Hybrid ARIMAX-ANFIS based on LM Test for Prediction of Time Series with Holiday Effect

Abstract

Abstract This paper aims to introduce the ARIMAX-ANFIS hybrid model based on LM test for forecasting time series that is influenced by holidays due to the calendar effect. The optimal ANFIS model architecture selection is made by selecting the input variable and determining the number of membership functions (MFs) based on the LM test. Simulation data and real data are used as case studies. The results showed that ARIMAX-ANFIS based on LM test could be used as an alternative procedure for selecting ANFIS architecture. In the simulation data, the best model is obtained with five input variables and four numbers of MFs. Meanwhile, the foodstuff price index data as real data gives optimal results with five input variables and two numbers of MFs. In general, the use of calendar effect dummy variables in the ARIMAX-ANFIS hybrid model shows more accurate results than the ARIMA-ANFIS model. The effect of holidays as a variation calendar also affects predictions’ accuracy, as seen from the RMSE, MAPE, and R2 values in the ANFIS training and testing process.