基于ARIMA-GARCH模型的上证综指实证分析

发布时间：2018-04-01 13:02

本文选题：ARIMA　切入点：ARCH效应　出处：《湘潭大学》2017年硕士论文

【摘要】：在时间序列的研究领域中,对于资产收益率的波动率进行相关的建模分析,探索其变化的规律,是非常具有实际指导意义的。股票证券等金融市场中,波动率是标的资产收益率的条件标准差,作为对资产风险的一种度量标准存在,常常用来衡量资产风险的大小。资产收益率的条件方差不同于在ARIMA过程中,时间间隔相等的情况下方差为常数,其条件方差会随着现在和过去的数值而变化,本身就是一个随机过程,波动率本身也具有一些特征,如波动率聚集与杠杆效应等。本文主要利用ARIMA-GARCH模型建模的方法,对股指的日收盘价进行取对数并一阶差分的处理,将其转化为平稳的时间序列,其经济学意义为资产收益率的波动率,又称指数收益率,通过对指数收益率进行平稳性检验,并选择适当的阶数建立ARIMA模型;并对残差进行ARCH效应的,通过建立GARCH模型,消除异方差性。实证分析方面,本文基于时间序列分析的理论对上证综指的指数收益率进行了模型的建立,通过对时序图进行分析,可以得知指数收益率序列存在波动集群效应;通过对ACF和PACF的观察,对指数收益率序列建立了ARMA(6,0)模型;在残差检验的过程中验证序列存在异方差性,通过建立GARCH(1,1)模型对序列的异方差性进行消除,并对模型的残差服从正态分布和偏斜t-学生分布进行对比,验证了上证综指的波动率存在尖峰厚尾的性质;并建立EGARCH(1,1)模型验证了波动率序列具有“杠杆效应”。
[Abstract]:In the field of time series research, it is very instructive to model and analyze the volatility of the return on assets and explore the law of its change. Volatility is the conditional standard deviation of the return on the underlying asset. As a measure of asset risk, volatility is often used to measure the size of the asset risk. The conditional variance of the return on assets is different from that in the ARIMA process. If the time interval is equal, the variance is constant, and the conditional variance will change with the present and past values, which is itself a random process, and the volatility itself has some characteristics. For example, volatility aggregation and leverage effect. In this paper, the daily closing price of stock index is treated with logarithm and first order difference by using ARIMA-GARCH model modeling method, which is transformed into a stable time series. Its economic significance is the volatility of the return on assets, also known as the rate of return of the index, by testing the stability of the rate of return on the index, and selecting the appropriate order to establish the ARIMA model, and establishing the GARCH model for the ARCH effect of the residual error. To eliminate heteroscedasticity. Empirical analysis, based on the theory of time series analysis, this paper establishes the model of the index yield of Shanghai Composite Index, through the analysis of time sequence diagram, It can be known that there is a volatility cluster effect in the exponential return series; through the observation of ACF and PACF, the ARMA-6 0) model is established, and the heteroscedasticity of the series is verified in the process of residual test. The heteroscedasticity of the series is eliminated by establishing the GARCH1) model, and the comparison between the normal distribution and the skew t- student distribution of the residual clothing of the model is carried out, which verifies that the volatility of the Shanghai Composite Index has the property of sharp peak and thick tail. The EGARCH1) model is established to verify the "leverage effect" of volatility series.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

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