关键词: 联跳, 宏观信息公告, 波动率预测, 异质自回归模型, 自回归条件风险模型, SPA检验

Abstract: The realized volatility calculated from intraday high-frequency data well measures the risk of financial assets. Therefore studying its forecasting models is of important value. The heterogeneous autoregressive (HAR-RV-CJ) model of realized volatility which uses lagged continuous-time volatilities and jumps as regressors well characterizes volatility's long memory property with competitive forecasting performance, and thus it has been widely adopted. Considering that the cojumps of component stocks can contain information that is not reflected in index jumps, expanding the HAR-RV-CJ model of index volatility with such cojump information is proposed. Specifically, cojumps are identified using the non-parametric mean cross-product statistic, cojump intensity is estimated using the autoregressive conditional hazard model, and then cojump intensity is included in the HAR-RV-CJ model of index realized volatility to analyze the corresponding forecasting performance improvements. Furthermore, considering that macro announcements can affect the whole stock market and thus the cojump probability, macro exogenous variables such as the consumer price index, the gross domestic product and the balance of trade announcements, etc., are included to augment the basic autoregressive conditional hazard model. Its value to cojump intensity estimation and index volatility forecasting is also considered. Using the high-frequency prices of Chinese CSI 300 index and its component stocks from January 1, 2011 to July 11, 2013 as empirical data, it is shown that component cojumps and index jumps do have different characteristics. Besides the fit performance of these HAR models, their out-of-sample forecasting performance is compared using the superior predictive ability test under four common loss functions. The HAR-RV-CI model which includes cojump intensity instead of past jumps as its regressors, has obviously better fit and forecasting performance than the original HAR-RV-CJ model, the HAR-RV-CJI model which includes both cojump intensity and past jumps, and the benchmark GARCH-jump model. Including macro announcements can improve the fit of the autoregressive conditional hazard model and the index volatility model. However, it does not help the out-of-sample forecasting of index volatility, partly due to the low frequency of the macro announcement variables. Above all, our research confirms the value of including component cojump information in the HAR-RV-CJ model of CSI 300 index volatility, and suggests the appropriate model form for superior forecasting performance. Direct extension would be including the cojump information in the vector HAR models to pursue forecasting performance improvements, which has great value for index futures hedging and portfolio allocation applications.

Key words: cojump, macro announcements, volatility forecasting, heterogeneous autoregressive model, autoregressive conditional hazard model, superior predictive ability test