Coal burn is a decent indicator as it makes up a big proportion of mix of power generation, which in turn is heavily dependant on heavy industry. Coal stocks at power stations have fallen quite quickly in the last month or so, with consumption rates up a very strong 40% since the end of September 2012. Coal burn in the corresponding period last year was up 17%, so the gains are partially seasonal.
Coal stocks of 18 days of consumption is a lot lower than the dramatically overstocked levels of ~30 days seen in mid-2012, but is not particularly low by the historical 15 days average.
The problem with this data at the moment is that they are also heavily affected by the weather and generation mix. The record cold weather in December has driven a big jump in electricity production, but the level of coal generation is actually still below that of mid January 2012. This is partly due to a big rebound in hydro generation, which continues to affect coal burn levels.
As I've put on here before, the China Iron and Steel Association (CISA) publish average 10-day production rates through the month for CISA member mills and estimates for smaller mills. The small mills are troublesome as they tend to under-report in some periods, but in all it gives a high-frequency look at steel production rates.
In early January, we have seen an uptick in production from late December, although production rates are only somewhat higher than the December average. This perhaps suggests that mills and consumers are not over stocked heading into the lull of Chinese New Year, but not dramatically understocked. This wasn't the case last year; Chinese New Year was earlier in January 2012 and the economy was weaker at that time.
So there are signs in high frequency data that actual activity has improved in early January, but it is somewhat ambiguous rather than suggesting a definite improvement in momentum.