Abstract: In consideration of the insufficience of the existing researches on co-jumps, co-jumps (co)variance and continuous sample path (co)variance are established using the common intraday jump test and the HAR-RV-CJ model is extended by taking (co)variance and co-jumps together into account, according to the existing theoretical framework. By virtue of high frequency data from Shanghai composite index and Shenzhen component index, the empirical analyses show that the number of the co-jumps of two indexes has a large proportion to their own jumps, most of the co-jumps are the same direction, co-jumps (co)variance and continuous sample path (co)variance both have significant effects on the (co)variance and considering co-jumps makes the extended model more accurate. This study makes contribution to the investment strategy optimization for investor and also provides regulatory basis for the regulatory authorities.

Key words: jump test, co-jumps, multivariate, volatility modeling, high frequency data