Analysis And Applications On Nonlinearity Of Financial Volatility

The estimation and forecasting of financial volatility with its special research background andstatistical characteristics are extensively concerned in finance and economic research fields.ARFIMA-EGARCH-GED model with random error obeying the generalized error distributionis established to analyze asymmetry and long memory of financial volatility. High order momentof squared error is proved to be bounded. Further, the asymptotic normality of the maximumlikelihood estimation is also proved.ARFIMA-EGARCH-GED model is the best to estimate financial volatility of Shanghai andShenzhen composite Indexes, compared with T distribution and normal distribution of error.The contrast of EGARCH and FIGARCH model, ARFIMA-EGARCH-GED model could solvewell fat tail, long memory and asymmetry of the two stock markets’ volatility, also is able to fitwell volatility. At last, a short-term prediction about the volatility is made.In view of ARFIMA-EGARCH-GED model with better fitting effect for financial volatility, therelation between returns and volatility, and the relation between different stock markets’ volatilityare discussed by two non-parametric kernel estimation methods, which are local polynomialestimation and N-W (Nadaraya-Watson) kernel estimation. In the Shanghai and Shenzhen stockmarkets, the volatility is greater as the absolute value of return is greater, and volatility is minimumas return is zero. The volatilities between Shanghai and Shenzhen stock markets appear positivecorrelation on the whole, while appear negative correlation in the part. Local polynomialestimation is superior to N-W kernel estimation.