Umu Sa’Adah, Subanar, Suryo Guritno, Suhartono
A forecasting model based on a hybrid wavelet transform and neural network for nonlinear-seasonal time series is proposed. The decomposition of Maximal Overlap Discrete Wavelet Transform (MODWT) is used as a method of data preprocessing to obtain wavelet and scaling coefficients. The main problem in a hybrid model of Wavelet Neural Network (WNN) is how to determine the optimal combination of the number of neurons in the hidden layer, the number of neurons in the input layer and which lags of the wavelet and scaling coefficients will be used at each scale. In this study, data were generated from a nonlinear-seasonal function. Learning algorithm used in Multi-Layer Perceptron (MLP) is the resilient backpropagation algorithm. Inputs of WNN are seasonal and near-seasonal lags from the wavelet and scaling coefficients, in addition to the same inputs as the Multiscale Autoregressive (MAR) model inputs. The neurons in the input layer are selected based on the Wald test statistic. The number of neurons in the hidden layer is determined by the Akaike’s Information Criterion (AIC). All experiments are performed using the R software. The result shows that the optimum WNN model architecture accommodates the seasonal and near-seasonal lags of the wavelet and scaling coefficients as input units. © Research India Publications.
Department of Mathematics, University of Brawijaya, Malang, Indonesia; Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia; Department of Statistics, Sepuluh November Institute of Technology, Surabaya, Indonesia
