Comparing generalized Pareto models fitted to extreme observations: an application to the largest temperatures in Spain

详细信息    查看全文

• 作者：Andrés M. Alonso (1)
  Patricia de Zea Bermudez (2)
  Manuel G. Scotto (3)
  
• 关键词：Extreme value theory ; Generalized Pareto distribution ; Peaks over threshold ; Subsampling ; Stationarity and non ; stationary time series
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：28
• 期：5
• 页码：1221-1233
• 全文大小：
• 参考文献：1. Alonso AM, Maharaj EA (2006) Comparison of time series using subsampling. Comput Stat Data Anal 50:2589-599 CrossRef
  2. Balkema A, de Haan L. (1974) Residual life time at great age. Ann Probab 2:792-04 CrossRef
  3. Brunet M, Jones PD, Sigro J, Saladi O, Aguilar E, Moberg A, Della-Marta PM, Lister D, Walther A, Lopez D (2007) Temporal and spatial temperature variability and change over Spain during 1850-005. J Geophys Res 112:D12117. doi:10.1029/2006JD008249 CrossRef
  4. Cameron D, Bevin K, Tawn J (2001) Modelling extreme rainfalls using a modified pulse Bartlett–Lewis stochastic rainfall model (with uncertainty). Adv Water Resour 24:203-11 CrossRef
  5. Castillo E, Hadi AS (1997) Fitting the generalized Pareto distribution to data. J Am Stat Assoc 92:1609-620 CrossRef
  6. Castillo E, Hadi AS, Balakrishnan N, Sarabia JM (2004) Extreme value and related models with applications in engineering and science. Wiley, New Jersey, p 362
  7. Chavez-Demoulin V, Embrechts P (2004) Smooth extremal models in finance and insurance. J Risk Insur 71:183-99 CrossRef
  8. Coles SG (2001) An introduction to statistical modeling of extreme values. Springer, London, p 228
  9. Davison AC, Smith RL (1990) Models for exceedances over high thresholds. J Roy Stat Soc B 52:393-42
  10. de Haan L, Ferreira A (2006) Extreme value theory: an introduction. Springer, New York, p 417
  11. de Zea Bermudez P, Kotz S (2010a) Parameter estimation of the generalized Pareto distribution. Part I. J Stat Plan Inference 40:1353-373 CrossRef
  12. de Zea Bermudez P, Kotz S (2010b) Parameter estimation of the generalized Pareto distribution. Part II. J Stat Plan Inference 40:1374-388 CrossRef
  13. Draghicescu D, Ignaccolo R (2009) Modeling threshold exceedance probabilities of spatially correlated time series. Electron J Stat 3:149-64 CrossRef
  14. DuMouchel WH (1983) Estimating the stable index α in order to measure tail thickness: a critique. Ann Stat 11:1019-031
  15. Eastoe EF, Tawn JA (2012) Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds. Biometrika 99:43-5 CrossRef
  16. Fernández-Montes S, Rodrigo FS (2012) Trends in seasonal indices of daily temperature extremes in the Iberian Peninsula, 1929-005. Int J Climatol 32:2320-332 CrossRef
  17. Furió D, Meneu V (2011) Analysis of extreme temperatures for four sites across Peninsular Spain. Theor Appl Climatol 104:83-9 CrossRef
  18. Furrer EM, Katz RW (2008) Improving the simulation of extreme precipitation events by stochastic weather generators. Water Resour Res 44, W12439. doi:10.1029/2008WR007316
  19. García-Herrera R, Díaz J, Trigo RM, Hernández E (2005) Extreme summer temperatures in Iberia: health impacts and associated synoptic conditions. Ann Geophys 23:239-51 CrossRef
  20. Gupta A, Liang B (2005) Do hedge funds have enough capital? A value at risk approach. J Financial Econ 77:219-53 CrossRef
  21. Jonathan P, Ewans K (2013) Statistical modelling of extreme ocean environments for marine design: a review. Ocean Eng 62:91-09 CrossRef
  22. Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Adv Water Resour 25:1287-304 CrossRef
  23. Kotz S, Nadarajah S (2000) Extreme value distributions: theory and applications. Imperial College Press, London, p 196
  24. Lauridsen S (2000) Estimation of value at risk by extreme value methods. Extremes 3:107-44 CrossRef
  25. Leadbetter MR, Lindgren G, Rootzén H (1983) Extremes and related properties of random sequences and processes. Springer, Berlin, p 336
  26. Letretel C, Marcos M, Martín-Míguez B, Woppelmann G (2010) Sea level extremes in Marseille (NW Mediterranean) during 1885-008. Cont Shelf Res 30:1267-274 CrossRef
  27. Mackay E, Challenor P, AbuBakr S (2011) A comparison of estimators for the generalised Pareto distribution. Ocean Eng 38:1338-346 CrossRef
  28. Mendes JM, de Zea Bermudez P, Pereira J, Turkman KF, Vasconcelos MJP (2009) Spatial extremes of wild fire sizes: Bayesian hierarchical models for extremes. Environ Ecol Stat 17:1-8 CrossRef
  29. Méndez FJ, Menéndez M, Luce?o A, Losada IJ (2007) Analyzing monthly extreme sea levels with a time-dependent GEV model. J Atmos Oceanic Technol 24:894-11 CrossRef
  30. Menéndez M, Méndez FJ, Izaguirre C, Losada IJ (2009) The influence of seasonality on estimating return values of significant wave height. Coast Eng 56:211-19 CrossRef
  31. Mínguez R, Tomás A, Méndez FJ, Medina R (2013) Mixed extreme wave climate model for reanalysis databases. Stoch Environ Res Risk Assess 27:757-68 CrossRef
  32. Naveau P, Nogaj M, Ammann C, Yiou P, Cooley D, Jomelli V (2005) Statistical methods for the analysis of climate extremes. C R Geosci 337:1013-022 CrossRef
  33. Niu XF (1997) Extreme value for a class of non-stationary time series with applications. Ann Appl Probab 7:508-22 CrossRef
  34. Nogaj M, Yiou P, Parey S, Malek F, Naveau P (2006) Amplitude and frequency of temperature extremes over the North Atlantic region. Geophys Res Lett 33:L10801. doi:10.1029/2005GL024251
  35. Northrop PJ, Jonathan P (2011) Threshold modelling of spatially-dependent non-stationary extremes with application to hurricane- induced wave heights (with discussion). Environmetrics 22:799-09 CrossRef
  36. Pickands J (1975) Statistical inference using extreme order statistics. Ann Stat 3:119-31 CrossRef
  37. Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer, New York, p 363
  38. Ribatet M, Sauquet E, Grésillon J-M, Ouarda TBMJ (2007) A regional Bayesian POT model for flood frequency analysis. Stoch Environ Res Risk Assess 21:327-39 CrossRef
  39. Scarrott C, MacDonald A (2012) A review of extreme value threshold estimation and uncertainty quantification. REVSTAT 10:33-0
  40. Scotto MG, Alonso AM, Barbosa SM (2010) Clustering time series of sea levels: extreme value approach. J Waterw Port Coast Ocean Eng 136:215-25 CrossRef
  41. Scotto MG, Barbosa SM, Alonso AM (2011) Extreme value and cluster analysis of European daily temperature series. J Appl Stat 38:2793-804 CrossRef
  42. Tobías A, Scotto MG (2005) Prediction of extreme ozone levels in Barcelona, Spain. Environ Monit Assess 100(1-):23-2 CrossRef
  43. Vanem E (2011) Long-term time-dependent stochastic modelling of extreme waves. Stoch Environ Res Risk Assess 25:185-09 CrossRef
  
• 作者单位：Andrés M. Alonso (1)
  Patricia de Zea Bermudez (2)
  Manuel G. Scotto (3)
  
  1. Department of Statistics and INEACU, Universidad Carlos III de Madrid, Madrid, Spain
  2. Department of Statistics and Operations Research and CEAUL, Universidade de Lisboa, Lisbon, Portugal
  3. Department of Mathematics, Universidade de Aveiro, Aveiro, Portugal
  
• ISSN：1436-3259

文摘

In this paper, a subsampling-based testing procedure for the comparison of the exceedance distributions of stationary time series is introduced. The proposed testing procedure has a number of advantages including the fact that the assumption of stationary can be relaxed for some specific forms of non-stationary and also that the two time series are not required to be independently-generated. For this purpose, a test based on the Kolmogorov–Smirnov and the L 1-Wasserstein distances between generalized Pareto distributions is introduced and studied in some detail. The performance of the testing procedure is illustrated through a simulation study and with an empirical application to a set of data concerning daily maximum temperature in the 17 autonomous communities of Spain for the period 1990-004. The autonomous communities were clustered according to the similarities of the fitted generalized Pareto models and then mapped. The cluster analysis reveals a clear distinction between the four northeast communities on the shores of the Bay of Biscay (which are the regions exhibiting milder temperatures) and the remaining regions. A second cluster corresponds to the southern Mediterranean area and the central region which corresponds to the communities with highest temperatures.