METODE WAVELET NEURAL NETWORKS UNTUK PEMODELAN TIME SERIES MUSIMAN; WAVELET NEURAL NETWORKS METHOD FOR SEASONAL TIME SERIES MODELING

Sa'adah, Umu, Lina Aryati

2015 | Tesis | FMIPA

This dissertation presents a new method for forecasting based on hybrid between wavelet transform and neural networks for seasonal time series data. This method utilizes decomposition of Maximal Overlap Discrete Wavelet Transform (MODWT) to obtain wavelet and scaling coefficients that are used as input variables of Neural Networks model. As in the Neural Networks model, a major problem in the Wavelet Neural Networks (WNN) model is how to determine the optimal combination between the number of neurons in the input layer and the number of neurons in the hidden layer. Specially for WNN model, which lags of the wavelet and scaling coefficients to be used on any scale is also a major problem. Renaud et al. (2003) proposed some lags of wavelet and scaling coefficients to be used on any scale as WNN inputs. However the lags have not yet accommodated seasonal lags, so it is less appropriate if applied to the seasonal time series data. Based on this background, this dissertation research proposes some addition lags i.e. seasonal lags with or without near seasonal lags from wavelet and scaling coefficients as potential input for WNN model. The developed model in this study is called Seasonal Multiscale Autoregressive Feedforward Neural Networks (MSAR-FFNN) model. Therefore, the detection of a characteristic of significant seasonal pattern of the historical data is very important to obtain good performance of WNN model for seasonal time series data. If seasonal pattern is significant, the seasonal lags with or without near seasonal lags from wavelet and scaling coefficients are potential inputs. In this dissertation research, we use simulated and real data containing seasonal pattern. MODWT decomposition using Haar and Daubechies 4 wavelet filters at some levels is applied as a data preprocessing method to obtain wavelet and scaling coefficients. We used FFNN with one hidden layer and resilient backpropagation algorithm. The neural networks inputs are seasonal lags and near seasonal lags from wavelet and scaling coefficients, as well as lags input proposed by Renaud et al. (2003). The number of neurons in the hidden layer is determined by the Akaike’s Information Criterion (AIC). While the lags input is selected based on Wald and F tests. All experiments were performed using Minitab and R software as well as some modifications to the program R. The 0 J xix results showed that consistent and asymptotic normality properties of a MSARFFNN estimator had been proven. For time series data forecasting, the resulting procedures can be implemented properly for simulation, Traffic Fatalities, Air Passengers and CO2 level data. Especially for forecasting seasonal time series data, the addition of seasonal lags with or without near seasonal lags produced higher prediction accuracy compared to that without the addition. For simulation and CO2 level data forecasting, MSAR-FFNN model had prediction accuracy level higher than SARIMA and Holt-Winters Exponential Smoothing model.

Kata Kunci : seasonal time series, Maximal Overlap Discrete Wavelet Transform, wavelet coefficient, scaling coefficient, Multiscale Seasonal Autoregressive Feedforward Neural Networks; resilient backpropagation algorithm; Akaike’s Information Criterion; Wald test.