Forecasting Simulation with ARIMA and Combination of Stevenson-Porter-Cheng Fuzzy Time Series

Abstract

The simulation was implemented to find out the perfomance for a combination of methods in Stevenson-Porter-Cheng Fuzzy Time Series (FTS) based on 100 replicates on 100 generated data following the model of ARIMA (1,0,0) or AR (1). There are 9 scenarios used as a combination between 3 data generation error variance values (0.5, 1, 3) and 3 AR(1) parameter values i.e. 0.3, 0.5, and 0.7. The results of the simulation showed the greater variance of error and the value of the of AR(1) parameter then the variance of the MSE results with ARIMA will be even greater (0.0634 – 15.7633). While the variance of the MSE results forecasting with Cheng and Cheng2 (no sub interval) FTS tend to be more stable (0.0712 – 2.9648 and 0.0640 – 2.7157). By using the percentage change of historical data as the set of universe, SP Cheng FTS produces MSE forecasting range values ranging from 0.0722 – 14.7045. While SP Cheng2 FTS using the difference of historical data resulted in MSE forecasting values ranging from 0.0759 – 4.6803. Although both MSE values do not look much better than Cheng and Cheng2 FTS, but the greater the AR(1) parameter then MSE forecasting of Cheng and Cheng2 FTS will be better than ARIMA and even closer to the Cheng and Cheng2 FTS.