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 :

  1. 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).
  2. Market is more complicated in some sense, while weather is ruled by physics laws (more understood structure).
  3. Weather is more periodic, which adds to the predictability.
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    $\begingroup$ I thought weather forecasters were using models similar to those used in general circulation models for predicting climate change. Hence they are modelling the system via the known physics, which will help. $\endgroup$ – Gavin Simpson Jul 24 '13 at 22:39
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    $\begingroup$ I think this worded a bit too loosely, what you mean about correct?. Broadly speaking, weather prediction for two months ahead is pretty much sci-fi; it is mostly based on historical data and a lot of simulation (if they have a lot of money). Climate-change models (so long-term weather predictions if you like) are really a hot-bed for Statistics now. For your second question: Play with a GARCH model. $\endgroup$ – usεr11852 Jul 24 '13 at 22:49
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    $\begingroup$ "My approach is rather naive ... why the weather forecast could be done so great?". Simply: because it's not so naive. $\endgroup$ – Glen_b Jul 24 '13 at 23:12
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    $\begingroup$ As a quick follow on, weather predictions based on physics are generally considered to have some added value out to about 14 days (10 is probably a better answer). Beyond that, either climatology (e.g. the average in some place at some point in the year) or persistence (e.g. the same weather as the day before) will generally beat physical forecast models on average. $\endgroup$ – Thursdays Coming Jul 25 '13 at 1:16
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    $\begingroup$ I just wanted to add that if you want to know a bit more about weather prediction, there's a whole chapter on it in Nate Silver's The Signal and the Noise (a pop science book.) $\endgroup$ – Flounderer Jul 25 '13 at 7:18
  1. 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.

  2. 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.

  3. 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.

  4. 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.

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    $\begingroup$ +1 I think one point should perhaps be emphasized and stated more forcefully: It's not merely a matter of understanding the mechanics to inform the model, whether we know the “laws“ of the market, etc. There is a fundamental between reflexive and non-reflexive phenomena. The weather does not “care” about predictions made about it, at least not from one day to the next, whereas most financial series result in part from the actions of many other people armed with ARMA models and the like. $\endgroup$ – Gala Jul 25 '13 at 16:36
  • $\begingroup$ @GaëlLaurans, good point, thanks for re-iterating! $\endgroup$ – sashkello Jul 25 '13 at 23:09

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