Estimation of the parameters of ETAS models by Simulated Annealing

This paper proposes a new algorithm to estimate the maximum likelihood parameters of an Epidemic Type Aftershock Sequences (ETAS) model. It is based on Simulated Annealing, a versatile method that solves problems of global optimization and ensures convergence to a global optimum. The procedure is tested on both simulated and real catalogs. The main conclusion is that the method performs poorly as the size of the catalog decreases because the effect of the correlation of the ETAS parameters is more significant. These results give new insights into the ETAS model and the efficiency of the maximum-likelihood method within this context.