Time series prediction using Neural Networks in MATLAB

Producing in MATLAB different Neural Networks (NN) for multivariate time series prediction. The data I have is about prices of a commodity in three cities over a period of 100 months. An extra feature of the project (depending on time- my deadline is approaching - 14 Sept.) would be the use of a method of AI to evolve the NN (Evolutionary Computing, Fuzzy Logic) I attach exept the excel file with the data set, the work I have done up to now in MATLAB which seems to work but not to forecast accurately. ## Deliverables The NN's that I expect to be produced in MATLAB, are Multi-Layer Perceptrons using the Backpropagation method with Learning Rate 0.3, Momentum 0.6, and the epochs 25,000-50,000. I need univariate and multivariate prediction for the three cities. The data set should be partitioned to two. The first 90 values would be for training the NN's and the remaining set (10 values) would be for the testing of the NN's. I have already normalized the data, using the logarithmic function. Both "one-lag" and "multi-lag" output predictions for the TEST samples are done with the produced models. In "one-lag" prediction I need to forecast commodity's prices of each month based only on past data. In 'Multi-lag" prediction, on the other hand, I append the predicted values to the input database and use these values also to predict future values. For example, if the network is used to predict a value n6 from observed input data i1,i2,.,i5 then the next network prediction n7 is made using inputs i2,i3,i4,i5,n6. (Multi-lag) The project has two approaches: 1st. Separate Modelling : Each univariate time series must be analysed seperately without utilizing their interdependencies. For example only the values of X1,X2,...,Xk will be used to predict Xk+1. After these NN's are trained and tested with the appropriate data sets will be compared with the ones that will follow in order to judge their performance in terms of MSE(Mean Squared Error). Experiments must be performed with 2-2-1, 4-4-1, 6-6-1 and 8-8-1 networks. [login to view URL] Modelling: For each series I must use information from all three series, instead of treating each series individually. Two kinds of experiments should be performed using this approach. The first kind is the one that Xt+1 is predicted from six preceding values (at time points t and t-1) from all three series.i.e (Xt,Yt,Zt,Xt-1,Yt-1,Zt-1) where X,Y,Z the three time series. This method determines the value of a variable (experiments must include the three of them) at any time t using strictly past data for all the variables in each training input. Experiments should be made with 6-h-1 NN's where h is the number of hidden neurons and the best NN is expected to be the 6-6-1 NN. However for the data I have, there is an implicit ordering among the three series: Xt values were available before Yt values and Yt values were available before Zt and naturally all these were available before Xt+1 values. This observation leads to the second kind of this approach in which, each training input pattern consists of past data items by the above criterion. For instance, if I want to predict a value Yt I should use Xt,Zt-1,Yt-1,Xt-1,Zt-2,Xt-2,Yt-2,Zt-3. Experiments should be made with 8-h-1 NN's. The best one would prove to be the 8-8-1. As final results, in order to make the comparisons I need, I should have: For the univariate analysis the MSE for training, for one-lag and for multi-lag, for each one of the cities and for all the NN's produced (2-2-1, 4-4-1, 6-6-1, 8-8-1). Thus 36 values of MSE. For the multivariate analysis I should have for each city the MSE and the CV (Coefficient of Variation) for the training, for one-lag and for multi-lag, for both NN architectures. Thus 18 MSE and 18 CV values. I should also have the code in MATLAB something that I have partially done but I am not too confident about it. I will probably have to supply you the data set but I still do not know in which form it would suit you. I have it in Excel. As far as the extra feature is concerned, what I want is to create a model that would choose automatically the best of these NN's probably using a method of AI. Since my deadline is approaching I don not know if there is time enough time so please also let me know how long you it would take you. Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. Complete copyrights to all work purchased ## Platform MATLAB 6.1 which runs under Windows XP For the extra feature if it is not possible to be done in MATLAB (although it is desired)any other programm is welcomed as long as I can download it for free, like FuzzyCOPE3 in [login to view URL] or GAOT in [login to view URL] ## Deadline information For each approach produced I would like the code to be sent to me in order to validate the results and obtain a "run" of my own.