Essay题目：Volatility in the stock market
Based on the stock exchange csi 300 index, the ARMA model and GARCH model are used to analyze the stock market volatility. The arma-garch model has good fitting effect, which can explain the persistence, clustering and leverage of volatility. TARCH and EGARCH models show that volatility has information asymmetry and obvious leverage effect. The regression results of mean TARCH model show that the expected return has no compensation for the expected conditional fluctuation, and the risk and return are asymmetric.
Accurate measurement of stock market volatility is not only the basis of asset pricing, portfolio selection and risk management, but also volatility itself is an important economic risk factor, which has a direct impact on macroeconomic and financial stability. As one of the emerging markets in the world, China's stock market is different from that of the mature market economies and has many new features. Many domestic scholars have applied the ARCH model to predict the stock market volatility. Empirical tests such as ma ji showed that the history of China's stock market did have high volatility. Using the second-order markov structure transformation model, guo mingyuan et al. found that the fluctuations of Shanghai market depend on the duration of the fluctuating state. Wanwei et al. used GARCH and TARCH models to analyze the volatility of Shanghai and shenzhen, and believed that the EARCH model can effectively fit the volatility of stock markets.
准确衡量股市波动性不仅是资产定价，投资组合选择和风险管理的基础，而且波动本身也是一个重要的经济风险因素，它直接影响着宏观经济和金融稳定。作为世界新兴市场之一，中国股市与成熟市场经济不同，具有许多新特点。国内许多学者应用ARCH模型预测股市波动性。 马吉等实证检验表明，中国股市的历史确实具有较高的波动性。使用二阶马尔可夫结构转换模型，郭明元等。发现上海市场的波动取决于波动状态的持续时间。Wanwei等。 使用GARCH和TARCH模型分析上海和深圳的波动性，并认为EARCH模型能够有效地适应股市的波动性。
Since 2005, great changes have taken place in China's stock market. With the continuous improvement of market environment, market trading volume has been expanding and price volatility has become increasingly frequent. In the past, scholars mostly studied the Shanghai and shenzhen stock markets separately or analyzed the single market separately, so it was difficult to comprehensively summarize the overall situation of China's stock market. The influence of the inconsistency of the scale and the incoherence of trading on the analysis results is easy to produce disturbance factors. The stock component of csi 300 index covers most of the current market value and can fully reflect the overall trend of stock prices. By using the latest data, we can select the most suitable conditional variance sequence model to better describe the new information of the dynamic development of the stock market. For financial yield time series rush thick tail, volatility clustering and leverage effect characteristics, this essay adopts the ARCH class models based on the csi 300 refers to the long-term volatility in the stock market dynamic analysis and empirical test, the ARMA model depicting average condition equation, the empirical analysis results on the stock market risk management and market management has important meaning.
The sample was selected as daily closing sequence of csi 300 index, with a duration of 4solstice in January 2005, and a sample capacity of 725 as at December 29, 2007. The data was obtained from CCFR financial data system. In practice, the log price ln(p) is taken as the absolute change quantity, and the logarithmic yield sequence rt=ln(pt)-ln(pt-1) is taken as the relative change quantity of the index. Pt is the closing price of the stock index on the day.
R (t) distribution features: the standard deviation is 0.017639, much higher than the mean value of 0.002284, indicating that China's stock market is at a higher risk at the present stage. The skewness was -0.571354, and the kurtosis was over 6.263, showing certain right skew and peak thick tail characteristics. According to the jarque-bera test of normality, the p value corresponding to the j-b statistic is zero, indicating that the yield sequence is significantly different from the normal distribution. Therefore, it is easy to use the normal distribution to fit the distribution shape of r(t), and the result of volatility analysis will be biased.
R (t) sequence volatility features: r(t) fluctuates around the zero mean, showing the typical explosive, cluster and persistent characteristics of financial time series data. The cluster bias became more obvious from 2007, indicating that the growth trend of the market in the sample interval was significant. Since January 2007, there has been considerable volatility in the market, with large positive and negative returns successively over a relatively short period of time, suggesting a significant increase in market risk.
Before establishing the model, the basic statistical test of r(t), including autocorrelation test, stationarity test and heteroscedasticity test, is required, respectively as follows.
In terms of the autocorrelation test, the autocorrelation and partial autocorrelation functions of r(t) are very significant in at least 3 periods. According to the ljung-box Q statistics and the corresponding P value, the null hypothesis without autocorrelation cannot be rejected with a lag of at least 12 months.