Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2010 | OriginalPaper | Chapter

6. Extreme Value Time Series

Author : Dr. Manfred Mudelsee

Published in: Climate Time Series Analysis

Publisher: Springer Netherlands

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Extreme value time series refer to the outlier component in the climate equation (Eq.​ 1.​2). Quantifying the tail probability of the PDF of a climate variable—the risk of climate extremes—is of high socioeconomical relevance. In the context of climate change, it is important to move from stationary to nonstationary (time-dependent) models: with climate changes also risk changes may be associated.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Spectral Analysis
next chapter Correlation
Literature
Abram NJ, Gagan MK, Cole JE, Hantoro WS, Mudelsee M (2008) Recent intensification of tropical climate variability in the Indian Ocean. Nature Geoscience 1(12): 849–853.
Abramowitz M, Stegun IA (Eds) (1965) Handbook of Mathematical Functions. Dover, New York, 1046 pp.
Alexander LV, Zhang X, Peterson TC, Caesar J, Gleason B, Klein Tank AMG, Haylock M, Collins D, Trewin B, Rahimzadeh F, Tagipour A, Rupa Kumar K, Revadekar J, Griffiths G, Vincent L, Stephenson DB, Burn J, Aguilar E, Brunet M, Taylor M, New M, Zhai P, Rusticucci M, Vazquez-Aguirre JL (2006) Global observed changes in daily climate extremes of temperature and precipitation. Journal of Geophysical Research 111(D5): D05109. [doi:10.1029/2005JD006290]
Ammann CM, Naveau P (2003) Statistical analysis of tropical explosive volcanism occurrences over the last 6 centuries. Geophysical Research Letters 30(5): 1210. [doi:10.1029/2002GL016388]
Angus JE (1993) Asymptotic theory for bootstrapping the extremes. Communications in Statistics–-Theory and Methods 22(1): 15–30.
Beirlant J, Goegebeur Y, Teugels J, Segers J (2004) Statistics of Extremes: Theory and Applications. Wiley, Chichester, 490 pp.
Beirlant J, Teugels JL, Vynckier P (1996) Practical Analysis of Extreme Values. Leuven University Press, Leuven, 137 pp.
Bengtsson L, Botzet M, Esch M (1996) Will greenhouse gas-induced warming over the next 50 years lead to higher frequency and greater intensity of hurricanes? Tellus, Series A 48(1): 57–73.
Beniston M (2004) The 2003 heat wave in Europe: A shape of things to come? An analysis based on Swiss climatological data and model simulations. Geophysical Research Letters 31(2): L02202. [doi:10.1029/2003GL018857]
Berman SM (1964) Limit theorems for the maximum term in stationary sequences. Annals of Mathematical Statistics 35(2): 502–516.
Bickel PJ, Freedman DA (1981) Some asymptotic theory for the bootstrap. The Annals of Statistics 9(6): 1196–1217.
Brooks MM, Marron JS (1991) Asymptotic optimality of the least-squares cross-validation bandwidth for kernel estimates of intensity functions. Stochastic Processes and their Applications 38(1): 157–165.
Buishand TA (1989) Statistics of extremes in climatology. Statistica Neerlandica 43(1): 1–30.
Butler A, Heffernan JE, Tawn JA, Flather RA (2007) Trend estimation in extremes of synthetic North Sea surges. Applied Statistics 56(4): 395–414.
Caers J, Beirlant J, Maes MA (1999a) Statistics for modeling heavy tailed distributions in geology: Part I. Methodology. Mathematical Geology 31(4): 391–410.
Caers J, Beirlant J, Maes MA (1999b) Statistics for modeling heavy tailed distributions in geology: Part II. Application. Mathematical Geology 31(4): 411–434.
Castillo E, Hadi AS (1997) Fitting the generalized Pareto distribution to data. Journal of the American Statistical Association 92(440): 1609–1620.
Chavez-Demoulin V, Davison AC (2005) Generalized additive modelling of sample extremes. Applied Statistics 54(1): 207–222.
Clarke RT (1994) Statistical Modelling in Hydrology. Wiley, Chichester, 412 pp.
Coles S (2001a) Improving the analysis of extreme wind speeds with information-sharing models. Institut Pierre Simon Laplace des Sciences de l’Environnement Global, Notes des Activitês Instrumentales 11: 23–34.
Coles S (2001b) An Introduction to Statistical Modeling of Extreme Values. Springer, London, 208 pp.
Coles S (2004) The use and misuse of extreme value models in practice. In: Finkenstädt B, Rootzén H (Eds) Extreme Values in Finance, Telecommunications, and the Environment. Chapman and Hall, Boca Raton, FL, pp 79–100.
Coles S, Pericchi L (2003) Anticipating catastrophes through extreme value modelling. Applied Statistics 52(4): 405–416.
Cooley D, Nychka D, Naveau P (2007) Bayesian spatial modeling of extreme precipitation return levels. Journal of the American Statistical Association 102(479): 824–840.
Cowling A, Hall P (1996) On pseudodata methods for removing boundary effects in kernel density estimation. Journal of the Royal Statistical Society, Series B 58(3): 551–563.
Cowling A, Hall P, Phillips MJ (1996) Bootstrap confidence regions for the intensity of a Poisson point process. Journal of the American Statistical Association 91(436): 1516–1524.
Cowling AM (1995) Some problems in kernel curve estimation. Ph.D. Dissertation. Australian National University, Canberra, 130 pp.
Cox DR, Isham V (1980) Point Processes. Chapman and Hall, London, 188 pp.
Cox DR, Isham VS, Northrop PJ (2002) Floods: Some probabilistic and statistical approaches. Philosophical Transactions of the Royal Society of London, Series A 360(1796): 1389–1408.
Cox DR, Lewis PAW (1966) The Statistical Analysis of Series of Events. Methuen, London, 285 pp.
Cramér H (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton, 575 pp.
Cutter SL, Emrich C (2005) Are natural hazards and disaster losses in the U.S. increasing? Eos, Transactions of the American Geophysical Union 86(41): 381, 389.
Dargahi-Noubary GR (1989) On tail estimation: An improved method. Mathematical Geology 21(8): 829–842.
Davison AC, Ramesh NI (2000) Local likelihood smoothing of sample extremes. Journal of the Royal Statistical Society, Series B 62(1): 191–208.
Davison AC, Smith RL (1990) Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society, Series B 52(3): 393–442.
Della-Marta PM, Haylock MR, Luterbacher J, Wanner H (2007) Doubled length of western European summer heat waves since 1880. Journal of Geophysical Research 112(D15): D15103. [doi:10.1029/2007JD008510]
Diggle P (1985) A kernel method for smoothing point process data. Applied Statistics 34(2): 138–147.
Diggle P, Marron JS (1988) Equivalence of smoothing parameter selectors in density and intensity estimation. Journal of the American Statistical Association 83(403): 793–800.
Easterling DR, Meehl GA, Parmesan C, Changnon SA, Karl TR, Mearns LO (2000) Climate extremes: Observations, modeling, and impacts. Science 289(5487): 2068–2074.
Eastoe EF, Tawn JA (2009) Modelling non-stationary extremes with application to surface level ozone. Applied Statistics 58(1): 25–45.
Efron B, Hinkley DV (1978) Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information (with discussion). Biometrika 65(3): 457–487.
Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. Chapman and Hall, London, 436 pp.
Elsner JB, Kara AB (1999) Hurricanes of the North Atlantic: Climate and Society. Oxford University Press, New York, 488 pp.
Elsner JB, Kara AB, Owens MA (1999) Fluctuations in North Atlantic hurricane frequency. Journal of Climate 12(2): 427–437.
Elsner JB, Kossin JP, Jagger TH (2008) The increasing intensity of the strongest tropical cyclones. Nature 455(7208): 92–95.
Emanuel K (2005) Increasing destructiveness of tropical cyclones over the past 30 years. Nature 436(7051): 686–688.
Emanuel KA (1987) The dependence of hurricane intensity on climate. Nature 326(6112): 483–485.
Emanuel KA (1999) Thermodynamic control of hurricane intensity. Nature 401(6754): 665–669.
Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling Extremal Events for Insurance and Finance. Springer, Berlin, 648 pp.
Engel H, Krahé P, Nicodemus U, Heininger P, Pelzer J, Disse M, Wilke K (2002) Das Augusthochwasser 2002 im Elbegebiet. Bundesanstalt für Gewässerkunde, Koblenz, 48 pp.
Fawcett L, Walshaw D (2006) A hierarchical model for extreme wind speeds. Applied Statistics 55(5): 631–646.
Fawcett L, Walshaw D (2007) Improved estimation for temporally clustered extremes. Environmetrics 18(1–2): 173–188.
Ferreira A, de Haan L, Peng L (2003) On optimising the estimation of high quantiles of a probability distribution. Statistics 37(5): 401–434.
Ferro CAT, Segers J (2003) Inference for clusters of extreme values. Journal of the Royal Statistical Society, Series B 65(2): 545–556.
Fischer H (1997) Räumliche Variabilität in Eiskernzeitreihen Nordostgrönlands. Ph.D. Dissertation. University of Heidelberg, Heidelberg, 188 pp.
Fischer K (1907) Die Sommerhochwasser der Oder von 1813 bis 1903. Jahrbuch für die Gewässerkunde Norddeutschlands, Besondere Mitteilungen 1(6): 1–101.
Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society 24(2): 180–190.
Fleitmann D, Dunbar RB, McCulloch M, Mudelsee M, Vuille M, McClanahan TR, Cole JE, Eggins S (2007b) East African soil erosion recorded in a 300 year old coral colony from Kenya. Geophysical Research Letters 34(4): L04401. [doi:10.1029/2006GL028525]
Fréchet M (1927) Sur la loi probabilité de l’écart maximum. Annales de la Société Polonaise de Mathématique 6: 93–116.
Frei C, Schär C (2001) Detection probability of trends in rare events: Theory and application to heavy precipitation in the Alpine region. Journal of Climate 14(7): 1568–1584.
Galambos J (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York, 352 pp.
Gardenier JS, Gardenier TK (1988) Statistics of risk management. In: Kotz S, Johnson NL, Read CB (Eds) Encyclopedia of statistical sciences, volume 8. Wiley, New York, pp 141–148.
Gasser T, Müller H-G (1979) Kernel estimation of regression functions. In: Gasser T, Rosenblatt M (Eds) Smoothing Techniques for Curve Estimation. Springer, Berlin, pp 23–68.
Gençay R, Selçuk F, Ulugülyağci A (2001) EVIM: A software package for extreme value analysis in MATLAB. Studies in Nonlinear Dynamics & Econometrics 5(3): 213–239.
Grünewald U, Chmielewski R, Kaltofen M, Rolland W, Schümberg S, Ahlheim M, Sauer T, Wagner R, Schluchter W, Birkner H, Petzold R, Radczuk L, Eliasiewicz R, Bjarsch B, Paus L, Zahn G (1998) Ursachen, Verlauf und Folgen des Sommer-Hochwassers 1997 an der Oder sowie Aussagen zu bestehenden Risikopotentialen. Eine interdisziplinäre Studie –- Langfassung. Deutsches IDNDR-Komitee für Katastrophenvorbeugung e.V., Bonn, 187 pp.
Girardin MP, Bergeron Y, Tardif JC, Gauthier S, Flannigan MD, Mudelsee M (2006b) A 229-year dendroclimatic-inferred record of forest fire activity for the Boreal Shield of Canada. International Journal of Wildland Fire 15(3): 375–388.
Girardin MP, Mudelsee M (2008) Past and future changes in Canadian boreal wildfire activity. Ecological Applications 18(2): 391–406.
Gnedenko B (1943) Sur la distribution limite du terme maximum d’une série aléatoire. Annals of Mathematics 44(3): 423–453. [English translation in: Kotz S, Johnson NL (Eds) (1992) Breakthroughs in Statistics, volume 1. Springer, New York, pp 195–225]
Goldenberg SB, Landsea CW, Mestas-Nuñez AM, Gray WM (2001) The recent increase in Atlantic hurricane activity: Causes and implications. Science 293(5529): 474–479.
Greenwood JA, Landwehr JM, Matalas NC, Wallis JR (1979) Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research 15(5): 1049–1054.
Gumbel EJ (1958) Statistics of Extremes. Columbia University Press, New York, 375 pp.
Hall P, Peng L, Tajvidi N (2002) Effect of extrapolation on coverage accuracy of prediction intervals computed from Pareto-type data. The Annals of Statistics 30(3): 875–895.
Hall P, Tajvidi N (2000) Nonparametric analysis of temporal trend when fitting parametric models to extreme-value data. Statistical Science 15(2): 153–167.
Hall P, Weissman I (1997) On the estimation of extreme tail probabilities. The Annals of Statistics 25(3): 1311–1326.
Hewa GA, Wang QJ, McMahon TA, Nathan RJ, Peel MC (2007) Generalized extreme value distribution fitted by LH moments for low-flow frequency analysis. Water Resources Research 43(6): W06301. [doi:10.1029/2006WR004913]
Hill BM (1975) A simple general approach to inference about the tail of a distribution. The Annals of Statistics 3(5): 1163–1174.
Holland GJ (2007) Misuse of landfall as a proxy for Atlantic tropical cyclone activity. Eos, Transactions of the American Geophysical Union 88(36): 349–350.
Hosking JRM (1985) Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. Applied Statistics 34(3): 301–310.
Hosking JRM (1990) L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B 52(1): 105–124.
Hosking JRM, Wallis JR (1987) Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29(3): 339–349.
Hosking JRM, Wallis JR (1997) Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge, 224 pp.
Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme value distribution by the method of probability-weighted moments. Technometrics 27(3): 251–261.
Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society 81(348): 158–171.
Johnson NL, Kotz S, Balakrishnan N (1994) Continuous Univariate Distributions, volume 1. Second edition. Wiley, New York, 756 pp.
Johnson NL, Kotz S, Balakrishnan N (1995) Continuous Univariate Distributions, volume 2. Second edition. Wiley, New York, 719 pp.
Jones MC, Lotwick HW (1984) A remark on algorithm AS 176. Kernel density estimation using the Fast Fourier Transform. Applied Statistics 33(1): 120–122.
Kallache M (2007) Trends and Extreme Values of River Discharge Time Series. Ph.D. Dissertation. University of Bayreuth, Bayreuth, 125 pp.
Karr AF (1986) Point Processes and Their Statistical Inference. Marcel Dekker, New York, 490 pp.
Katz RW, Parlange MB, Naveau P (2002) Statistics of extremes in hydrology. Advances in Water Resources 25(8–12): 1287–1304.
Keigwin LD (1996) The Little Ice Age and Medieval Warm Period in the Sargasso Sea. Science 274(5292): 1504–1508.
Khaliq MN, Ouarda TBMJ, Ondo J-C, Gachon P, Bobée B (2006) Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review. Journal of Hydrology 329(3–4): 534–552.
Khaliq MN, St-Hilaire A, Ouarda TBMJ, Bobée B (2005) Frequency analysis and temporal pattern of occurrences of southern Quebec heatwaves. International Journal of Climatology 25(4): 485–504.
Kharin VV, Zwiers FW (2005) Estimating extremes in transient climate change simulations. Journal of Climate 18(8): 1156–1173.
Knutson TR, McBride JL, Chan J, Emanuel K, Holland G, Landsea C, Held I, Kossin JP, Srivastava AK, Sugi M (2010) Tropical cyclones and climate change. Nature Geoscience 3(3): 157–163.
Kotz S, Nadarajah S (2000) Extreme value distributions: Theory and applications. Imperial College Press, London, 187 pp.
Kullback S (1983) Fisher information. In: Kotz S, Johnson NL, Read CB (Eds) Encyclopedia of statistical sciences, volume 3. Wiley, New York, pp 115–118.
Kürbis K, Mudelsee M, Tetzlaff G, Brázdil R (2009) Trends in extremes of temperature, dew point, and precipitation from long instrumental series from central Europe. Theoretical and Applied Climatology 98(1–2): 187–195.
Kyselý J (2002) Temporal fluctuations in heat waves at Prague–Klementinum, the Czech Republic, from 1901–97, and their relationships to atmospheric circulation. International Journal of Climatology 22(1): 33–50.
Kyselý J (2008) A cautionary note on the use of nonparametric bootstrap for estimating uncertainties in extreme-value models. Journal of Applied Meteorology and Climatology 47(12): 3236–3251.
Landsea CW (2007) Counting Atlantic tropical cyclones back to 1900. Eos, Transactions of the American Geophysical Union 88(18): 197, 202.
Landsea CW, Glenn DA, Bredemeyer W, Chenoweth M, Ellis R, Gamache J, Hufstetler L, Mock C, Perez R, Prieto R, Sánchez-Sesma J, Thomas D, Woolcock L (2008) A reanalysis of the 1911–20 Atlantic hurricane database. Journal of Climate 21(10): 2138–2168.
Landsea CW, Nicholls N, Gray WM, Avila LA (1996) Downward trends in the frequency of intense Atlantic hurricanes during the past five decades. Geophysical Research Letters 23(13): 1697–1700.
Landsea CW, Nicholls N, Gray WM, Avila LA (1997) Reply. Geophysical Research Letters 24(17): 2205.
Landsea CW, Pielke Jr RA, Mestas-Nuñez AM, Knaff JA (1999) Atlantic basin hurricanes: Indices of climatic changes. Climatic Change 42(1): 89–129.
Landsea CW, Vecchi GA, Bengtsson L, Knutson TR (2010) Impact of duration thresholds on Atlantic tropical cyclone counts. Journal of Climate 23(10): 2508–2519. [doi:10.1175/2009JCLI3034.1]
Lang M, Ouarda TBMJ, Bobée B (1999) Towards operational guidelines for over-threshold modeling. Journal of Hydrology 225(3–4): 103–117.
Leadbetter MR, Lindgren G, Rootzén H (1983) Extremes and Related Properties of Random Sequences and Processes. Springer, New York, 336 pp.
Leadbetter MR, Rootzén H (1988) Extremal theory for stochastic processes. The Annals of Probability 16(2): 431–478.
Ledford AW, Tawn JA (2003) Diagnostics for dependence within time series extremes. Journal of the Royal Statistical Society, Series B 65(2): 521–543.
Loader CR (1992) A log-linear model for a Poisson process change point. The Annals of Statistics 20(3): 1391–1411.
Lu L-H, Stedinger JR (1992) Variance of two- and three-parameter GEV/PWM quantile estimators: Formulae, confidence intervals, and a comparison. Journal of Hydrology 138(1–2): 247–267.
Luterbacher J, Rickli R, Xoplaki E, Tinguely C, Beck C, Pfister C, Wanner H (2001) The late Maunder Minimum (1675–1715)–-A key period for studying decadal scale climatic change in Europe. Climatic Change 49(4): 441–462.
Macleod AJ (1989) A remark on algorithm AS 215: Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution. Applied Statistics 38(1): 198–199.
Mann ME, Emanuel KA (2006) Atlantic hurricane trends linked to climate change. Eos, Transactions of the American Geophysical Union 87(24): 233, 238, 241.
Mann ME, Emanuel KA, Holland GJ, Webster PJ (2007a) Atlantic tropical cyclones revisited. Eos, Transactions of the American Geophysical Union 88(36): 349–350.
Mann ME, Woodruff JD, Donnelly JP, Zhang Z (2009) Atlantic hurricanes and climate over the past 1,500 years. Nature 460(7257): 880–883.
Martins ES, Stedinger JR (2000) Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research 36(3): 737–744.
Martins ES, Stedinger JR (2001) Generalized maximum likelihood Pareto–Poisson estimators for partial duration series. Water Resources Research 37(10): 2551–2557.
Meehl GA, Tebaldi C (2004) More intense, more frequent, and longer lasting heat waves in the 21st century. Science 305(5686): 994–997.
Meehl GA, Zwiers F, Evans J, Knutson T, Mearns L, Whetton P (2000) Trends in extreme weather and climate events: Issues related to modeling extremes in projections of future climate change. Bulletin of the American Meteorological Society 81(3): 427–436.
Michener WK, Blood ER, Bildstein KL, Brinson MM, Gardner LR (1997) Climate change, hurricanes and tropical storms, and rising sea level in coastal wetlands. Ecological Applications 7(3): 770–801.
Monro DM (1975) Complex discrete Fast Fourier Transform. Applied Statistics 24(1): 153–160.
Monro DM (1976) Real discrete Fast Fourier Transform. Applied Statistics 25(2): 166–172.
Mudelsee M (1999) On an interesting statistical problem imposed by an ice core. Institute of Mathematics and Statistics, University of Kent, Canterbury, 12 pp. [Technical Report UKC/IMS/99/21]
Mudelsee M, Börngen M, Tetzlaff G, Grünewald U (2003) No upward trends in the occurrence of extreme floods in central Europe. Nature 425(6954): 166–169. [Corrigendum: Insert in Eq. (1) on the right-hand side a factor \({{h}^{-1}}\) before the sum sign.]
Mudelsee M, Deutsch M, Börngen M, Tetzlaff G (2006) Trends in flood risk of the River Werra (Germany) over the past 500 years. Hydrological Sciences Journal 51(5): 818–833.
Mueller M (2003) Damages of the Elbe flood 2002 in Germany–-A review. Geophysical Research Abstracts 5: 12992.
Naveau P, Nogaj M, Ammann C, Yiou P, Cooley D, Jomelli V (2005) Statistical methods for the analysis of climate extremes. Comptes Rendus Geoscience 337(10–11): 1013–1022.
Nogaj M, Yiou P, Parey S, Malek F, Naveau P (2006) Amplitude and frequency of temperature extremes over the North Atlantic region. Geophysical Research Letters 33(10): L10801. [doi:10.1029/2005GL024251]
Nyberg J, Malmgren BA, Winter A, Jury MR, Kilbourne KH, Quinn TM (2007) Low Atlantic hurricane activity in the 1970s and 1980s compared to the past 270 years. Nature 447(7145): 698–701.
Parent E, Bernier J (2003a) Bayesian POT modeling for historical data. Journal of Hydrology 274(1–4): 95–108.
Parent E, Bernier J (2003b) Encoding prior experts judgments to improve risk analysis of extreme hydrological events via POT modeling. Journal of Hydrology 283(1–4): 1–18.
Pauli F, Coles S (2001) Penalized likelihood inference in extreme value analyses. Journal of Applied Statistics 28(5): 547–560.
Pickands III J (1975) Statistical inference using extreme order statistics. The Annals of Statistics 3(1): 119–131.
Pielke Jr RA, Landsea C, Mayfield M, Laver J, Pasch R (2005) Hurricanes and global warming. Bulletin of the American Meteorological Society 86(11): 1571–1575.
Pielke Jr RA, Landsea CW (1998) Normalized hurricane damages in the United States: 1925–95. Weather and Forecasting 13(3): 621–631.
Prescott P, Walden AT (1980) Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67(3): 723–724.
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran 77: The Art of Scientific Computing. Second edition. Cambridge University Press, Cambridge, 933 pp.
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1996) Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing. Second edition. Cambridge University Press, Cambridge, pp 935–1486.
Pujol N, Neppel L, Sabatier R (2007) Regional tests for trend detection in maximum precipitation series in the French Mediterranean region. Hydrological Sciences Journal 52(5): 956–973.
Ramesh NI, Davison AC (2002) Local models for exploratory analysis of hydrological extremes. Journal of Hydrology 256(1–2): 106–119.
Rao AR, Hamed KH (2000) Flood Frequency Analysis. CRC Press, Boca Raton, FL, 350 pp.
Reis Jr DS, Stedinger JR (2005) Bayesian MCMC flood frequency analysis with historical information. Journal of Hydrology 313(1–2): 97–116.
Reiss R-D, Thomas M (1997) Statistical Analysis of Extreme Values. Birkhäuser, Basel, 316 pp.
Resnick SI (1987) Extreme Values, Regular Variation, and Point Processes. Springer, New York, 320 pp.
Robock A (2000) Volcanic eruptions and climate. Reviews of Geophysics 38(2): 191–219.
Rust HW, Maraun D, Osborn TJ (2009) Modelling seasonality in extreme precipitation: A UK case study. European Physical Journal Special Topics 174(1): 99–111.
Sankarasubramanian A, Lall U (2003) Flood quantiles in a changing climate: Seasonal forecasts and causal relations. Water Resources Research 39(5): 1134. [doi:10.1029/2002WR001593]
Sercl P, Stehlik J (2003) The August 2002 flood in the Czech Republic. Geophysical Research Abstracts 5: 12404.
Silverman BW (1982) Kernel density estimation using the Fast Fourier Transform. Applied Statistics 31(1): 93–99.
Smith RL (1985) Maximum likelihood estimation in a class of nonregular cases. Biometrika 72(1): 67–90.
Smith RL (1987) Estimating tails of probability distributions. The Annals of Statistics 15(3): 1174–1207.
Smith RL (1989) Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone (with discussion). Statistical Science 4(4): 367–393.
Smith RL (2004) Statistics of extremes, with applications in environment, insurance, and finance. In: Finkenstädt B, Rootzén H (Eds) Extreme Values in Finance, Telecommunications, and the Environment. Chapman and Hall, Boca Raton, FL, pp 1–78.
Smith RL, Shively TS (1994) A Point Process Approach to Modeling Trends in Tropospheric Ozone Based on Exceedances of a High Threshold. National Institute of Statistical Sciences, Research Triangle Park, NC, 20 pp. [Technical Report Number 16]
Smith RL, Shively TS (1995) Point process approach to modeling trends in tropospheric ozone based on exceedances of a high threshold. Atmospheric Environment 29(23): 3489–3499.
Smith RL, Tawn JA, Coles SG (1997) Markov chain models for threshold exceedances. Biometrika 84(2): 249–268.
Solomon S, Qin D, Manning M, Marquis M, Averyt K, Tignor MMB, Miller Jr HL, Chen Z (Eds) (2007) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, 996 pp.
Solow AR (1991) An exploratory analysis of the occurrence of explosive volcanism in the northern hemisphere, 1851–1985. Journal of the American Statistical Association 86(413): 49–54.
Strupczewski WG, Kaczmarek Z (2001) Non-stationary approach to at-site flood frequency modelling II. Weighed least squares estimation. Journal of Hydrology 248(1–4): 143–151.
Strupczewski WG, Singh VP, Feluch W (2001a) Non-stationary approach to at-site flood frequency modelling I. Maximum likelihood estimation. Journal of Hydrology 248(1-4): 123–142.
Strupczewski WG, Singh VP, Mitosek HT (2001b) Non-stationary approach to at-site flood frequency modelling. III. Flood analysis of Polish rivers. Journal of Hydrology 248(1–4): 152–167.
Thywissen K (2006) Components of Risk: A Comparative Glossary. United Nations University, Institute for Environment and Human Security, Bonn, 48 pp. [Studies of the University: Research, Counsel, Education No. 2]
Ulbrich U, Brücher T, Fink AH, Leckebusch GC, Krüger A, Pinto JG (2003a) The central European floods of August 2002: Part 1 – Rainfall periods and flood development. Weather 58(10): 371–377.
Van Montfort MAJ, Witter JV (1985) Testing exponentiality against generalised Pareto distribution. Journal of Hydrology 78(3–4): 305–315.
Vecchi GA, Knutson TR (2008) On estimates of historical North Atlantic tropical cyclone activity. Journal of Climate 21(14): 3580–3600.
WAFO group (2000) WAFO: A Matlab Toolbox for Analysis of Random Waves and Loads. Lund Institute of Technology, Lund University, Lund, 111 pp.
Wagenbach D (1989) Environmental records in Alpine glaciers. In: Oeschger H, Langway Jr CC (Eds) The Environmental Record in Glaciers and Ice Sheets. Wiley, Chichester, pp 69–83.
Wagenbach D, Preunkert S, Schäfer J, Jung W, Tomadin L (1996) Northward transport of Saharan dust recorded in a deep Alpine ice core. In: Guerzoni S, Chester R (Eds) The Impact of Desert Dust Across the Mediterranean. Kluwer, Dordrecht, pp 291–300.
Weikinn C (2000) Quellentexte zur Witterungsgeschichte Europas von der Zeitwende bis zum Jahr 1850: Hydrographie, Teil 5 (1751–1800). Gebrüder Borntraeger, Berlin, 674 pp. [Börngen M, Tetzlaff G (Eds)]
Wilson RM (1997) Comment on “Downward trends in the frequency of intense Atlantic hurricanes during the past 5 decades” by C. W. Landsea et al. Geophysical Research Letters 24(17): 2203–2204.
Worsley KJ (1986) Confidence regions and tests for a change-point in a sequence of exponential family random variables. Biometrika 73(1): 91–104.
Yee TW, Wild CJ (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B 58(3): 481–493.
Yiou P, Ribereau P, Naveau P, Nogaj M, Brázdil R (2006) Statistical analysis of floods in Bohemia (Czech Republic) since 1825. Hydrological Sciences Journal 51(5): 930–945.
Zhang X, Zwiers FW, Li G (2004) Monte Carlo experiments on the detection of trends in extreme values. Journal of Climate 17(10): 1945–1952.
Zielinski GA, Mayewski PA, Meeker LD, Whitlow S, Twickler MS (1996) A 110,000-yr record of explosive volcanism from the GISP2 (Greenland) ice core. Quaternary Research 45(2): 109–118.
Zielinski GA, Mayewski PA, Meeker LD, Whitlow S, Twickler MS, Morrison M, Meese DA, Gow AJ, Alley RB (1994) Record of volcanism since 7000 B.C. from the GISP2 Greenland ice core and implications for the volcano-climate system. Science 264(5161): 948–952.
Prueher LM, Rea DK (2001) Volcanic triggering of late Pliocene glaciation: Evidence from the flux of volcanic glass and ice-rafted debris to the North Pacific Ocean. Palaeogeography, Palaeoclimatology, Palaeoecology 173(3–4): 215–230.
Metadata
Title
Extreme Value Time Series
Author
Dr. Manfred Mudelsee
Copyright Year
2010
Publisher
Springer Netherlands
Book
Climate Time Series Analysis

Print ISBN: 978-90-481-9481-0

Electronic ISBN: 978-90-481-9482-7

Copyright Year: 2010

DOI
https://doi.org/10.1007/978-90-481-9482-7_6