本文選題：ARIMA　切入點：ARCH效應(yīng)　出處：《湘潭大學(xué)》2017年碩士論文

【摘要】：在時間序列的研究領(lǐng)域中,對于資產(chǎn)收益率的波動率進(jìn)行相關(guān)的建模分析,探索其變化的規(guī)律,是非常具有實際指導(dǎo)意義的。股票證券等金融市場中,波動率是標(biāo)的資產(chǎn)收益率的條件標(biāo)準(zhǔn)差,作為對資產(chǎn)風(fēng)險的一種度量標(biāo)準(zhǔn)存在,常常用來衡量資產(chǎn)風(fēng)險的大小。資產(chǎn)收益率的條件方差不同于在ARIMA過程中,時間間隔相等的情況下方差為常數(shù),其條件方差會隨著現(xiàn)在和過去的數(shù)值而變化,本身就是一個隨機(jī)過程,波動率本身也具有一些特征,如波動率聚集與杠桿效應(yīng)等。本文主要利用ARIMA-GARCH模型建模的方法,對股指的日收盤價進(jìn)行取對數(shù)并一階差分的處理,將其轉(zhuǎn)化為平穩(wěn)的時間序列,其經(jīng)濟(jì)學(xué)意義為資產(chǎn)收益率的波動率,又稱指數(shù)收益率,通過對指數(shù)收益率進(jìn)行平穩(wěn)性檢驗,并選擇適當(dāng)?shù)碾A數(shù)建立ARIMA模型;并對殘差進(jìn)行ARCH效應(yīng)的,通過建立GARCH模型,消除異方差性。實證分析方面,本文基于時間序列分析的理論對上證綜指的指數(shù)收益率進(jìn)行了模型的建立,通過對時序圖進(jìn)行分析,可以得知指數(shù)收益率序列存在波動集群效應(yīng);通過對ACF和PACF的觀察,對指數(shù)收益率序列建立了ARMA(6,0)模型;在殘差檢驗的過程中驗證序列存在異方差性,通過建立GARCH(1,1)模型對序列的異方差性進(jìn)行消除,并對模型的殘差服從正態(tài)分布和偏斜t-學(xué)生分布進(jìn)行對比,驗證了上證綜指的波動率存在尖峰厚尾的性質(zhì);并建立EGARCH(1,1)模型驗證了波動率序列具有“杠桿效應(yīng)”。
[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.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.51

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