"The CAP has five components, but nearly all of the recent strength has come from just one: electricity output," he said, adding that electricity output signals activity in largely state owned heavy industry.
Three of the other components – business and leisure travel, property construction, and freight volumes – have all slowed by contrast, he said. The remaining component – the volume of cargo moving through China's seaports – has seen some smaller gains.
Because the recent pickup in growth is not evenly spread across these components, Williams said recent signs of a stabilization in China's economy are unlikely to be sustained.
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"The recent rebound closely resembles the pick-up late last year, which fizzled out far sooner than most had expected," said Williams, referring to China's 7.9 percent growth in the final quarter of 2012, which then fell to 7.7 percent in the first quarter of this year and 7.5 percent in the second quarter.
"Further acceleration over the next couple of quarters cannot be ruled out, particularly when credit is still growing at a rapid pace. But policy makers are unlikely to welcome another prolonged investment-driven surge in the economy. Given that, we expect the rebound to falter over the months ahead," he added.
Other analysts were less convinced that the fact that China's growth was stemming from one part of the economy would be enough to derail the current momentum.
"Yes, China's current rebound is largely investment and heavy industry based," said Alaistair Chan, economist at Moody's Analytics. "That said, there is no reason why it won't be sustained. These investment projects, such as for rail, will last for some time and certainly well into 2014," he said.
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Meanwhile, Rajiv Biswas, Asia-Pacific chief economist at IHS, was also confident that China's recent economic momentum would carry through into 2014.
He acknowledged that China's heavy reliance on investment and exports as growth engines was a vulnerability, but said improvements elsewhere in the global economy would help counteract this risk.
"IHS forecasts that Chinese GDP growth will gradually improve from 7.7 percent growth in 2013 to 7.9 percent growth in 2014, helped by the strengthening U.S. recovery and a return to positive growth in the euro zone in 2014," he said.
—By CNBC's Katie Holliday: Follow her on Twitter