A new approach to model the counts of earthquakes: INARPQX(1) process

摘要

This paper introduces a first-order integer-valued autoregressive process with a new innovation distribution, shortlyINARPQX(1) process. A new innovation distribution is obtained by mixing Poisson distribution with quasi-xgamma distribution.The statistical properties and estimation procedure of a new distribution are studied in detail. The parameterestimation of INARPQX(1) process is discussed with two estimation methods: conditional maximum likelihood and Yule-Walker. The proposed INARPQX(1) process is applied to time series of the monthly counts of earthquakes. The empiricalresults show that INARPQX(1) process is an important process to model over-dispersed time series of counts and can beused to predict the number of earthquakes with a magnitude greater than four.