Chinese indexes rose after the holiday. The Shanghai Composite jumped 0.33%, and the Shenzhen Composite added 0.49%. At the same time, Hong Kong's Hang Seng Index and South Korea's KOSPI were down slightly, while Australia's S&P/ASX 200 was up 0.9%. Japan's Nikkei 225 was the biggest gainer. It jumped 1.6%.

Stock market indicators show an increase due to positive statistics from the PRC. The Caixin/Markit services Purchasing Managers' Index (PMI) rose to 53.4 from 46.7 in August. Analysts expected a smaller increase, to 49 points.

Meanwhile, investors are looking ahead to the upcoming US jobs data. This information could have an impact on the Fed's interest rates decision. The US lawmakers reached an agreement to temporarily extend the debt limit, avoiding a potential default. This accord would reportedly increase the debt ceiling by $480 billion, allowing the Treasury to continuing paying its bills. This information had a positive effect on the stock markets.

The Japanese indicator was boosted by Fast Retailing, Sony and SoftBank Group, which rose 2.4%, 1.5% and 3% respectively. At the same time, Rakuten shares fell by 3.7%.

Alibaba Group Holding Ltd. shares jumped as much as 3,9% and Tencent Holdings added 1,7%. Meituan climbed 0,6%, while CNOOC Ltd rose 0,8%.

On the Korean stock exchange, Hyundai Motor gained 1.7% and Samsung Electronics Co. added 0,1%. Australia's largest companies, BHP Group and Rio Tinto, rose 3% and 4%, respectively.

A positive signal for investors is Samsung Electronics' interim statistical report for the third quarter of 2021. According to the forecast, the company expects earnings to jump by 28% due to a significant increase in demand for smartphones and the rising cost of semiconductors.