Why can weather prediction be so correct? I've done a test using ARMA model on some financial series.  It turns out the prediction rate is really very bad – close to half time correct and half time wrong…
I am new to ARMA model so what I tried is very simple, following the textbook of deciding (p,q) for ARMA model by ACF and PACF first, and then use half data to do regression and half data to do test.
I often heard that weather forecasting is used time series model. And in my daily experience, I feel it is pretty good forecasting.
I wonder why the weather forecast could be done so great?
Also, if I want to push my toy ARMA model to next level, what is the direction that I should put into effort ? 
Following up:
There are good answers below, so I am summarize it a little up : 


*

*From a systematic point of view, market as a system is evolving, while weather is more stable from one year to another (truth doesn't change).  

*Market is more complicated in some sense, while weather is ruled by physics laws (more understood structure).  

*Weather is more periodic, which adds to the predictability.

 A: *

*Historical weather is able to predict future weather MUCH better than historical financial data can predict future financial data. Technologies of trading/investing change quickly and market mechanics of 80's is very different from  current behaviour. Weather has periodicity and pretty smooth predictable patterns, unlike financial series where you can observe spikes, lack of mean reversion etc.

*Good quality weather observations can go back to early 1900s cmp. to financial data which usually spans 2 decades or even less (again, early data wouldn't make any sense anyway). So it has much more training data.

*Certainly, weather prediction takes into account not only the time series values (same for financial predictions). But even the most naive approach "predict December weather as average of past 10 years Decembers" will give pretty good approximation (financial prediction like this will be complete nonsense). There are laws of physics which come into play and they are much more strict than laws of financial markets - after all, the amount of randomness in cyclones and winds is much less than in market movements.

*To improve your model you need to firstly understand the mechanics of time series you are trying to predict and base your model on it, not vice versa. Most likely, taking into account only the stock prices you won't be able to predict anything - try to see other parameters and indicators, maybe looking at volumes and open interest, trying to find some correlations there. It is much harder than it seems because if it would be easy everyone would do it which would force prices to converge to 'fair values', thus making it useless again. I suggest not making your model more complicated, but rather spending your time researching market mechanics and only then going into building it - you won't get far by just feeding data into some standard predictor and expecting it to make good predictions.
