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The GARCH And The Fuzzy Time Series Models

Posted on:2013-02-05Degree:MasterType:Thesis
Country:ChinaCandidate:Y F LiFull Text:PDF
GTID:2309330395473477Subject:Applied Mathematics
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The volatility is the measurement of the market variations; its value reflects the degree of the risk of the market. The characteristics and prediction of the volatility is the core of the risk measurement, portfolio investment, risk management and derivatives pricing. Therefore, the research of the volatility is very important.This thesis is based on previous studies of the volatility, firstly analysis the statistical properties, advantages and disadvantages of the ARCH and GARCH model, respectively, and tell their forecasting processes. Furthermore, a study of quasi maximum likelihood estimation and the variance targeting estimation was given for the GARCH model. Secondly, it applies fuzzy theory into time series analysis and builds a new volatility prediction pattern based on fuzzy time series. Then we define the fuzzy functions and make fuzzy pairs of the four variables:stock market volatility series, yield sequence, the sequence of volume, and DHL by the fuzzy C-means clustering algorithm. And get predict value of the volatility through the fuzzy rules. Finally, it apply the above models to the prediction of the volatility of the Shanghai Composite Index, then compare the results with that of the GARCH family models through the common model evaluation criterions:Mean Absolute Error、Root Mean Squared Error、Mean Absolute Percentage Error and Theil unequal coefficient. The errors get by the GARCH-t model are:0.1615%,0.2003%,15.3776%and5.9656%, respectively, while the fuzzy time series model are:0.0710%,0.0897%,5.7817%and2.7431%, which are significantly lower than those of GARCH-t model. The result indicates that the fuzzy time series models works better in the market forecast.
Keywords/Search Tags:Fuzzy Time Series, Quasi-maximum Likelihood Estimation, GARCHModel, Volatility Forecast, Error Analysis, the Shanghai Composite Index
PDF Full Text Request
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