The research entitled “The Wavelet Radial Basis Model for Forecasting Time Series With Jumps” was conducted by **Rukun Santoso** under the guidance of Prof. Drs. Subanar, Ph.D., Prof. Dr. Dedi Rosadi, M.Sc., and Dr. Suhartono, M.Sc. in 2017.

The following is the abstract of this research.

**ABSTRACT**

This dissertation research has resulted new computation mathematics model called as Wavelet Radial Basis (WRB) model. This model can be used for nonlinear time series forecasting, especially when clustering effect was occurred. The model construction consist of three stage, i.e. prepossessing through wavelet transformation, filtering the clustering effect through radial basis function, and estimation of model parameters. If the result of radial basis filtering support the linear regression assumption, then ordinary least squared method can be used for parameters estimation. In other case, an empirical solution becomes an alternative solution. One of the recommended solution can be reached by neural network (NN) method.

In the beginning of research, it was successful to be uncovered the fact that if a time series is stationer and follows an AR(1), then the Haar wavelet coefficients of MODWT which are elected as predictors in the MAR model has auto-correlation less than the auto-correlation of AR(1). Under these circumstances the OLS method may be used to estimate the model parameters, but the statistic test of parameters may not significant. The MAR model able to make one step ahead predictions of time series properly when the auto-correlation in the data is quite high. This capability will decline in the situation of auto-correlation in the data is small enough, heteroskedastic existence or jumps existence. The jumps will lead to change the average process which means that the process is not stationary. The addition of radial basis layers in the MAR model architecture will transform wavelet coefficients which are elected as predictors into a new variables which more homogeneous. This condition becomes a strongly support to the fulfillment of linear model assumptions that allows the use of OLS method to estimate the model parameters. The application of WRB model to the simulation data and observation data has pointed out that the assumption of classical regression model are fulfilled, especially refers to the error normality.

**Keywords** : wavelet, radial basis, nonlinear time series, WRB model, neural network.