* Asian stock markets: tmsnrt.rs/2zpUAr4
* Markets nervous before non-farm payrolls
* U.S. short-term Treasury yields continue to fall
* Central banks struggling with response to trade friction
* Asia ex-Japan stocks headed for third weekly decline
By Stanley White
TOKYO, Oct 4 (Reuters) - Asian stocks edged higher on Friday, thanks to gains on Wall Street, but the mood was cautious before a key U.S. job report that could help determine whether the Federal Reserve cuts interest rates further.
Investors have been caught out by a set of weak U.S. data this week, including surveys on services and manufacturing sectors, deepening fears the Sino-U.S. trade war is starting to hurt growth in the world's biggest economy.
"We'll probably see a bounce in Asian shares, but then nervousness will creep into the markets as the day progresses," said Shane Oliver, head of investment strategy and chief economist at AMP Capital Investors in Sydney.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3%. Japan's Nikkei stock index lost 0.17%, but Australian shares edged 0.05% higher.
U.S. stock futures fell 0.15% in Asia on Friday, though that followed a 0.80% increase in the S&P 500 on Wall Street overnight on hopes that future Fed rate cuts will support corporate profits.
"The bounce on Wall Street is not a definitive sign. It's actually pessimistic for stocks that two-year yields are falling this much. It shows the bond market hasn't gotten on board with this positive growth story," AMP's Oliver said.
That sentiment was underscored by a frail performance for world stocks in recent weeks, hurt by political uncertainty in the United Stated and Hong Kong, geopolitical tensions in the Middle East, Brexit and a drumroll of weak global data.
In Asia, excluding Japan, equities were on course for the third weekly decline, their worst performance since four weeks of declines ended Aug. 16.
Japan's Nikkei was down 2.6% for the week, on course for its biggest weekly decline since Aug. 2, pressured by worries about trade friction and a resurgent yen.
Hong Kong shares were down 0.13% and though they are on track for a 0.65% weekly gain, sentiment is fragile as the territory's government mulls emergency laws to contain months of often violent protest against China's rule of the former British colony.
U.S. Treasury prices fell slightly but two-year yields remained near the lowest in two years due to growing signs the United States is feeling an economic chill from its trade war with China.
The dollar traded near a one-month low versus the yen, while it was stuck near a one-week trough versus the euro as traders increased bets that the Fed will have to cut rates further to keep growth in the U.S. economy on track.
Data due later on Friday are forecast to show the U.S. economy added 145,000 new jobs in September, more than an increase of 130,000 in the previous month.
However, some traders are braced for a disappointing result after the surprisingly soft data earlier this week on U.S. manufacturing, job creation, and the services sector.
The two-year yield, which tracks expectations for U.S. monetary policy, rose slightly to 1.3981% in Asia but was still close to a two-year low of 1.3680%.
Traders see a 85.2% chance the Fed will cut rates by 25 basis points to 1.75%-2.00% in October, up from 39.6% on Monday, according to CME Group's FedWatch tool.
The Fed has already cut rates twice this year as policymakers try to limit the damage caused by the bruising Sino-U.S. trade war.
The dollar edged down to 106.79 yen, close to a one-month low of 106.48 yen reached on Thursday. The euro was a shade higher at $1.0983, near a one-week high.
For the week, the dollar was down 1.07% versus the yen and off 0.3% against the common currency.
U.S. crude rose 0.36% to $52.64 a barrel. Oil futures on Thursday touched the lowest in nearly two months as the weak U.S. economic data heightened concerns that excess supplies will push prices lower.
For the week, U.S. crude futures were on course for a 5.8% decline, which would be the worst performance since July 19.
Spot gold, a safe-haven asset that investors often buy during times of heightened risk, rose 0.29% to $1,509.11 per ounce, on course for a 0.84% weekly gain. (Editing by Shri Navaratnam)