Paper:

# Fuzzification Methods and Prediction Accuracy of Fuzzy Autocorrelation Model

## Yoshiyuki Yabuuchi

Faculty of Economics, Shimonoseki City University

2-1-1 Daigaku-cho, Shimonoseki, Yamaguchi 751-8510, Japan

The fuzzy autocorrelation model is a fuzzified autoregressive (AR) model. The aim of the fuzzy autocorrelation model is to describe the possible states of the system with high accuracy. This model uses autocorrelation similar to the Box–Jenkins model. The fuzzy autocorrelation model occasionally increases the vagueness. Although the problem can be mitigated using fuzzy confidence intervals instead of fuzzy time-series data, the unnatural estimations do not improve. Subsequently, an alternate method was used to fuzzify the time-series data and mitigate the unnatural estimation problem. This method also improved the model prediction accuracy. This paper focuses on fuzzification method, and discusses the prediction accuracy of the model and fuzzification of the time-series data. The analysis of the Nikkei stock average shows a high prediction accuracy and manageability of a fuzzy autocorrelation model. In this pape, a quartile is employed as an alternate fuzzification method. The model prediction accuracy and estimation behavior are verified through an analysis. Finally, the proposed method was found to be successful in mitigating the problems.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.21 No.6, pp. 1009-1016, 2017.

- [1] K. Ozawa, T. Niimura, and T. Nakahima, “Fuzzy Time-Series Model of Electric Power Consumption,” J. of Advanced Computational Intelligence, Vol.4, No.3, pp. 188-194, 2000.
- [2] Y. Yabuuchi and J. Watada, “Fuzzy Autocorrelation Model with Confidence Intervals of Fuzzy Random Data,” Proc. of the 6th Int. Conf. on Soft Computing and Intelligent Systems, and the 13th Int. Symp. on Advanced Intelligent Systems, pp. 1938-1943, 2012.
- [3] Y. Yabuuchi and J. Watada, “Building Fuzzy Autocorrelation Model and Its Application to Analyzing Stock Price Time-Series Data,” in W. Pedrycz and S.-M. Chen (eds.), Time Series Analysis, Modeling and Applications, Springer-Verlag Berlin Heidelberg, pp. 347-367, 2012.
- [4] Y. Yabuuchi and T. Kawaura, “Analysis of Japanese National Consumer Price Index using Fuzzy Autocorrelation Model with Fuzzy Confidence Intervals,” Proc. Int. Conf. on Advanced Mechatronic Systems, pp. 264-269, 2014.
- [5] Y. Yabuuchi, T. Kawaura, and J. Watada, “Fuzzy Autocorrelation Model and Its Evaluation,” Proc. the 11th Int. Symp. on Management Engineering, pp. 47-54, 2015.
- [6] Y. Yabuuchi, T. Kawaura, and J. Watada, “Fuzzy Autocorrelation Model with Fuzzy Confidence Intervals and Its Evaluation,” J. Adv. Comput. Intell. Intell. Inform. (JACIII), Vol.20, No.4, pp. 512-520, 2016.
- [7] Y. Yabuuchi and T. Kawaura, “Japanese Economic Analysis using Fuzzy Autocorrelation Model with Fuzzy Confidence Intervals,” Int. J. of Advanced Mechatronic Systems, Vol.7, No.1, pp. 46-60, 2016.
- [8] H. Kwakernaak, “Fuzzy random variables – I. definitions and theorems,” Information Sciences, Vol.15, Issue 1, pp. 1-29, 1978.
- [9] H. Kwakernaak, “Fuzzy random variables – II. Algorithms and examples for the discrete case,” Information Sciences, Vol.17, Issue 3, pp. 253-278, 1979.
- [10] M. L. Puri and D. A. Ralescu, “The Concept of Normality for Fuzzy Random Variables,” Ann. Probab., Vol.13, No.4, pp. 1373-1379, 1985.
- [11] Y. Yabuuchi, “Prediction Accuracy of Fuzzy Autocorrelation Model and Fuzzification of Time-Series Data,” Proc. the 12th Int. Symp. on Management Engineering, N.P., 2016.
- [12] F. M. Tseng, G. H. Tzeng, H. C. Yu, and B. J. C. Yuan, “Fuzzy ARIMA Model for forecasting the foreign exchange market,” Fuzzy Sets and Systems, Vol.118, Issue 1, pp. 9-19, 2001.
- [13] F .M. Tseng and G. H. Tzeng, “A fuzzy seasonal ARIMA model for forecasting,” Fuzzy Sets and Systems, Vol.126, Issue 3, pp. 367-376, 2002.
- [14] J. Watada, “Possibilistic Time-series Analysis and Its Analysis of Consumption,” D. Dubois, H. Prade, and R. R. Yager (eds.), Fuzzy Information Engineering, John Wiley & Sons, Inc., pp. 187-217, 1996.
- [15] A. Colubi, “Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data,” Fuzzy Sets and Systems, Vol.160, Issue 3, pp. 344-356, 2009.
- [16] J. Chachi and S. M. Taheri, “Fuzzy confidence intervals for mean of Gaussian fuzzy random variables,” Expert Systems with Applications, Vol.38, Issue 5, pp. 5240-5244, 2011.
- [17] I. Couso, D. Dubois, S. Montes, and L. Sánchez, “On various definitions of the various of a fuzzy random variable,” Proc. 5th Int. Symp. on Imprecise Probabilities: Theories and Applications, pp. 135-144, 2007.
- [18] I. Couso and L. Sánchez, “Upper and lower probabilities induced by a fuzzy random variable,” Fuzzy Sets and Systems, Vol.165, Issue 1, pp. 1-23, 2011.
- [19] B. Liu and Y.-K. Liu, “Expected value of fuzzy variable and fuzzy expected value models,” IEEE Trans. Fuzzy Syst., Vol.10, No.4, pp. 445-450, 2002.
- [20] J. Watada, S. Wang, and W. Pedrycz, “Building Confidence-Interval-Based Fuzzy Random Regression Models,” IEEE Trans. on Fuzzy Systems, Vol.17, No.6, pp. 1273-1283, 2009.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.