Data on Saturday showed a 0.3 percent fall in exports in September from a year earlier, versus market expectations for a 6 percent rise.
"The weaker-than-expected export growth is indicative of the lingering external challenges," HSBC economists said in a note. "With external demand conditions offering limited support, domestic demand needs to strengthen further to sustain the economic recovery."
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Economists polled by Reuters forecast that China's economy grew at an annual rate of 7.8 percent in the third quarter, compared with a rate of 7.5 percent in the previous quarter.
Industrial output is forecast to rise 10.1 percent in the year to September, compared with a 10.4 percent rise a month earlier.
"Chinese GDP [gross domestic product] growth for the September quarter is expected to confirm a pick-up in the pace of growth after a first half soft patch," Shane Oliver, chief economist at AMP Capital in Sydney, said in a note.
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"The more timely September data for industrial production, retail sales and fixed asset investment is likely to show some moderation or stabilization in growth consistent with annual GDP growth this year coming in around the official 7.5 percent target rather than continuing to accelerate," he added.
Analysts say markets in Asia and globally will continue to keep a watchful eye on political developments in Washington.
Senate leaders at the weekend began last-ditch talks on reopening the government and raising the debt ceiling as negotiations between House Republicans and the White House collapsed, dashing hopes for an agreement to end the political crisis.
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Back in Asia, the Monetary Authority of Singapore (MAS) maintained its monetary policy stance early Monday. Thailand's central bank is expected to follow suit when it meets on Wednesday.
Singapore will release its latest export data on Thursday, while the minutes from the latest Reserve Bank of Australia (RBA) meeting will be published on Tuesday.
"Minutes from the last RBA board meeting will be looked at for a return of an explicit easing bias that has been absent from the last three post meeting statements but evident in the minutes to the August and September meetings," AMP's Oliver said.
Elsewhere, Japanese markets are closed on Monday for Health and Sports Day. Singapore, Malaysia, Indonesia and the Philippines are shut on Tuesday for a public holiday.
— CNBC.Com's Dhara Ranasinghe; Follow her on Twitter