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A non‐homogeneous hidden Markov model for precipitation occurrence

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  • J. P. Hughes
  • P Guttorp
  • S. P. Charles

Abstract

A non‐homogeneous hidden Markov model is proposed for relating precipitation occurrences at multiple rain‐gauge stations to broad scale atmospheric circulation patterns (the so‐called ‘downscaling problem’). We model a 15‐year sequence of winter data from 30 rain stations in south‐western Australia. The first 10 years of data are used for model development and the remaining 5 years are used for model evaluation. The fitted model accurately reproduces the observed rainfall statistics in the reserved data despite a shift in atmospheric circulation (and, consequently, rainfall) between the two periods. The fitted model also provides some useful insights into the processes driving rainfall in this region.

Suggested Citation

  • J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non‐homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
    • Handle: RePEc:bla:jorssc:v:48:y:1999:i:1:p:15-30
    DOI: 10.1111/1467-9876.00136
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    Cited by:

    1. Spezia, Luigi, 2020. "Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    2. Guillermo Ferreira & Jorge Mateu & Emilio Porcu, 2018. "Spatio-temporal analysis with short- and long-memory dependence: a state-space approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 221-245, March.
    3. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    4. Jonsson, Robert, 2011. "A Markov Chain Model for Analysing the Progression of Patient’s Health States," Research Reports 2011:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    5. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    6. Hie Joo Ahn & Bart Hobijn & Ayşegül Şahin, 2023. "The Dual U.S. Labor Market Uncovered," NBER Working Papers 31241, National Bureau of Economic Research, Inc.
    7. Lopes, Hedibert Freitas & Gamerman, Dani & Salazar, Esther, 2011. "Generalized spatial dynamic factor models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1319-1330, March.
    8. K. Shuvo Bakar, 2020. "Interpolation of daily rainfall data using censored Bayesian spatially varying model," Computational Statistics, Springer, vol. 35(1), pages 135-152, March.
    9. David J. Allcroft & Chris A. Glasbey, 2003. "A latent Gaussian Markov random‐field model for spatiotemporal rainfall disaggregation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 487-498, October.
    10. Gallego, C. & Pinson, P. & Madsen, H. & Costa, A. & Cuerva, A., 2011. "Influence of local wind speed and direction on wind power dynamics – Application to offshore very short-term forecasting," Applied Energy, Elsevier, vol. 88(11), pages 4087-4096.
    11. Pierre Ailliot & Craig Thompson & Peter Thomson, 2009. "Space–time modelling of precipitation by using a hidden Markov model and censored Gaussian distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 405-426, July.
    12. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.
    13. M. Ritter & O. Mußhoff & M. Odening, 2014. "Minimizing Geographical Basis Risk of Weather Derivatives Using A Multi-Site Rainfall Model," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 67-86, June.
    14. Abhay Srivastava & Mrinal Mishra & Manoj Kumar, 2015. "Lightning alarm system using stochastic modelling," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 75(1), pages 1-11, January.
    15. Demian Pouzo & Zacharias Psaradakis & Martín Sola, 2024. "On the Robustness of Mixture Models in the Presence of Hidden Markov Regimes with Covariate-Dependent Transition Probabilities," Department of Economics Working Papers 2024_04, Universidad Torcuato Di Tella.
    16. Francesca Bassi & Jacques A. Hagenaars & Marcel A. Croon & Jeroen K. Vermunt, 2000. "Estimating True Changes when Categorical Panel Data are Affected by Uncorrelated and Correlated Classification Errors," Sociological Methods & Research, , vol. 29(2), pages 230-268, November.
    17. Francesca Bassi, 1997. "Identification of latent class Markov models with multiple indicators and correlated measurement errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(3), pages 201-211, December.
    18. Monbet, Valérie & Ailliot, Pierre, 2017. "Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 40-51.
    19. Regnier, Eva, 2008. "Doing something about the weather," Omega, Elsevier, vol. 36(1), pages 22-32, February.
    20. Savannah Wei Shi & Hai Che & Lang Jin, 2021. "Strategic Product Displays Across Different Assortment Levels," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 8(3), pages 84-101, September.
    21. Andriyas, Sanyogita & McKee, Mac, 2014. "Exploring irrigation behavior at Delta, Utah using hidden Markov models," Agricultural Water Management, Elsevier, vol. 143(C), pages 48-58.
    22. Jonsson, Robert, 2011. "Tests of Markov Order and Homogeneity in a Markov Chain," Research Reports 2011:7, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

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