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Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels

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  • Zhang, Zhikun
  • Dai, Min
  • Wang, Xiangjun

Abstract

Describing the non-stationarity of mixed stochastic jump processes presents a formidable challenge. This study employs a mixed compound Poisson process by Markov switching model (CPMSM) to address the issue of overdispersed data of random jumps. The Poisson rate is governed by a continuous-time Markov chain in this model. By assuming independence of the compound Poisson process and jump sizes, we present a generalized algorithm to estimate the parameters of CPMSM and try to predict the future behavior of this stochastic system. To investigate the potential application of this model and the accuracy of our algorithm, we provide a numerical simulation example in the context of the auto insurance payout scenario. The results suggest that CPMSM is an effective method of describing jump behavior controlled by random counts with mode switching via a Markov chain. Furthermore, we demonstrate a specific application of this model in identifying seismicity levels of Greek earthquake data and identify four hidden states. Finally, we compare its fitting effectiveness with the ETAS model using two public earthquake datasets in Japan and Iran.

Suggested Citation

  • Zhang, Zhikun & Dai, Min & Wang, Xiangjun, 2023. "Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    • Handle: RePEc:eee:phsmap:v:632:y:2023:i:p1:s0378437123008464
    DOI: 10.1016/j.physa.2023.129291
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    References listed on IDEAS

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    1. Bountzis, P. & Papadimitriou, E. & Tsaklidis, G., 2020. "Earthquake clusters identification through a Markovian Arrival Process (MAP): Application in Corinth Gulf (Greece)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    4. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Wang, J.P. & Chang, Su-Chin, 2015. "Evidence in support of seismic hazard following Poisson distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 207-216.
    7. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    8. Ting Wang & Mark Bebbington & David Harte, 2012. "Markov-modulated Hawkes process with stepwise decay," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 521-544, June.
    9. Shuanming Li, 2006. "The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 73-85.
    10. Lim, Hwa Kyung & Li, Wai Keung & Yu, Philip L.H., 2014. "Zero-inflated Poisson regression mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 151-158.
    11. David Landriault & Tianxiang Shi, 2014. "First passage time for compound Poisson processes with diffusion: ruin theoretical and financial applications," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(4), pages 368-382.
    12. Majeske, Karl D., 2007. "A non-homogeneous Poisson process predictive model for automobile warranty claims," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 243-251.
    13. Fiorentini, Gabriele & Planas, Christophe & Rossi, Alessandro, 2016. "Skewness and kurtosis of multivariate Markov-switching processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 153-159.
    14. Shaochuan Lu, 2017. "A continuous-time HMM approach to modeling the magnitude-frequency distribution of earthquakes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 71-88, January.
    15. Pang, Guodong & Zheng, Yi, 2017. "On the functional and local limit theorems for Markov modulated compound Poisson processes," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 131-140.
    16. Paul S. Albert & Lori E. Dodd, 2004. "A Cautionary Note on the Robustness of Latent Class Models for Estimating Diagnostic Error without a Gold Standard," Biometrics, The International Biometric Society, vol. 60(2), pages 427-435, June.
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