  In this study, we apply a multidimensional self-exciting negative binomial
distribution (SE-NBD) process to default portfolios with 13 sectors. The SE-NBD
process is a Poisson process with a gamma-distributed intensity function. We
extend the SE-NBD process to a multidimensional process. Using the
multidimensional SE-NBD process (MD-SE-NBD), we can estimate interactions
between these 13 sectors as a network. By applying impact analysis, we can
classify upstream and downstream sectors. The upstream sectors are real-estate
and financial institution (FI) sectors. From these upstream sectors, shock
spreads to the downstream sectors. This is an amplifier of the shock. This is
consistent with the analysis of bubble bursts. We compare these results to the
multidimensional Hawkes process (MD-Hawkes) that has a zero-variance intensity
function.
