Affiliations: Statistics Department, Universitas Diponegoro, Semarang, Indonesia
Corresponding author: Tarno Tarno, Statistics Department, Universitas Diponegoro, Semarang, Indonesia. E-mail: [email protected]
Abstract: The aim of this research is to develop the novel procedure of Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling for forecasting time series data. The procedure development applies statistical inference based on Lagrange Multiplier (LM) test for selecting input variables, determining the number of clusters, and generating the rule-bases. For selecting inputs, several lags which are indicated significantly different to zero are divided into 2 clusters (minimum number of clusters), and then the lags are selected as optimal inputs of ANFIS based on LM test procedure. The cluster numbers of optimal inputs are added using LM-test procedure such optimal clusters are obtained. Based on those results, a number of rule-bases are generated. The developed model is applied for forecasting cayenne production data in Central Java. The result of proposed procedure is that the optimal inputs consist of 2 lags (lag-1 and lag-3) which are divided into 2 clusters. In this case, the two rules are selected as optimal rules. Finally, the model can work well, and generates very satisfying result in forecasting cayenne production data. Based on the Root Mean Squares Error (RMSE) value, the ANFIS performance is better than performance of Autoregressive Integrated Moving Average (ARIMA) for forecasting cayenne production data in Central Java.
Keywords: Time series, cayenne production, forecasting, ARIMA, ANFIS, LM-test