Re: Time series prediction

[Fredrik Lingvall]

On 12/30/11 23:48, miro99_ale wrote:
> Hi everybody,
> I need your help! :-)
> I have a series of data, registered from a sensor regarding the power
> consuming of a server in a time series... Something like this:
>
> timestamp   power
> 5   288,6
> 16   289,1
> 26   289,4
> 80   286,3
> 134   286,3
> 190   288,2
> 244   ...
>
> What I intended to do is to configure a time series predictor with octave in
> order to obtain the best ever possibile prediction on the next value (I have
> a set of constraints on the data to respect, e.g. data<  300 W, so I need
> the most accurate prediction as possible).

I'm not sure what you mean with "best ever possibile prediction", but in 
any case the prediction (estimation) performance depends on what 
information you have about your system. That is, what do you know about 
the dynamics ("how fast can it change"),  how accurate are your sensors 
(i.e., how large is the measurement errors) etc. etc.

If you are not sure what model (or model order) that is suitable then 
there are statistical methods to compare different models given your 
data (and background info); that is, you can find the best one from a 
set of models (Google for Bayesian Model Selection).

> The increasing gap between the timestamp is not a problem: I can assume this
> is a discrete time series and timestamp could also be called "1, 2, 3, 4,
> etc"...
> So, how I could solve this mess?
> I already read something about time series prediction, here in the general
> forum, that suggest the use of TISEAN or something related to the System
> Identification Toolbox... Anyway, what I think I really need, before a magic
> code which solve my problem, is a way to act:
> - I need to identify an ARMA model on my data? How I can do it with octave?
> - I need to calculate the W(z)? How I can do it with octave?
> - Which is the minimum number of data whit which I could have an optimum
> prediction?

There is no "global optimal prediction". You will always have some 
uncertainty about your predictions. If you have more (informative) data 
then your predictions will be better than if you have less data (less 
information).


> - How I can calculate the probability that the prediction match with the
> next real value? How I can do it with octave?

This is given by the probability density function (PDF)  associated with 
your prediction, the so called posterior PDF.

See for example: "Bayesian Logical Data Analysis for the Physical 
Sciences" by Phil Gregory.

/Fredrik