U.S. stock index futures indicated a flat to mildly higher open on Thursday, trying for a positive start to the last quarter of the year after the worst one in four years.

Wednesday saw a nearly 2 percent rally, and while most Wall Street strategists believe the stock market will bounce back in the fourth quarter, the potential for headwinds is high.

Topping the list of worries is China, which clearly has a slowing economy, although it is unclear how slow. The market also faces a potentially rocky earnings season, with profits expected to shrink about 3 percent, and traders wondering whether there will be a China chilling effect on corporate outlooks, either directly or indirectly.

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The other big factor hanging over markets continues to be the Fed, which could potentially raise interest rates for the first time in nine years at one of two meetings — October 28 or December 16.

The fourth quarter is usually a positive time for stocks, so if the market does not rally as some analysts suspect, the debate will turn to whether 2016 will bring the first bear market in seven years.

On the data front, initial jobless claims showed a slight increase to 277,000.

Construction spending and ISM manufacturing data are due at 10:00 a.m ET. Data for light vehicle sales will also be released Thursday.

The number of announced layoffs by U.S.-based companies surged 43 percent in September from the previous month, driven by job cuts at Hewlett-Packard, global outplacement firm Challenger, Gray & Christmas reported Thursday.

In oil markets, Brent crude traded up 1.3 percent just below $49 a barrel, while U.S. crude was around $46.19 a barrel, up 2 percent.

In Europe, the pan-European Stoxx 600 index was around 0.4 percent higher on Thursday, boosted by rallies in Asia and Wall Street overnight. In Asia, Japan's Nikkei finished 1.92 percent higher.

Chinese stock markets in both the mainland and Hong Kong were closed for the National Day Holiday. On Wednesday, the Shanghai Composite index closed up 0.50 percent.

No significant earnings are expected today.

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--CNBC's Patti Domm contributed to this report.

CORRECTION: An earlier version misstated the day the Shanghai composite closed up 0.5 percent.