The research entitled “wavelet Neural Network Modeling With Genetic Algorithm” was conducted by **Budi Warsito** under the guidance of Prof. Drs. Subanar, Ph.D., and Dr. Abdurakhman, M.Si. in 2017.

The following is the abstract of this research.

**ABSTRACT**

Neural Network (NN) is one of the non-linear model which has been developed a lot in statistical modeling, especially in time series analysis. Many researches have shown the advantages of this model compared to the others. However, there are still some problems in NN modeling for time series, including the handling of the input preprocessing, inconsistency of the estimation results and the selection of optimal architecture. The handling of the input preprocessing problem is carried out through the separation of data based on the original components and the noise using wavelet decomposition. Wavelet coefficients resulting from the decomposition are then become the inputs of NN model.Wavelet transformation which is regarded more appropriate for time series data is Maximal Overlap Discrete Wavelet Transform (MODWT), because each level of the decomposition contained wavelet coefficients and scaling coefficients as many as the length of the data. This advantage reduces the weaknesses of filtering by Discrete Wavelet Transform (DWT) which can not be performed on any sample size. The next problems arising is how to determine the level of decomposition and the number of coefficients in each level. In this study, the Maximal Relevance Minimum Redundancy (mRMR) criteria is applied in MODWT decomposition to obtain the optimal input. The criteria based on the Mutual Information (MI) value has been selected due to consider the redundancy between the input variable itself, as well as its value is based on the relevance of input variables with the target.

The optimal input obtained from the wavelet decomposition, then used as input of NN model. The hybrid model formed is named Wavelet Neural Network (WNN) model. Determination of the number of units in the hidden layer emphasizes aspects of computing, through the selection of multiple architectures from simple to more complex and then choose the best one. On the issues relating to the inconsistency of the parameters (weights) estimation which often reach only a local optimum is done through the use of genetic algorithms. The analysis showed that the addition of a super individual would make a genetic algorithm converges to a global optimum.

There are two main contributions of this research. The first is the establishment procedure of determining the optimal architecture of WNN model through the input selection of wavelet coefficients resulting from MODWT decomposition with mRMR criterion. The second contribution is the analysis of convergence of genetic algorithm in time series modeling. Furthermore, the model formed was applied in time series data, either by generating data from a certain model randomly and the real data in financial fields. The experimental results showed that, in general, the stability of the predicted results with the genetic algorithm is better than the conventional methods, especially in the simulation data generated from AR(2), GARCH and nonlinear models. Analysis in real data at the financial fields also shows the stability of predictions resulting from genetic algorithm, especially for the training data.

**Keywords**: Time series, MODWT, WNN, mRMR, genetic algorithm