A Time Series Forecast Based on Fuzzy-Markov-Fourier Grey Model

• Main Authors: Ming-Chung Liu, 劉銘中
• Other Authors: Yen-Tseng Hsu
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/13080954630566877379

博士 === 國立臺灣科技大學 === 電機工程系 === 97 === The main purpose of this dissertation is to develop an effective prediction model that forecasts time series data based on grey theory, Fourier series theory, Markov chain theory, and Fuzzy theory. First, the grey relational grade (GRG) by relative distance is employed to analyze the relationship between the moving average of price (MAP) and the Taiwan weighted stock index (TAIEX) for the purpose of constructing the grey prediction model. Secondly, based on both the grey prediction model GM(1,1) and metabolizing checking, the grey metabolizing model is used to forecast the next value of the TAIEX and to generate the optimal number of modeling data. In spite of the fact that the grey prediction model has shown a respectable performance for the TAIEX time series prediction, in order to lower the residual error for enhancing the prediction accuracy, this study utilizes the Fourier series to correct the residual errors generated by the grey metabolizing prediction model. This method of using the Fourier correction approach [42] to modify the residual error of GMM is called the Fourier Grey Model (FGM). As indicated by the simulation results, it is evident that the FGM method can improve forecasting accuracy. Next, in order to improve prediction capability, an effective method that is based on the grey model, the Fourier series and the Markov state transition matrices (termed the Markov-Fourier Grey Model, MFGM), is proposed in this dissertation. The proposed method is not only applied to forecast the TAIEX time series, but also used to predict enrollment at the University of Alabama as well as the Gross Domestic Product (GDP) of Taiwan, in order to demonstrate its superiority, robustness and general suitability. The simulation results reveal that the proposed schemes outperform the previously proposed methods found in the literature. From the simulation results, it was determined that in utilizing the Markov state transition matrices to deal with the predictive value produced by the Fourier Grey model (FGM), the prediction results of choosing the entire body of data will be superior to only using the most recent data. Finally, based on the idea that ‘some are better and none is best’, this research applied the rules of fuzzy theory to select the forecasting results of various prediction models used, to obtain a high level of prediction accuracy. The simulation results prove that this method that integrates fuzzy rules with MFGM, entitled FMFGM, is feasible.