Gold Price Prediction Using Type-2 Neuro-Fuzzy Modeling and ARIMA Chintya Christina, Rian Febrian Umbara School of Computing Telkom University Bandung, Indonesia chintya.christina@gmail.com, rianum@telkomuniversity.ac.id Abstract— In this research, gold price prediction is conducted using type-2 neuro-fuzzy modeling. Gold price data history is divided into several clusters using Self-Constructing Clustering and produces some type-2 fuzzy rules. The rules of fuzzy parameters which are preceding and consequent are sought and optimized using Particle Swarm Optimization and Least Square Estimation. The gold price prediction result using type-2 neuro-fuzzy modeling is compared to ARIMA method, which is a method that has been widely used for data prediction. The result from this experiment shows that the gold price prediction using type-2 neuro-fuzzy modeling has smaller error compared to the one obtained using ARIMA method. Keywords— Type-2 Neuro-Fuzzy Modeling, gold price prediction, ARIMA I. INTRODUCTION Gold is an investment product preferred by people for its price tends to increase. A prediction or forecasting of a gold price is needed in order to obtain profits and benefits according to what has been planned. The conducted forecasting generally was based on data in the past that was analyzed using certain ways, because there was a suspicion that the patterns of data changes might occur in the present. Those data were studied, analyzed, and connected with the time changes. For time factor is included, therefore that analysis results will state an uncertainty result which might occur in the future. It means the forecasting result obtained is not always exactly 100% correct. However, it does not mean the forecasting is wasted, on the other hand forecasting proven to be a helpful way and have been applied as the base for planning and decision-making, in terms of gold investment. Type-2 neuro-fuzzy modeling has been applied in the previous research to predicting stock [2]. In the research, the accuracy of stock prediction was compared using Fuzzy Time Series Method, Conventional Regression, Neural Network, Neural Network-based Fuzzy Time Series, Neural Network- based Fuzzy Time Series with substitutes. Among all of those methods, type-2 neuro–fuzzy modeling has the smallest RMSE. In this paper, the accuracy in predicting gold price using type-2 neuro-fuzzy modeling will be compared to the most used method in predicting called ARIMA (Autoregressive Integrated Moving Average). The purpose of this paper is to predict the gold price using type-2 neuro-fuzzy modeling and compare the accuracy of the prediction using type-2 neuro- fuzzy modeling and ARIMA. On the second section, it will be explained the use of ARIMA method for forecasting time series data. Furthermore, an explanation regarding the structure of type-2 neuro-fuzzy model will be included. This explanation will be preceded by an explanation about self- constructing clustering method, type-2 fuzzy set, type-2 TSK model, and crisp set. Meanwhile, on the third section, the forecasting of a gold price will be performed using type-2 neuro-fuzzy modeling and ARIMA, including the error prediction comparison between both methods. II. THEORETICAL FOUNDATION A. ARIMA Model Generally ARIMA model or Box-Jenkins defined by the following notation [4]: ARIMA (p,d,q) (1) where p refers to order/degree of Autoregressive (AR), d refers to order/degree of Differencing and q refers to order/degree of Moving Average (MA). Generally ARIMA model for the first difference order is stated as follow: ݐ=ߜ+׎ 1 ݐí1 +׎ 2 ݐí2 +...+ߝ ݐí Ĭ 1 ߝݐí1 í Ĭ 2 ߝݐí2 - … (2) where Z t = ¨Y = Y t -Y t-1 , Y t is the observation value at time t, ߜǡ׎ ଵ ǡ׎ ଶ ǡǥǡȣ ଵ ǡȣ ଶ is a parameter (constants and coefficients) of autoregressive analysis, and ߝ ௧ is a random error prediction at certain time t. B. Self-Constructing Clustering Method Self-Constructing Clustering Method divide the training data set into several clusters through input-similarity test and output-similarity test. In this research, Self-Constructing Clustering Method is needed to be done before doing type- neuro-fuzzy modeling. 2015 3rd International Conference on Information and Communication Technology (ICoICT) 978-1-4799-7752-9/15/$31.00 ©2015 IEEE 272