【作者】 刘娟；

【导师】 江慧；

【作者基本信息】 华中科技大学 ， 应用统计， 2021， 硕士

【摘要】 对学术研究者与技术投资者来说,股市的收益率、波动率是他们必定要研究的课题之一。可以说,股市波动性是金融领域最关键的要素。研究股票的收益率及波动率,能给个人投资者提供相应的参考,使得个人投资者能够理性认识风险,从而有效地管理投资风险。针对个人股票投资面对的风险,也能提出应对风险的合理化建议,帮助个人投资者更好地做出判断。本文首先选取沪深指数的月度数据,建立ARMA、GARCH模型,选出最优的参数模型并进行拟合预测;再建立局部多项式回归、光滑样条回归的非参数模型,并对比参数、非参数模型的预测结果。其次,选取波动性较大、较小、居中的三只股票,建立ARIMA模型,检验其优良性,并利用GARCH对收益率序列的残差进行异方差检验,并对模型进行修正,得到每支股票的波动率区间范围。最后,建立更细致的风险等级划分标准,利用非参数光滑样条回归对三只股票的月度数据进行预测,并利用划分标准对其进行短期的风险评价,给予投资者建议。对上证指数进行分析,发现该序列的自相关性很低,且存在ARCH效应,故直接建立GARCH(1,1)模型以描述其波动性。对比上证指数,深证成指存在自相关性,最终建立ARMA(1,1)模型,并且发现具有ARCH效应,最终建立GARCH(1,1)模型。利用局部一元多项式回归、光滑样条回归的非参数模型对样本进行拟合,发现拟合效果较好。通过对比参数ARMA模型和非参数模型,发现两个非参数模型的拟合效果、预测效果均优于参数ARMA模型,且局部多项式回归的拟合效果优于光滑样条回归。对三只波动性不同的股票进行研究,发现股票000661(长春高新股票)的收盘价波动从期初的[350,400]达到期末的[420,480],总体呈现上升趋势,波动率最小。股票600584(长电科技股票)呈现一个凹状走势,期末较期初上升幅度不大,其波动率最大。股票002444(巨星科技股票)从期初的[10.5,13.5]到期末的[9,10.3],总体呈现下降趋势,其波动率介于股票600584和股票000661两者的波动率之间。最后,通过非参数光滑样条的预测结果,发现股票000661的风险级别最高,股票002444的风险级别最低,而股票600584居中。更多还原

【Abstract】 For academic researchers and technology investors,the return and volatility of the stock market is one of the topics they must study.It can be said that stock market volatility is the most critical factor in the financial field.The study of stock returns and volatility can provide the corresponding reference for individual investors,so that individual investors can rationally understand the risk,integrate the cognition into the actual investment strategy,and then effectively manage the investment risk of the stock.In view of the risks faced by individual stock investment,we can also put forward reasonable suggestions to deal with the risks,so as to help individual stock investors make better judgment of investment direction.This paper first selects the monthly data of Shanghai and Shenzhen index,establishes ARMA and GARCH models,selects the best parametric model and makes fitting prediction;then establishes the nonparametric model of local polynomial regression and smooth spline regression,and compares the prediction results of parametric and nonparametric models.Secondly,we select three stocks with high volatility,low volatility and medium volatility,and establish ARIMA model to test their advantages and disadvantages.We use GARCH to test the heteroscedasticity of the residual of the return series,and modify the model to get the range of volatility of each stock.Finally,a more detailed risk classification standard is established,and the monthly data of three stocks are predicted by nonparametric smooth spline regression,and the short-term risk evaluation is carried out by using the classification standard to give investors suggestions.The analysis of Shanghai stock index shows that the autocorrelation of the sequence is very low and arch effect exists.Therefore,GARCH(1,1)model is established to describe its volatility.Comparing with Shanghai index,there is self correlation between Shenzhen and Shenzhen Chengzhi.Finally,ARMA(1,1)model is established,and arch effect is found.Finally,GARCH(1,1)model is established.The non parametric model of local one-dimensional polynomial regression and smooth spline regression is used to fit the samples,and the fitting results are better.By comparing the parameter ARMA model and the nonparametric model,it is found that the fitting effect and prediction effect of the two nonparametric models are better than that of the parametric ARMA model,and the fitting effect of local polynomial regression is better than that of smooth spline regression.The paper studies three different volatility stocks,and finds that the closing price fluctuation of 000661(Changchun high tech stock)has reached [420480] at the end of the period from [350400] at the beginning of the period,and the overall trend is rising,with the lowest volatility.The stock 600584(long-term electric technology stock)presents a concave trend,and the rise rate is not large compared with the beginning of the period,and its volatility is the largest.The stock 002444(Superstar technology stock)has declined from [9,10.3] at the end of the maturity of [10.5,13.5] at the beginning of the period,and its volatility is between the volatility of 600584 and 000661.Finally,through the prediction results of nonparametric smooth spline,it is found that the risk level of stock 000661 is the highest,that of stock 002444 is the lowest,while that of stock600584 is in the middle.更多还原