Abstract
The Philippines, as part of the Circum-Pacific belt, is considered as one of the most seismically active countries in the world. Earthquake occurrence is frequent and its effects vary depending on its size. Understanding how the occurrences happen is therefore important. Stochastic models of earthquake occurrence have been used to study seismic activities in various active earthquake zones globally. In this paper, we apply Poisson hidden Markov models (PHMM) using the January 1, 1960 to January 20, 2019 earthquake data of Metro Manila, Philippines. The parameters in the models are estimated using expectation-maximization (EM) algorithm. We determine using various statistical tests that the 5-state PHMM best represents the earthquake data and implement bootstrap algorithm to validate the acceptability of its parameter estimates. Moreover, we investigate the forecasting capability of the 5-state PHMM by comparing it to the ARIMA model. Using unscaled mean bounded relative absolute error (UMBRAE), we find that the 5-state PHMM gives closer one-step ahead forecasts and is a better forecasting model for the considered data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike H (1974) Information theory and an extension of the maximum likelihood principle. In: Petrov B (ed) 2nd International Symposium on Information Theory, pp 267–281. Akademiai
Amei A, Fu W, Ho C (2012) Time series analysis for predicting the occurrences of large scale earthquakes. International Journal of Applied Science and Technology 2(7):64–75
Bansal A, Dimri V, Babu K (2012) Epidemic type aftershock sequence (etas) modeling of northeastern himalayan seismicity. J Seismol 17:255–264. https://doi.org/10.1007/s10950-012-9314-7
Baum L, Petrie T (1966) Statistical inference for probabilistic functions of finite state markov chains. The Annals of Mathematical Statistics 37(6):1554–1563
Baum L, Petrie T, Soules G, Weiss N (1970) A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains. The Annals of Mathematical Statistics 41(1):164–171
Bautista B, Bautista M, Stein R, Barcelona E, Punongbayan R, Laguerta E, Rasdas A, Ambubuyog G, Amin E (1996) Relationship of regional and local structures to mount pinatubo activity. Fire and Mud: Eruptions and Lahars of Mount Pinatubo, Philippines. https://pubs.usgs.gov/pinatubo/bbautist/
Bhaduri M (2020) On modifications to the poisson-triggered hidden markov paradigm through partitioned empirical recurrence rates ratios and its applications to natural hazards monitoring. Scientific Reports 10:15,889–15,907
Bhaduri M, Ho C (2019) On a temporal investigation of hurricane strength and frequency. Environ Model Assess 24:495– 507
Can C, Ergun G, Gokceoglu C (2014) Prediction of earthquake hazard by hidden markov model (around bilecik, nw turkey). Central European Journal of Geosciences 6:403–414
Chen C, Twycross J, Garibaldi J (2017) A new accuracy measure based on bounded relative error for time series forecasting. PLOS ONE 12:1–23
Dionysiou D, Papadopoulos G (1992) Poissonian and negative binomial modelling of earthquake time series in the aegean area. Physics of The Earth and Planetary Interiors - PHYS EARTH PLANET INTERIORS 71:154–165
Doganer A, Calik S (2013) Estimates of earthquake with markov models in the east anatolian fault zone. Turkish Journal of Science and Technology 8(1):55–61
Elliott R, Aggoun L, Moore J (1995) Hidden Markov models: Estimation and control Springer-Verlag
Fattah J, Ezzine L, Aman Z, Moussami H, Lachhab A (2018) Forecasting of demand using arima model. International Journal of Engineering Business Management 10:1–9. 10.1177/1847979018808673
Fukao Y, Furumoto M (1975) Foreshocks and multiple shocks of large earthquakes. Physics of The Earth and Planetary Interiors - PHYS EARTH PLANET INTERIORS 10:355–368
Goh C, Dauwels J, Mitrovic N, Asif M, Oran A, Jaillet P (2012) Online map-matching based on hidden markov model for real-time traffic sensing applications. pp 776–781
Ho C, Bhaduri M (2015) On a novel approach to forecast sparse rare events: Applications to parkfield earthquake prediction. Nat Hazards 78(1):669–679
Ho C, Bhaduri M (2017) A quantitative insight into the dependence dynamics of the kilauea and mauna loa volcanoes, hawaii. Math Geosci 49:893–911
Hopkins D, Clark W, Matuschka T, Sinclair J (1991) The philippines earthquake of july 16, 1990. Bulletin of the New Zealand Society for Earthquake Engineering 24:3–95
Hyndman R, Khandakar Y (2008) Automatic time series forecasting: the forecast package for R. Journal of Statistical Software 26(3):1–22. https://www.jstatsoft.org/article/view/v027i03
Kannan S (2014) Improving innovative mathematical model for earthquake prediction. Eng Fail Anal 41:89–95
King G, Stein R, Lin J (1994) Static stress changes and the triggering of earthquakes. Bulletin - Seismological Society of America 84(3):935–953
Krogh A, Larsson B, Heijne G, Sonnhammer E, Bioinformatics S (2001) Predicting transmembrane protein topology with a hidden markov model: Application to complete genomes. J Mol Biol 305:567–580
Le Thanh N, Kaito K, Kobayashi K (2015) Infrastructure deterioration prediction with a poisson hidden markov model on time series data. Journal of Infrastructure Systems 21(3):04014,051
Lomnitz C (1974) Global tectonics and earthquake risk, Developments in Geotectonics, vol 46. Elsevier
Orfanogiannaki K, Karlis D (2018) Multivariate poisson hidden markov models with a case study of modelling seismicity. Australian and New Zealand Journal of Statistics 60:301– 322
Orfanogiannaki K, Karlis D, Papadopoulos G (2011) Identifying seismicity levels via poisson hidden markov models. Pure Appl Geophys 167:65–77
Orfanogiannaki K, Karlis D, Papadopoulos G (2018) Identification of temporal patterns in the seismicity of sumatra using poisson hidden markov models. Bull Geol Soc Greece 40:1–7
Pachter L, Alexandersson M, Cawley S (2002) Applications of generalized pair hidden markov models to alignment and gene finding problems. Journal of Computational Biology: A Journal of Computational Molecular Cell Biology 9:389– 399
Paroli R, Redaelli G, Spezia L (2002) Poisson hidden markov models for time series of overdispersed insurance counts. In: Proceedings of the XXXI International ASTIN Colloquium, XXXI International ASTIN Colloquium, pp 461–474
PHIVOLCS (2017) Primer on the april 2017 series of earthquakes in batangas province. https://www.phivolcs.dost.gov.ph/index.php/news/628-primer-on-the-april-2017-series-of-earthquakes-in-batangas-provincehttps://www.phivolcs.dost.gov.ph/index.php/news/628-primer-on-the-april-2017-series-of-earthquakes-in-batangas-provincehttps://www.phivolcs.dost.gov.ph/index.php/news/628-primer-on-the-april-2017-series-of-earthquakes-in-batangas-province
PHIVOLCS (2019) Primer on the 22 april 2019 magnitude 6.1 central luzon earthquake. https://www.phivolcs.dost.gov.ph/index.php/news/8233-primer-on-the-22-april-2019-magnitude-6-1-central-luzon-earthquake-23-april-2019https://www.phivolcs.dost.gov.ph/index.php/news/8233-primer-on-the-22-april-2019-magnitude-6-1-central-luzon-earthquake-23-april-2019https://www.phivolcs.dost.gov.ph/index.php/news/8233-primer-on-the-22-april-2019-magnitude-6-1-central-luzon-earthquake-23-april-2019
PHIVOLCS (2019) Primer on the 23 april 2019 magnitude 6.5 eastern samar earthquake. https://www.phivolcs.dost.gov.ph/index.php/news/8234-primer-on-the-23-april-2019-magnitude-6-5-eastern-samar-earthquakehttps://www.phivolcs.dost.gov.ph/index.php/news/8234-primer-on-the-23-april-2019-magnitude-6-5-eastern-samar-earthquakehttps://www.phivolcs.dost.gov.ph/index.php/news/8234-primer-on-the-23-april-2019-magnitude-6-5-eastern-samar-earthquake
Rabiner L (1989) A tutorial on hidden markov models and selected. Proc IEEE 77:257–286
Rao N, Kaila K (2010) Application of the negative binomial to earthquake occurrences in the alpide-himalayan belt. Geophys J R Astron Soc 85:283–290
Rappler.com (2013) Strong quake rocks visayas; 28 dead. https://www.rappler.com/nation/41372-central-bohol-earthquake
Rappler.com (2019) Magnitude 6.5 earthquake rocks parts of mindanao. https://www.rappler.com/nation/243810-strong-aftershock-mindanao-october-31-2019
Rappler.com (2019) Magnitude 6.9 earthquake strikes davao del sur. https://www.rappler.com/nation/247244-earthquake-davao-del-sur-updates-december-15-2019https://www.rappler.com/nation/247244-earthquake-davao-del-sur-updates-december-15-2019
Rossi L, Chakareski J, Frossard P, Colonnese S (2015) A poisson hidden markov model for multiview video traffic. IEEE/ACM Trans Networking 23:547–558
Ryden T (1996) An em algorithm for estimation in markov-modulated poisson processes. Computational Statistics and Data Analysis 21:431–447
Schwarz G (1978) Estimating the dimension of a model. Annals Statistics 6(2):461–464
Spassiani I, Sebastiani G (2016) Magnitude-dependent epidemic-type aftershock sequences model for earthquakes. Phys Rev E 93(042):134. https://doi.org/10.1103/PhysRevE.93.042134
Tobyás V, Mittag R (1991) Local magnitude, surface wave magnitude and seismic energy. Studia Geophysica Et Geodaetica - STUD GEOPHYS GEOD 35:354–357
Utsu T (1969) Aftershocks and earthquake statistics(1) : Some parameters which characterize an aftershock sequence and their interrelations. Journal of the Faculty of Science, Hokkaido University, Series 7, Geophysics 3:129–195
Xiong H, Mamon R (2017) Putting a price tag on temperature. CMS 15:259–296. https://doi.org/10.1007/s10287-017-0291-8
Yip T, Ng W, Yau C (2017) A hidden markov model for earthquake prediction. Stoch Env Res Risk A 32:44–53
Acknowledgments
We extend our gratitude to the Department of Science and Technology - Philippine Institute of Volcanology and Seismology (DOST-PHIVOLCS) for sharing the necessary earthquake data for the completion of the study.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interest.
Additional information
Communicated by: H. Babaie
Supplementary Files
The R Code for PHMM model and ARIMA model, as well as the data, can be found online at: https://github.com/EddFelix/PHMM-Research-Codes-and-Data.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix: State distributions
Appendix: State distributions
State distributions under 2-state PHMM
State distributions under 3-state PHMM
State distributions under 4-state PHMM
State distributions under 5-state PHMM
State distributions under 6-state PHMM
Rights and permissions
About this article
Cite this article
Felix, E.F.O., Buhat, C.A.H. & Mamplata, J.B. Poisson hidden markov model on earthquake occurrences in Metro Manila, Philippines. Earth Sci Inform 15, 1635–1645 (2022). https://doi.org/10.1007/s12145-022-00810-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-022-00810-x