×

Hidden Markov model for discrete circular-linear wind data time series. (English) Zbl 1510.62467

Summary: In this work, we deal with a bivariate time series of wind speed and direction. Our observed data have peculiar features, such as informative missing values, non-reliable measures under a specific condition and interval-censored data, that we take into account in the model specification. We analyse the time series with a non-parametric Bayesian hidden Markov model, introducing a new emission distribution, suitable to model our data, based on the invariant wrapped Poisson, the Poisson and the hurdle density. The model is estimated on simulated datasets and on the real data example that motivated this work.

MSC:

62P12 Applications of statistics to environmental and related topics
62M05 Markov processes: estimation; hidden Markov models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Ailliot P, Monbet V. Markov-switching autoregressive models for wind time series. Environ Modell Software. 2012;30:92-101. doi: 10.1016/j.envsoft.2011.10.011[Crossref], [Web of Science ®], [Google Scholar]
[2] Belu R, Koracin D. Statistical and spectral analysis of wind characteristics relevant to wind energy assessment using tower measurements in complex terrain. J Wind Energy. 2013;2013. doi: 10.1155/2013/739162[Crossref], [Google Scholar]
[3] Lojowska A, Kurowicka D, Papaefthymiou G, Sluisvan der L. Advantages of ARMA-GARCH wind speed time series modeling. In: 2010 IEEE 11th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), Delft, Netherlands. June, 2010. p. 83-88. [Google Scholar]
[4] Zárate-Miñano R, Anghel M, Milano F. Continuous wind speed models based on stochastic differential equations. Appl Energy. 2013;104:42-49. doi: 10.1016/j.apenergy.2012.10.064[Crossref], [Web of Science ®], [Google Scholar]
[5] Martin M, Cremades L, Santabarbara J. Analysis and modelling of time series of surface wind speed and direction. Int J Climatol. 1999;19:197-209. doi: 10.1002/(SICI)1097-0088(199902)19:2<197::AID-JOC360>3.0.CO;2-H[Crossref], [Web of Science ®], [Google Scholar]
[6] Holzmann H, Munk A, Suster M, Zucchini W. Hidden Markov models for circular and linear-circular time series. Environ Ecol Stat. 2006;13:325-347. doi: 10.1007/s10651-006-0015-7[Crossref], [Web of Science ®], [Google Scholar]
[7] Bulla J, Lagona F, Maruotti A, Picone M. A multivariate hidden Markov model for the identification of sea regimes from incomplete skewed and circular time series. J Agric Biol Environ Stat. 2012;17:544-567. doi: 10.1007/s13253-012-0110-1[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1302.62246
[8] Lagona F, Picone M, Maruotti A. A hidden Markov model for the analysis of cylindrical time series. Environmetrics. 2015. [Web of Science ®], [Google Scholar] · Zbl 1316.62164
[9] Mastrantonio G, Maruotti A, Jona Lasinio G. Bayesian hidden Markov modelling using circular-linear general projected normal distribution. Environmetrics. 2015;26:145-158. doi: 10.1002/env.2326[Crossref], [Web of Science ®], [Google Scholar]
[10] Lindsey JC, Ryan LM. Methods for interval-censored data. Stat Med. 1998;17:219-238. doi: 10.1002/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[11] Teh YW, Jordan MI, Beal MJ, Blei DM. Hierarchical Dirichlet Processes. J Am Stat Assoc. 2006;101:1566-1581. doi: 10.1198/016214506000000302[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1171.62349
[12] Fox EB, Sudderth EB, Jordan MI, Willsky AS. A sticky HDP-HMM with application to speaker diarization. Ann Appl Stat. 2011;5:1020-1056. doi: 10.1214/10-AOAS395[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1232.62077
[13] Rubin DB. Inference and missing data. Biometrika. 1976;63:581-592. doi: 10.1093/biomet/63.3.581[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0344.62034
[14] Mullahy J. Specification and testing of some modified count data models. J Econom. 1986;33:341-365. doi: 10.1016/0304-4076(86)90002-3[Crossref], [Web of Science ®], [Google Scholar]
[15] Girija SVS, Rao AVD, Srihari GVLN. On wrapped binomial model characteristics. Math Stat. 2014;2:231-234. [Google Scholar]
[16] Sarma R, Rao AVD, Girija SV. On characteristic functions of the wrapped lognormal and the wrapped Weibull distributions. J Stat Comput Simul. 2011;81:579-589. doi: 10.1080/00949650903436547[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1221.62084
[17] Mastrantonio G, Jona Lasinio G, Maruotti A, Calise G. On initial direction, orientation and discreteness in the analysis of circular variables; 2015. ArXiv e-prints. [Google Scholar] · Zbl 1412.62032
[18] Coles S. Inference for circular distributions and processes. Stat Comput. 1998;8:105-113. doi: 10.1023/A:1008930032595[Crossref], [Web of Science ®], [Google Scholar]
[19] Jona Lasinio G, Gelfand A, Jona Lasinio M. Spatial analysis of wave direction data using wrapped Gaussian processes. Ann Appl Stat. 2012;6:1478-1498. doi: 10.1214/12-AOAS576[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1257.62094
[20] Mastrantonio G, Gelfand AE, Jona Lasinio G. The wrapped skew Gaussian process for analyzing spatio-temporal data. Stochastic Environ Res Risk Assess; 2015. doi:10.1007/s00477-015-1163-9. [Crossref], [Google Scholar]
[21] Cappé O, Moulines E, Ryden T. Inference in hidden Markov models. Springer Series in Statistics. Paris, France: Springer; 2005. [Google Scholar] · Zbl 1080.62065
[22] Teh YW, Jordan MI. Hierarchical Bayesian nonparametric models with applications. In: Hjort N, Holmes C, Müller P, Walker S, editors. Bayesian nonparametrics: principles and practice. Cambridge, UK: Cambridge University Press; 2010. pp. 158-207. [Google Scholar]
[23] Van Gael J, Saatci Y, Teh YW, Ghahramani Z. Beam sampling for the infinite hidden Markov model. In: Proceedings of the 25th International Conference on Machine Learning. ICML’08, Helsinki, Finland ACM, New York, NY (USA); 2008. p. 1088-1095. [Google Scholar]
[24] Scot H. Defining the wind: the Beaufort scale, and how a 19th century admiral turned science into poetry. Prof Geograph. 2005;57:474-475. doi: 10.1111/j.0033-0124.2005.493_1.x[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.