursday.

Back in Asia, South Korean shares rose 0.4% after the Bank of Korea kicked off its easing cycle with a quarter-point move, a decision that was widely expected.

China's blue chips fell 1% on Friday and were down 1.5% for the week. Hong Kong's Hang Seng, which is closed for a public holiday, fell 6.5% for the week, the biggest weekly drop in two years.

Ting Lu, chief China economist at Nomura, said markets were "laser-focused" on the Saturday's stimulus announcement.  

"As any specific numbers on the extra budget and bond quota will require the approval of the National People's Congress or its Standing Committee, which is highly unlikely to meet before the briefing, the market is keen to know what else the MOF might deliver," Lu said.

Overnight, Wall Street was slightly lower while Treasury yields were mixed. Oil is the major mover, gaining more than 3% overnight thanks to a spike in U.S. fuel use before Hurricane Milton and the Middle East supply risks.

Brent futures fell 0.5% on Friday to $78.95 a barrel, having jumped 3.7% a day earlier. [O/R]

Bond yields climbed for the week as traders pared expectations for outsized U.S. rate cuts.

Atlanta Fed Bank President Raphael Bostic on Thursday told the Wall Street Journal that he is open to a pause next month, although others supported more gradual rate cuts.

Two-year Treasury yields are up 2 basis points for the week to 3.9552%, while 10-year yields climbed 8 bps to 4.0628%.

Traders still price in an about 83% probability that the Fed will cut rates by 25 basis points next month and a 17% chance it would leave rates unchanged, according to CME's FedWatch.

"We think the FOMC remains on track to continue its level adjustment in policy rates with a 25bp cut in November. But our forecast for further easing in December is now being challenged by firm growth and inflation readings," said analysts at JPMorgan.

Currency market movements were subdued on Friday. The U.S. dollar is set for the second straight week of gains, hovering near a two-month top against major peers.

The euro lost 0.4% this week to $1.0934, undermined by expectations that the European Central Bank is almost certain to lower rates in both October and December.

Gold was last up 0.15% at $2,633.31 an ounce, holding ground above the key $2,600 level.