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Second Phase:- Financial Forecasting Models using Non-linear Statistical and Soft Computing Methods

The second phase of the project will involve selecting and developing forecasting models based on the classification of the behavior of the financial time series analyzed in phase one. Financial time series that exhibit chaotic behavior will be used in this phase. This will involve applying soft computing methods, specifically Artificial Neural Networks and Genetic Algorithms, and non-linear statistical methods and combinations of the methodologies e.g. ANNWAR (ANN With AR) model first proposed by Tan [1995,1997] that incorporates the output of an AR model to an ANN to enhance the capability of the model. We intend to extend this method to ARCH and GARCH models.

**Soft Computing Methods- Artificial Neural Networks**

In traditional statistical analysis, the modeller is required to specify the precise relationship between inputs and outputs and any restrictions that may be implied by theory. ANNs differ from conventional techniques in that the analyst is not required to specify the nature of the relationships involved; the analyst simply identifies the inputs and the outputs. No knowledge of ANNs training methods such as back-propagation is required to use ANNs.

In addition, the ANNs’ main strength lies in its ability to vary in complexity, from a simple parametric model to a highly flexible, nonparametric model. For example, an ANN that is used to fit a nonlinear regression curve, using one input, one linear output, and one hidden layer with a logistic transfer function, can function like a polynomial regression or least squares spline. It has some advantages over the competing methods. Polynomial regression are linear in parameters and thus are fast to fit but suffers from numerical accuracy problems if there are too many wiggles.

Smoothing splines are also linear in parameters and do not suffer from the numerical accuracy problems but pose the problem of deciding where to locate the knots. ANNs with nonlinear transfer function, on the other hand, are genuinely nonlinear in the parameters and thus require longer computational processing time. They are more numerically stable than high-order polynomials and do not require knot location specification like splines.

**Constructing the ANN**

The ANN time series modeling technique will be similar to those done by Tan [1993ab, 1995ab] on forecasting financial time series. Setting up an ANN is essentially a 4 step procedure.

Firstly, the data to be used need to be defined and presented to the ANN as a pattern of input data with the desired outcome or target.

Secondly, the data are categorized to be either in the training testing or validation (out-ofsample) set. The ANN only uses the training set in its learning process in developing the model. The test set is used to test the model for its predictive ability and when to stop the training of the ANN.

Thirdly, the ANN structure is defined by selecting the number of hidden layers to be constructed and the number of neurons for each hidden layer.

Finally, all the ANN parameters are set before starting the training process.

As there are no fixed rules in determining the ANN structure or its parameter values, a large number of ANNs may have to be constructed with different structures and parameters before determining an acceptable model. The trial and error process can be tedious and the experience of the ANN user in constructing the networks is invaluable in the search for a good model. Determining when the training process needs to be halted is of vital importance in obtaining a good model.

If an ANN is overtrained, a curve-fitting problem may occur whereby the ANN starts to fit itself to the training set instead of creating a generalized model. This typically results in poor predictions of the test and validation data set. On the other hand, if the ANN is not trained for long enough, it may settle at a local minimum, rather than the global minimum solution. This typically generates a suboptimal model. By performing periodic testing of the ANN on the test set and recording both the results of the training and test data set results, the number of iterations that produces the best model can be obtained. All that is needed is to reset the ANN and train the network up to that number of iterations.

Prof. Clarence N W Tan

**Next: **Third Phase:- Financial Trading and Portfolio Management System

**Summary: **Index