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Problem statement: The aim of this research was to study further some latest progress of&#13; wavelet transform for time series forecasting, particularly about Neural Networks Multiscale&#13; Autoregressive (NN-MAR). Approach: There were three main issues that be considered further in this&#13; research. The first was some properties of scale and wavelet coefficients from Maximal Overlap&#13; Discrete Wavelet Transform (MODWT) decomposition, particularly at seasonal time series data. The&#13; second focused on the development of model building procedures of NN-MAR based on the properties&#13; of scale and wavelet coefficients. Then, the third was empirical study about the implementation of the&#13; proposed procedure and comparison study about the forecast accuracy of NN-MAR to other&#13; forecasting models. Results: The results showed that MODWT at seasonal time series data also has&#13; seasonal pattern for scale coefficient, whereas the wavelet coefficients are stationer. The result of&#13; model building procedure development yielded a new proposed procedure of NN-MAR model for&#13; seasonal time series forecasting. In general, this procedure accommodated input lags of scale and&#13; wavelet coefficients and other additional seasonal lags. In addition, the result showed that the proposed&#13; procedure works well for determining the best NN-MAR model for seasonal time series forecasting.&#13; Conclusion: The comparison study of forecast accuracy showed that the NN-MAR model yields better&#13; forecast than MAR and ARIMA models

Seasonal Time Series Data Forecasting by Using Neural Networks Multiscale Autoregressive Model