Multi-Dimensional self exciting NBD process and Default portfolios

In this article we apply the multi dimensional self exciting negative binomial distribution (SE-NBD) process to the default portfolios which have 13 sectors. SE-NBD process is the Poisson process with the gamma distributed intensity function. We extend SE-NBD process to the multi dimensional process. Using the multi dimensional SE-NBD process (MD-SE-NBD), we can estimate the interactions of among these sectors as the network. Applying the impact analysis, we can classify the upstream and downstream sectors. The upstream sectors are the real estate and financial institution (FI) sectors. From these upstream sectors the shock spreads to the downstream sectors and returns to the upstream sectors. This is the amplifier of the shock. It is consistent with the narrative understandings of the bubble burst. We compare these results to the multi dimensional Hawkes process (MD-Hawkes) which has the zero variance intensity function.