Volatility Modeling Of High-Frequency Intraday Data Based On Independent Components Analysis

With the integration of the world economy, the connection between financial markets both at home and abroad is becoming closer. As an important component in China’s financial market, more and more attentions are paid to the stock market. In addition, the stock market is in the developing and improving, all participants should be fully aware of the risks of it and have a strong awareness of risk prevention.Volatility modeling is very important in the management of risk. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Stochastic Volatility (SV) model are the most important volatility models of financial time series modeling. In the case of multivariate, GARCH model is generalized to the multivariate case. The Multivariate GARCH model plays a significant role in the asset allocation and portfolio selection. In this paper, we succinctly summary the development of the Multivariate GARCH model and then apply them to analyze the volatility of the returns. We suggest using DCC-GARCH model with dynamic correlation and ICA-GARCH model based on the Independent Components Analysis (ICA) to analyze the volatility and links between eight sliver-related stocks like Yuguang Gold&lead, Tongling Nonferrous Metals, Jiangxi copper, Yunnan Chihong Zinc&Germanium,Western Mining, Shengda Mining, Zijin Mining and Shenzhen Zhongjin Lingnan based on high-frequency intraday data of five-minute returns. The experimental results show that there exists correlations between the sliver-related stocks and the correlations are varying over time. We also find that ICA-GARCH model is more effective to model multivariate time series than DCC-GARCH model by comparing the autocorrelation of the two models’residuals and ICA-GARCH model costs less time than the DCC-GARCH model.Meanwhile, we introduce ICA to the study of the realized volatility and the conditional covariance matrix and propose an ICA-ARFIMA model to analyze the volatility and the correlations. When we use ICA-ARFIMA model to analyze the high-frequency data, firstly we employ ICA to decompose the multivariate returns into several statistically independent components and then compute the realized volatility of every component. Then we use the fractionally integrated autoregressive moving-average time series (ARFIMA) model to capture the long-memory of the series. The experimental results display that ICA-ARFIMA model is efficient to model the realized volatility and the conditional covariance matrix.In addition, we apply the ICA-ARFIMA model to manage risk and compute the value at risk (VaR). The experimental results indicate that the ICA-ARFIMA model performs well at risk management.