Differencing effect in series-parallel architecture of NARX model for time series forecasting

Abstract

This study proposes a NARX model with a series-parallel architecture for forecasting time series data. In this study, the determination of the input variables of the NARX model uses an approach based on the length of the seasonal period from time-series data. At the same time, the number of neurons in the hidden layer uses trial and error from one neuron to the number of input variables. The case study was carried out on real data, namely data on the inflation rate in Indonesia with the exogenous variable of the interest rate of Bank Indonesia. In addition, the data were given two treatments, namely raw data (without the first differencing process) and data with the first differencing process. The best model on training data for the NARX model without the first differencing process data obtained MSE of 0.032737 and MAPE of 0.016193. While the NARX model with the first differencing process data obtained MSE of 0.004944 and MAPE of 0.006778. It can be seen that the NARX model with the first differencing process data gives better results on the training data. In addition, the comparison of MSE and MAPE was also carried out on testing data with ARIMA, ARIMAX, and NAR models. The best model was obtained with the same model in the testing data, namely the NARX model with the first differencing process data (MSE of 0.006521 and MAPE of 0.008182). Based on these results, specifically, the proposed NARX model effectively improves forecasting accuracy. Further research on the NARX model can be developed on a parallel architecture.