The Simultaneous Multivariate Hawkes-type Point Processes and Their Application to Financial Markets

In economic and financial time series we sometimes observe sudden and large jumps. Although these events are relatively rare, they would have significant influence not only on a financial market but also several different markets and macro economies. By using the simultaneous Hawkes-type multivariate point processes (SHPP) models, it is possible to analyze the causal effects of large events in the sense of the Granger-non-causality (GNC) and the instantaneous Granger-non-causality (IGNC). We investigate the financial market of Tokyo and other markets, and apply the Granger non-causality tests. We have found several important empirical findings among financial markets and macro economies.