A Study On Volatility Based On Fuzzy GARCH Model In Chinese Stock Market

In general, the performance of stock market is time-varying and nonlinear, and exhibits volatility clustering. This means simply that certain large changes tend to follow other large changes, and in general small changes tend to follow other small changes. Therefore, Engle(1982) proposed the autoregressive conditional hetero-scedasticity (ARCH) model. Building on Engle's ARCH(q) model, Bollerslev(1986) made use of the Autoregressive Moving Average (ARMA) model to introduce the GARCH model. But this model is not appropriate when the market is asymmetric. To address this issue, other researchers introduced various asymmetric GARCH models, including GARCH-M(1987),EGARCH(1991), GJR-GARCH (1993), and so on.But our human mind is unpredictable, when we encounter uncertainty problems in the process of decision-making, These uncertainties are often not only caused by random,also may be:incomplete information, some of the known knowledge, vague description of the environment. This information comes from the uncertainty in the measurement and perception factors, some of the main concepts of the human mind caused by the expression of fuzzy, and these uncertainties are often more complicated than we thought.In the financial markets, people's thinking is not always fully rational. Especially when market volatility is often vague, investor's risk appetite is even more uncertain, that will be affected by information, environment, personality, attitude, knowledge and other various factors. This ambiguity of the investment market can not be completely dependent on the probability of randomness to explain, this is non-random uncertainty. The phenomenon of uncertainty can be divided into random phenomenon, fuzzy phenomenon and the phenomenon of other uncertainties. In the 21st century, with advances in technology and business development, socio-economic research shows more and more complex. The research of fuzzy theories has been promoted from the application of cybernetics to the social scientific research; especially fuzzy statistics has been all over the fields. In economic decision-making, financial analysis and management, fuzzy theory has been indispensable to decision makers important information. At this point, the use of traditional research methods of analysis and modeling will inevitably result in significant loss of observational information that may lead to model specification error, forecast results and expand the deviation between the actual situations. Therefore, the fuzzy analysis of statistical theory has become such a powerful tool for the uncertainty, the use of fuzzy thinking to analyze the stock market are closer to objective reality.This paper analyzes and draws on previous research results, first summarized the concept of fuzzy rationality. The hypothesis of "economic man" has full rationality, bounded rationality, not fully rational, fully rational is extreme assumption, in reality, there is almost no completely rational behavior; the research of limited rationality is most. When there is ambiguity in human thinking, their behavior may be based on a very vague form, that will be psychological, emotional, learning and other effects, and indeed had an impact on its course of action, in this case,it can be said human behavior is fuzzy rational. Secondly, based on fuzzy rational assumption, the use of fuzzy mathematics and fuzzy statistical tools, the traditional GARCH model was improved, and we analyze the rate of return of stock market volatility. In previous studies, GARCH model was used to analyze volatility of financial data, observational data is not random, but also ambiguity, the traditional methods ignore ambiguity. Therefore, with another perspective, in this paper, fuzzy idea is instead of random idea. Based on traditional GARCH model, we use fuzzy mathematics and fuzzy statistical tools, propose asymmetric Fuzzy GARCH model, and estimate parameters of the model with genetic algorithm. Then we select the Shanghai and Shenzhen stock returns as samples, analyze their volatility, and compare with normal GARCH models. Finally, we compare the prediction of GARCH model, GJR-GARCH model, Fuzzy GARCH model and Fuzzy GJR-GARCH model.We use qualitative and quantitative analysis methods. It contains financial theory and the construction of econometric models, both financial theories and empirical testing and experience. From related disciplines, we use fuzzy mathematics, financial econometrics and time series analysis.This article is mainly composed by the theory and empirical analysis. In the theoretical part, based on fuzzy theory, we try to summarize the concept of fuzzy rational. Secondly, based on fuzzy mathematics and fuzzy statistical theory, we established Fuzzy GJR-GARCH model, analyze the volatility of Shanghai and Shenzhen stock. Finally compare the forecasting ability of Fuzzy GJR-GARCH, Fuzzy GARCH and GARCH model within the sample.The results of this study are as follows:(1) There is ambiguity in human thinking, decision-making results not only affected by a number of clear information, while a lot of fuzzy factors also affect the ultimate decision-making results. By analyzing the fuzziness of human thinking, analyzing the reasons for the formation of ambiguity, summarized the concept of fuzzy rational, The concept of fuzzy rational is followed:In action-selection process, the rational factor is a very vague form, and affected by expectation cognitive and knowledge, actors may not be clearly aware of these rational factors, but it does have a great impact on the results.(2)Based on Fuzzy GARCH model and the GJR-GARCH model, we established Fuzzy GJR-GARCH model, estimate parameters of GARCH, GJR-GARCH model and estimate parameters of Fuzzy GARCH, Fuzzy GJR-GARCH model using a genetic algorithm.(3) The empirical results show that there is a fat tail characteristic in China's Shanghai and Shenzhen stock return series, which exist volatility clustering and the leverage effect that is bad news has greater impact on volatility. Further the predictive ability of each model were compared, the results show that the Fuzzy GJR-GARCH model forecasts the best, Fuzzy GARCH model is followed, GARCH model predictive ability of the worst. Visibly, Fuzzy GJR-GARCH model can solve asymmetry, and capture the "fuzzy" information.This paper is structured as follows:The first chapter is introduction. The main topic of this article describes the background and significance, purpose, content, methods, ideas, innovation and so The second chapter is the literature review. We overview the development of the fuzzy statistics theory and rate of return on the stock market volatility analysis, and review the current situationThe third chapter describes the ambiguity of the human mind, the development of fuzzy mathematics, fuzzy rational, and fuzzy theory, explained some basic concepts such as fuzzy set, membership function and so on. This chapter aims to illustrate the necessity of using fuzzy method.The fourth chapter is Fuzzy GARCH model and its improvement. In this chapter, based on the GARCH model and the Fuzzy GARCH model, we establish the Fuzzy GRJ-GARCH model, and introduced the genetic algorithm (GA) method. This chapter is the theoretical basis of the fifth chapter.The fifth chapter is empirical analysis. We described and examined the statistical characteristics of Shanghai and Shenzhen stock index, and analyze the volatility. Traditional GARCH models were compared with Fuzzy GRJ-GARCH mode.The sixth chapter is a summary and outlook, in this chapter we summarizes the main conclusions of this paper, point out some deficienciesThe main contributions of this paper are the following two points:(1) By reading and summarizing literature, we elaborated on the fuzziness of human thinking and the concept of fuzzy rationality.(2) In this paper, fuzzy theory, the fuzzy mathematics and the GARCH model are combined, and genetic algorithm is used to estimate the model parameters, Fuzzy GARCH model was modified to establish an asymmetric Fuzzy GARCH model, and empirical results indicate that its prediction effect is remarkable.