Statistical trading

interesting :)

In my humble opinion...to use statistics in trading, instead of for one days movement, its better to use it for something more general, 

For example you mentioned weather, we can divide United States into a few regions, and look at these regions historical weather/temperature. Then we look at this year's weather/temperature and look for opportunities. This year's winter is much warmer compared to historical temperatures at this time of the year. This could be a chance to trade stuff about heating. 

Alot of consumer and commercial usage of Natural gas is for space heating. If winter is warmer than usual, this means usage of natural gas will be lower. We can play this by: 

1) short NG contract, or buy a put option...

2) do a seasional spread (short near term, long further term)

3) butterfly