Extremes and local dependence in stationary sequences

Leadbetter, M. R.

doi:10.1007/bf00532484

Cited by 350 publications

(234 citation statements)

References 13 publications

Supporting

Mentioning

231

Contrasting

Order By: Relevance

“…The notion of the EI was latent in the work of Loynes [124] but was established formally by Leadbetter in [122]. The parameter θ quantifies the strength of the dependence of X 0 , X 1 , .…”

Section: Definition 324mentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

194

253

View full text Add to dashboard Cite

ii 4.1.2 The New Conditions 44 4.1.3 The Existence of EVL for General Stationary Stochastic Processes under Weaker Hypotheses 46 4.1.4 Proofs of Theorem 4.1.4 and Corollary 4.1.5 48 4.2 Extreme Values for Dynamically Defined Stochastic Processes 53 4.2.1 Observables and Corresponding Extreme Value Laws 55 4.2.2 Extreme Value Laws for Uniformly Expanding Systems 59 4.2.3 Example 4.2.1 revisited 61 4.2.4 Proof of the Dichotomy for Uniformly Expanding Maps 63 4.3 Point Processes of Rare Events 64 4.3.1 Absence of Clustering 64 4.3.2 Presence of Clustering 65 4.3.3 Dichotomy for Uniformly Expanding Systems for Point Processes 67 4.4 Conditions Д q (u n ), D 3 (u n ), D p (u n ) * and Decay of Correlations 68 4.5 Specific Dynamical Systems where the Dichotomy Applies 71 4.5.1 Rychlik Systems 72 4.5.2 Piecewise Expanding Maps in Higher Dimensions 73 4.6 Extreme Value Laws for Physical Observables 74

show abstract

Section: Definition 324mentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

194

253

View full text Add to dashboard Cite

show abstract

“…A generalization of the GEV theorem holds for time series that are realizations of stationary stochastic processes such that the long-range dependence is weak at extreme levels (Leadbetter 1974(Leadbetter , 1983. In the applications, this property is assumed to hold whenever the block maxima are uncorrelated for sufficiently large block sizes.…”

Section: Gev Modelling For Non-stationary Time Series 3a Stationary mentioning

confidence: 99%

Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

Felici

Lucarini

Speranza

et al. 2007

Journal of the Atmospheric Sciences

View full text Add to dashboard Cite

A baroclinic model for the atmospheric jet at middle-latitudes is used as a stochastic generator of non-stationary time series of the total energy of the system. A linear time trend is imposed on the parameter T E , descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent Generalized Extreme Value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location µ and scale parameters σ depend quadratically and linearly on time, respectively, while the shape parameter ξ is kept constant. From this family, a model is selected by using diagnostic graphical tools, such as probability and quantile plots, and by means of the likelihood ratio test. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on T E . In particular, power-law dependences of µ and σ on T E are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of T E spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

show abstract

“…It is widely used for analysis of hydrologic extremes (Stedinger and Lu, 1995;Hosking and Wallis, 1996;Katz et al, 2002). This is a continuous distribution with three parameters (location, scale, and shape), and represents the limiting distribution resulting from maxima of identically distributed and independent or weakly dependent random variables (Leadbetter, 1983). In previous studies (Morrison and Smith, 2002;Northrop, 2004;Lima and Lall, 2010;Villarini et al, 2011aVillarini et al, , 2011d, the location and scale parameters were found to scale linearly in the log-log domain (power law behaviour).…”

mentioning

confidence: 99%

Analyses of extreme flooding in Austria over the period 1951–2006

Villarini

Smith

Serinaldi

et al. 2011

Intl Journal of Climatology

102

View full text Add to dashboard Cite

ABSTRACT:Analyses of extreme flooding in Austria is performed using daily discharge time series from 27 stations over the period . The main research questions revolve around: (1) temporal non-stationarities in the flood record, (2) upper tail and scaling properties of the flood peak records, and (3) relation between magnitude and frequency of flooding and the North Atlantic Oscillation (NAO). Two datasets are derived from the daily discharge time series: annual maximum daily discharge and peaks-over-threshold (POT) data. The validity of the stationarity assumption in the annual maximum discharge record is assessed by investigating the presence of abrupt and slowly varying changes using nonparametric tests. The time series are tested for abrupt changes both in the mean and variance of the flood peak distributions by means of the Pettitt test. The presence of monotonic trends is investigated by means of the Mann-Kendall and Spearman tests. Violations of the stationarity assumption are associated with abrupt rather than gradual changes. These step changes generally involve river regulation through construction of dams or other major engineering works. It is not possible to make conclusive statements about the presence of an anthropogenic climate change signal in the flood peak record. Similar conclusions are obtained when focussing on the frequency of POT floods. The Generalised Extreme Value distribution is used to study the upper tail and scaling properties of annual maximum daily discharge records. The location and scale parameters exhibit power-law behaviour as a function of drainage area. The shape parameters indicate that the flood peak distributions for Austria have a heavy tail. Non-stationary modelling of the annual maximum daily discharge and POT time series is used to explore the relation between flood magnitude and frequency and NAO. The results indicate that NAO is a significant covariate in explaining the magnitude and frequency of occurrence of flooding over a large part of Austria.

show abstract

Extremes and local dependence in stationary sequences

Cited by 350 publications

References 13 publications

Extremes and Recurrence in Dynamical Systems

Extremes and Recurrence in Dynamical Systems

Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

Analyses of extreme flooding in Austria over the period 1951–2006

Contact Info

Product

Resources

About