# Multivariate integer-valued autoregressive models applied to earthquake counts

@article{Boudreault2011MultivariateIA, title={Multivariate integer-valued autoregressive models applied to earthquake counts}, author={Mathieu Boudreault and Arthur Charpentier}, journal={arXiv: Applications}, year={2011} }

In various situations in the insurance industry, in finance, in epidemiology, etc., one needs to represent the joint evolution of the number of occurrences of an event. In this paper, we present a multivariate integer-valued autoregressive (MINAR) model, derive its properties and apply the model to earthquake occurrences across various pairs of tectonic plates. The model is an extension of Karlis & Pedelis (2011) where cross autocorrelation (spatial contagion in a seismic context) is considered…

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## References

SHOWING 1-10 OF 36 REFERENCES

Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes

- Mathematics
- 1988

Several classes of stochastic models for the origin times and magnitudes of earthquakes are discussed and the utility of seismic quiescence for the prediction of a major earthquake is investigated.

Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences

- Geology
- 2003

Residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space–time–magnitude distribution of earthquake occurrences,…

Stochastic Declustering of Space-Time Earthquake Occurrences

- Geology
- 2002

This article is concerned with objective estimation of the spatial intensity function of the background earthquake occurrences from an earthquake catalog that includes numerous clustered events in…

BRANCHING PROCESSES WITH IMMIGRATION AND INTEGER-VALUED TIME SERIES

- Mathematics
- 1995

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the…

Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process

- Mathematics
- 1998

A simple criterion is given for the existence of a generalized integer‐valued autoregressive (GINAR(p)) process. We show that the GINAR(p) process is nothing but an AR(p) process. The spectral…

Long-term earthquake clustering

- Geology
- 1991

SUMMARY We analyse statistically the long-term properties of several instrumental earthquake catalogues. Complete catalogues exhibit both short- and long-term clustering for earthquakes of all depth…

Identifying Seismicity Levels via Poisson Hidden Markov Models

- Geology
- 2010

Poisson Hidden Markov models (PHMMs) are introduced to model temporal seismicity changes. In a PHMM the unobserved sequence of states is a finite-state Markov chain and the distribution of the…

Integer‐Valued GARCH Process

- Mathematics
- 2006

Abstract. An integer‐valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) (p,q) model with Poisson deviates is proposed and a condition for the existence…

Foundations of Statistical Seismology

- Geology
- 2010

A brief account is given of the principles of stochastic modelling in seismology, with special regard to the role and development of stochastic models for seismicity. Stochastic models are seen as…