Estimating long-range dependence in the presence of periodicity: An empirical study

Montanari, Alberto; Taqqu, Murad S.; Teverovsky, Vadim

doi:10.1016/s0895-7177(99)00104-1

Cited by 134 publications

(112 citation statements)

References 18 publications

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“…tens of years, hundreds of years, etc.). It has been proposed that such fluctuations, either periodical or irregular, occurring either on a single time scale or on multiple time scales simultaneously, constitute the physical basis of the well-known Hurst phenomenon (Klemeš, 1974;Montanari et al, 1999;Koutsoyiannis, 2002). Here it should be noted that such fluctuations may not be detected in series of maxima, which typically satisfy Leadbetter's (1974) condition of the absence of long-range dependence, but surely affect the parent distribution of rainfall at low-and intermediate-level exceedences.…”

Section: Theoretical Study Of the Appropriateness Of The Gumbel Distrmentioning

confidence: 97%

Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

Koutsoyiannis

2004

Hydrological Sciences Journal

196

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The Gumbel distribution has been the prevailing model for quantifying risk associated with extreme rainfall. Several arguments including theoretical reasoning and empirical evidence are supposed to support the appropriateness of the Gumbel distribution. These arguments are examined thoroughly in this work and are put into question. Specifically, theoretical analyses show that the Gumbel distribution is quite unlikely to apply to hydrological extremes and its application may misjudge the risk, as it underestimates seriously the largest extreme rainfall amounts. Besides, it is shown that hydrological records of typical length (some decades) may display a distorted picture of the actual distribution, suggesting that the Gumbel distribution is an appropriate model for rainfall extremes while it is not. In addition, it is shown that the extreme value distribution of type II (EV2) is a more consistent alternative. Based on the theoretical analysis, in the second part of this study an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100-154 years of data. This verifies the inappropriateness of the Gumbel distribution and the appropriateness of EV2 distribution for rainfall extremes.Key words design rainfall; extreme rainfall; generalized extreme value distribution; Gumbel distribution; hydrological design; hydrological extremes; probable maximum precipitation; risk Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théoriqueRésumé La distribution de Gumbel a longtemps été le modèle régnant pour la quantification du risque associé aux précipitations extrêmes. Plusieurs arguments comprenant à la fois un raisonnement théorique et des faits empiriques sont censés soutenir la pertinence de la distribution de Gumbel. Ces arguments sont examinés exhaustivement dans ce travail et sont mis en question. Spécifiquement, des analyses théoriques montrent que la distribution de Gumbel est peu susceptible de s'appliquer aux valeurs extrêmes de variables hydrologiques et que son application peut conduire à une mauvaise estimation du risque par une sérieuse sous-estimation des plus grandes valeurs extrêmes de précipitations. En outre, il est montré que les séries hydrologiques de longueur typique (quelques décennies) peuvent montrer une image déformée de la distribution réelle, ce qui suggère que la distribution de Gumbel est le modèle approprié pour les précipitations extrêmes alors qu'elle ne l'est pas. En outre, on montre que la distribution de valeurs extrêmes du type II (EV2) est une alternative plus cohérente. Dans la deuxième partie de cette étude, une recherche empirique étendue est effectuée, en se basant sur l'analyse théorique, avec une collection de 169 séries de précipitations, parmi les plus longues de celles qui sont disponibles dans le monde entier, comportant chacune 100-154 ans de données. Ceci permet de vérifier la non-pertinence de la distribution de Gumbel et la pertinence de la dist...

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Section: Theoretical Study Of the Appropriateness Of The Gumbel Distrmentioning

confidence: 97%

Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

Koutsoyiannis

2004

Hydrological Sciences Journal

196

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“…There are a lot of methods developed to extract temporal correlation in time series, among which the detrended fluctuation analysis (DFA) is the most popular method due to its easy implementation and robust estimation even for short time series [33,34,35]. DFA was invented originally to study the longrange dependence in coding and noncoding DNA nucleotides sequence [36] and then applied to various fields including finance.…”

Section: Detrended Fluctuation Analysismentioning

confidence: 99%

Statistical properties of daily ensemble variables in the Chinese stock markets

Zhou

2007

Physica A: Statistical Mechanics and its Applications

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We study dynamical behavior of the Chinese stock markets by investigating the statistical properties of daily ensemble returns and varieties defined respectively as the mean and the standard deviation of the ensemble daily price returns of a portfolio of stocks traded in China's stock markets on a given day. The distribution of the daily ensemble returns has an exponential form in the center and power-law tails, while the variety distribution is log-Gaussian in the bulk followed by a powerlaw tail for large varieties. Based on detrended fluctuation analysis, R/S analysis and modified R/S analysis, we find evidence of long memory in the ensemble returns and strong evidence of long memory in the evolution of variety.

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“…The most usual records of observable quantities in real world are in the form of time series and their fractal and multifractal properties have been extensively investigated. There are many methods proposed for this purpose [2,3]. For a single nonstationary time series, the detrended fluctuation analysis (DFA) can be adopted to explore its long-range autocorrelations [4,5] and multifractal features [6].…”

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confidence: 99%