LONDON, June 30 (Reuters) - Global shares stocks were firmer on Friday after data showed that inflation in the euro zone continued to fall this month, and attention turned to U.S. prices figures before the opening bell on Wall Streeet.

Oil was poised for its fourth straight quarterly decline amid concerns over sluggish global economic activity and fuel demand.

The dollar and U.S. stock index futures were firm ahead of the U.S. Personal Consumption Expenditures (PCE) index reading due at 1230 GMT, the Fed's favoured inflation gauge.

Federal Reserve Chair Jerome Powell signalled on Thursday that the U.S. central bank was likely to resume its monetary tightening campaign after a break earlier this month.

Euro zone inflation fell to 5.5% in June as the cost of fuel tumbled, with Germany the only country to report an increase, with the European Central Bank still on course for a ninth consecutive rate hike next month, sending euro zone government bond yields higher.

"The ECB thinks it is more costly to do too little in terms of hikes than to do too much, which means that we expect the ECB to continue hiking in July and September," ING bank said.

The MSCI All Country stock index was slightly firmer and heading for first-half gains of about 11.5%, recouping over half of last year's losses, thanks in part to the AI boom lighting a fire under Big Tech.

"Despite rising rates and worries of a recession, the market continues to climb a wall of worry and I think earnings will justify the multiples expansion that we've seen this year," said Patrick Spencer, vice chair of equities as RW Baird.

"We have got to accept that we're moving into a period of normalised interest rates of 3, 4 or 5%, and historically they are not particularly high rates... but the disinflationary argument is very much there," Spencer said.

In Europe, the STOXX index of 600 companies was 1% ahead, and ahead 7.5% so far this year.

CHINA STIMULUS?

Stocks in Asia inched higher as weak factory activity data from China stoked expectations of fresh stimulus.

Copper prices were set for their biggest quarterly fall since September 2022 on the weak Chinese data and prospects of further U.S. rate hikes.

The yen remained fragile after hitting the psychologically important barrier of 145 per dollar, fuelling intervention worries as Japan's Finance Minister Shunichi Suzuki issued another warning against excessive weakening of the currency.

MSCI's broadest index of Asia-Pacific shares outside Japan was flat but on course to eke out a gain of 1.3% in the first half of the year.

"There is a growing divergence in the path of inflation across the region, which is leading to some disagreement about the right path for policy," said Rob Carnell, ING's regional head of research, Asia-Pacific.

China's blue-chip CSI300 Index and the Shanghai Composite Index rose about 0.6%, while Hong Kong's Hang Seng Index was flat.

Japan's Nikkei ended slightly lower but surged 27% in the first half, driven by a boom in chip-related companies and inflows into trading houses.

Strong U.S. economic data sent Treasury yields higher, with the yield on 10-year Treasury notes touching a three-month high on Thursday. It was last at 3.8740%.

U.S. crude eased to $69.77 per barrel and Brent was flat at $74.34.

Gold was set for its worst quarter since September last year on expectations of more rate hikes. Spot gold was slightly weaker at $1,905 per ounce, after briefly dropping below the key $1,900 level on Thursday for the first time since mid-March.

(Reporting by Huw Jones, additional reporting by Ankur Banerjee; Editing by Stephen Coates, Kim Coghill and Chizu Nomiyama)