Abstract
This paper introduces a first-order integer-valued autoregressive process with a new innovation distribution, shortly INARPQX(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 parameter estimation 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 empirical results show that INARPQX(1) process is an important process to model over-dispersed time series of counts and can be used to predict the number of earthquakes with a magnitude greater than four.
Highlights
Destructive earthquakes are one of the biggest problems of all humanity
We model the monthly counts of earthquakes by INAR(1) processes with several innovation distributions as well as PQX distribution
Based on the results given in this table, it is clear that the estimated biases and mean square errors (MSEs) are very near the their desired value, zero
Summary
Destructive earthquakes are one of the biggest problems of all humanity. Earthquakes are natural disasters that threaten the people’s lives, and affect the economies of the countries negatively. After the important researches of McKenzie [17, 18] and Al-Osh and Alzaid [2], the researches have focussed on the distribution of an innovation process of INAR(1) to develop new models for over-dispersed or under-dispersed time series of counts. We introduce a new INAR(1) model by using the PQX distribution as an innovation process and called this process as a INARPQX(1). The goal of the presented study is to open a new opportunity to model over-dispersed time series of counts with a more flexible innovation distribution than existing ones. We model the monthly counts of earthquakes by INAR(1) processes with several innovation distributions as well as PQX distribution.
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