Time Series Prediction Based On Fuzzy Theory

Time series prediction can provide support of decision-making for us, as such it is widely applied in many fields. Fuzzy time series model provides a framework for dealing with pre-diction of data with the shortcomings of incompleteness, inaccuracies and vagueness. With the coming of the era of data, time series model and fuzzy time series model have received more and more attention. Based on the research of fuzzy time series model and time series model, some new results and methods are obtained. Main topics include:1. With the deep development of information, the prediction models with high accuracy and poor interpretability cannot satisfy requirements already for actual application. Therefore, there is still a burning need to develop models that are not only accurate but interpretability as well. Aiming at the preceding problem, this thesis proposes a new fuzzy time series model designed with the use of the two key techniques, namely clustering and axiomatic fuzzy set classification. The drawback of the static length of intervals is that the historical data are roughly put into the intervals, even if the variance of the historical data is not high. To overcome the drawback, clustering algorithm is applied to generate clustering-based intervals. The AFS classification is exploited to yield the semantic interpretation of each fuzzy trend, which makes the model more transparent and easier to comprehend by humans. The proposed model can predict the fuzzy trend of forecasted data. This trend prediction will help the decision maker to be extra cautious well in advance. Then, combining the fuzzy time series and classical time series analysis, a novel fuzzy time series model based on trend prediction and the autoregressive model is proposed. The model can mine the significant trend of time series, and utilize the autoregressive model to determine the fluctuation quantity of the forecasted data. The forecasted data can be obtained by integrating trend prediction with fluctuation quantity. The two proposed models have been experimented on the real-world time series, and the results show the models achieve higher forecasting accuracy than other models.2. The thesis presents two one-step-ahead time series forecasting models based on fuzzy data mining and fuzzy clustering, respectively. According to the principle that the later and the closer, the first model applies the affinity propagation to cluster the subsequences, and identifies the last subsequence which cluster belongs. Fuzzy data mining technology is used to analyze the fuzzy itemsets and obtain the linguistic rules of this cluster, and the finally forecasting is performed. Many well-known distance-based clustering algorithms require data of the same dimensionality. In order to avoid this drawback, a modified fuzzy c-means based on dynamic time warping is proposed. The second model employs the algorithm to cluster the time series data, and the phase of forecasting is applied by using the information provided by this clustering. The two proposed models have been experimented on TAIEX time series, the results show the models produce better forecasting results than several existing models.3. With the deepening of research, relative to the one-step-ahead prediction, multi-step-ahead prediction has more important value in theory and practical significance. The thesis pro-poses a time series long-term forecasting model based on information granules and fuzzy clus-tering. The role of information granulation is in the organization of detailed numerical data into some meaningful and operationally viable abstract knowledge, which makes the interpretation of data easier and more transparent. Therefore, the design of time series forecasting models used the information granulation is interpretable and easily comprehended by humans. The predicted multiple values can be done in one step instead of iteratively prediction each value separately. The proposed model can simplify the forecasting problem and reduce computational overhead of modeling. An illustrative example for forecasting a synthetic time series is used to verify the effectiveness of the proposed model. Moreover, we conduct the experiments on some classical time series, the results show the proposed model produces better forecasting results than those provided by several existing models.