Analysis And Application Of Multivariable Fuzzy Time Series

In recent years, more and more attention has been focused on the innovation and improvement of forecasting techniques. As a result, the standards of accuracy in forecasting have been reached higher and higher. Especially, on the issues of economy developments, population policies, and management planning and control, forecasting has indeed provided indispensable information in decision-making process. In time series analysis, the trend of data serves as the basis for detecting events' occurrence, which can be defined as increase, decrease, seasonal cycles or outliers. Hence, by observing certain characteristics, an optimal fitting model can be selected from a prior modes family, such as ARIMA models, regression models, Threshold models, and so forth. Nevertheless, errors in data collection, time lag, or the correlations among variables all can lead to the uncertainty of the data accuracy .For example, should we take the total number of students in the beginning, the middle, or the end of a school year as the number of registration of the year. Similar situation occurs in the stock market.Hence, the dynamic data which look like precise numbers, are actually a set of possible numbers in some intervals. Therefore, an attempt to construct a mathematical model via the traditional models and analytical methods to interpret the data and trends of a time series may result in the risk of producing over-fitting model. Because of object events' occurrence being uncertain and indistinct, it is necessary to introduce fuzzy theory for forecasting models. By this study, we believe that it can increase scientific and forecasting accuracy, it also extent the new application area for statistics.This thesis explored the application of the forecasting methods of ARIMA time series and multivariate fuzzy time series: Two-factors models, proposed by Chen and Hwang (2000), Heuristic models, proposed by Huamg (2001), and Markov models, proposed by Wu et. al.(2003). This thesis employed five to sixteen intervals to instead of the method proposed by Huarng(2001). Finally this thesis applied time series models to forecast the exports of Taiwan and Mainland China in the years of Asian Financial Crisis (1997) and, then, compared the forecasting power of the multivariable fuzzy time series models and the ARIMA time series model.The thesis consists of five chapters:Chapterl: Fuzzy theoiy. This chapter introduces the origin of the fuzzy theory, the meaning of fuzzy set, the membership function and some basic conceptions. Chapter2: Traditional time series models and multivariate fuzzy time series models. The chapter introduces the vector ARMA model, transfer ARIMA model, seasonal ARIMA, and ARIMA model of traditional time series models, and Two-factors models,Heuristic models, and Markov models of multivariate fuzzy time series models. Idevise the process of the model construction, and propose the findings.Chapter3: The selection of effective lengths of intervals in fuzzy time series. The thesisused five to sixteen intervals analysis method to replace Huarng's analyzing method(2001), and concludes the findings.Chapter4: Application. Finally this thesis apply time series models to forecast theexports of Taiwan and Mainland China and, then, compares the forecasting power ofthe multivariable fuzzy time series models and the ARIMA time series model based ondifferent models, the number of variables, interval length, the time period, modelsrevised.Chapter5: Conclusion and suggestion.The contributions of the thesis are as follows:(1). Introduce multivariate fuzzy time series models, compares the merits and defects of different models, and propose the improved method.(2). Revise the process of model construction, compares forecasting results by different conditions.(3). Compare forecasting results by different multivariate fuzzy time series models based on different length of intervals.(4). Apply time series models to analyze the impact of Asian financial crisis on the dynamic process of the...