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Various models used in stock market forecasting presented have been classified according to the data preparation, forecasting methodology, performance evaluation, and performance measure. However, these models have not sufficiently discussed in data preparation to overcome randomness, as well as uncertainty and volatility of stock prices issues in achieving high forecasting accuracy. Therefore, the focus of this paper is the data preparation procedure of triangular fuzzy number to build an improved fuzzy random auto-regression model using non-stationary stock market data for forecasting purposes. The improved forecasting model considers two types of input, which are data with low-high and single point values of stock market prices. Even though, low-high data present variability and volatility in nature, the single data has to be form in symmetry left-right spread to present variability and standard error. Then, expectations and variances, confidence-intervals of fuzzy random data are constructed for fuzzy input-output data. By using the input-output data and simplex approach, parameters of the model can be estimated. In this study, some real data sets were used to represent both types of inputs, which are the Kuala Lumpur stock exchange and Alabama University enrollment. The study found that variability and spread adjustment are important factors in data preparation to improve accuracy of the fuzzy random auto-regression model. [ABSTRACT FROM AUTHOR]

Fuzzy time series has been implemented for data prediction in the various sectors, such as education, finance-economic, energy, traffic accident, others. Moreover, many proposed models have been presented to improve the forecasting accuracy. However, the interval-length adjustment and the out-sample forecast procedure are still issues in fuzzy time series forecasting, where both issues are yet clearly investigated in the previous studies. In this paper, a new adjustment of the interval-length and the partition number of the data set is proposed. Additionally, the determining of the out-sample forecast is also discussed. The yearly oil production (OP) and oil consumption (OC) of Malaysia and Indonesia from 1965 to 2012 are examined to evaluate the performance of fuzzy time series and the probabilistic time series models. The result indicates that the fuzzy time series model is better than the probabilistic models, such as regression time series, exponential smoothing in terms of the forecasting accuracy. This paper thus highlights the effect of the proposed interval length in reducing the forecasting error significantly, as well as the main differences between the fuzzy and probabilistic time series models.

In fuzzy time series forecasting, the weight of fuzzy logical relationships and the midpoint of interval values are extensively used in the product of defuzzified matrix and the transpose of the weight matrix into the final forecast model. An improved forecast can be achieved through this model. Additionally, because of its excellent performance, successful applications can be widely achieved by exploiting real life data such as enrollment, stock indices and exchange rates for example. However, the improvement of mean square error is still not significant when the midpoint and the weight values are strictly increased in both of the matrixes. In order to reduce the mean square error, a reversal model in which the weight elements are reversed in the transpose matrix is proposed in this paper. Moreover, a theorem is also proposed to justify this reversal model and the annual data of electricity load by regions of Taiwan from 1981 to 2000 is examined as further evidence. The result indicate a consistently significant advantage in the proposed reversal model, i.e. the mean square error is smaller than the non-reversal model for each region.