Without any relation to the type of your data (stock market) : ARMA is a
way to model a data with no long-range dependence. Correlation among
observations dies out really fast ( at exponential rate ), so when you
trying to forecast out of sample, you realise very soon that the past data
contains no information about future, and the best possible predictor is
unconditional mean. So if you want "non-flat" predictor you should move to
statistical models which allow for long-range dependence. An example is
fractional ARIMA or ARFIMA. Jan Beran "Statistics for Long-Memory
processes" is the best book (very expensive) on that subject ( and the
only ?). You can find also some information (but not very much) in Hamilton "Time
Series"
and Gourieroux "Time Series and Dynamic Models".
In your case, it turns out that expected price change (?) is zero, and the
best predictor of future price is its today value. It sounds like
efficient market hypothesis, and if you belive in it you should not have
been trying to forecast it in the first place.
If you do not believe in efficient market hypothesis, and think that
today financial data contains some information about future that can be
extracted using statistical methods, you should use something more
advanced than simple ARIMA. I am sure that any possible correlation of
that type has been exploited already. I am sure also that there is no good
univariate statistical model for financial data, and if somebody has one,
I am sure he would not tell anyone :)
But you can try multivariate models, for example Multifactor Pricing
Models (see, for example, "The Econometrics of Financial Markets" by Campbell).
If you can specify all factors affecting prices and if you have a good
idea about those factors future values then you can do a good prediction.
But again, it's very hard to come out with a predictor of future prices
that is better than today's price, you know why :) But it's much more
easier to model/predict second moments or volatility. Check out GARCH
models (Campbell's book again is one of sources for references).
Vadim
On 10 Apr 2001, Matt Kaar wrote:
> I have a question that probably applies to ARIMA forecasting in general,
> but the specific piece of econometrics software I'm using is EViews.
>
> When I use an ARIMA(1,1,0) model to model ~150 pieces of stock market
> data and then use the EViews software to forecast the next 100 values,
> Every forecast after about the sixth forecasted value is the same to
> around 10 significant figures.
>
> My question is: Why is this happening? My professor said that ARIMA(1,1,0)
> should be able to forecast varying values way past the sixth value.
>
> Thanks,
> Matt
>
> --
> Matt Kaar
> Georgia Tech, CS Major
> Email: [EMAIL PROTECTED]
>
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