Hi Atiya. What do you mean by chaotic? Nonlinear deterministic, like the Mackey-Glass equations (so without randomness), or something stochastic with random noise? For nonlinear models you can use a multilayer perceptron which is a feedforward neural network and captures nonlinear ARX processes. Their track record in time series prediction has been quite good, but the actual specification depends on the actual data generating process.

Hope this helps, Sven

By chaotic i mean specifically a UASB reactor ....so the biogas generation depends on previous inputs..and the reaction delay is significant (of the order of days). Apart from the time dependence the chemical oxygen demand and the volatile fatty acids also contribute to the process dynamics. Can you help me out with a solution to this?? I have already used a NARX approach but the network is unable to capture fully the essence of the deviation in the variables. 

I am not sure how I can help, as this would require to buidl models and I am sorry to say that I dont have time for this. If you read up on how to specify the input vector of a MLP for forecasting and how to assess it you should be on a good route. Check out some of my paperson time series prediction with MLPS, as I dont know how knowledgable you ar ein this.

Best of luck,Sven 

i already told you i have fitted an NARX model on this but it is not giving very accurate results. I need a better option and yes, i built a model for it in MATLAB from neural network code. 

Atiya,

I have never seen the definition you give for a chaotic time series. It is rather unique.

In any events, if you wish to model and predict chaotic time series, you need to (a) test for non-linearity of the series, and (b) test whether the nonlinear system is chaotic.  After establishing that your series is chaotic, then consult Soofi, A. and L. Cao Modeling and Forecasting Financial Data: Techniques of Nonlinear Dynamics, Kluwer Academic Publishers, 2002. There you'll find all sundry methods for modeling and prediction of nonlinear, (often but no always) chaotic time series. To have chaotic behaviors, a series must be non-linear; however, not all nonlinear series show chaotic behaviors.

I hope this helps.

Abdol

Mr.Abdol,

First, I have not defined what a nonlinear series is. So, i agree it is inadequate and imprecise. Secondly, the data that i have for simulation is highly noisy since i have tried to fit the model using standard NARX method. All generated networks yielded ineffective training and predictions were unacceptable. Hence, i needed some strategy to improve this model. I request you to please provide me a link to your publication regarding such a chaotic prediction.

Thanks and regards,

Atiya 

Atiya,

Here is one reference to our work on the subject.

 Cao, L. and Soofi, A. (1999) “Nonlinear Deterministic Forecasting of Daily Dollar Exchange Rates”, International Journal of Forecasting, 15: 421-430.