Altun E, Bhati D, Khan NM. A new approach to model the counts of earthquakes: INARPQX(1) process.
SN APPLIED SCIENCES 2021;
3:274. [PMID:
33554048 PMCID:
PMC7856626 DOI:
10.1007/s42452-020-04109-8]
[Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 12/29/2020] [Indexed: 11/25/2022] Open
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.
Collapse