Extreme Value Time Series

2014 ◽  
pp. 217-267
Author(s):  
Manfred Mudelsee
Keyword(s):  
Time Series ◽  
Extreme Value

Efficient filtering of financial time series and extreme value theory

2005 ◽  
Vol 7 (2) ◽  
pp. 63-84 ◽  
Author(s):  
Kaj Nyström ◽  
Jimmy Skoglund
Keyword(s):  
Time Series ◽  
Extreme Value Theory ◽  
Financial Time Series ◽  
Value Theory ◽  
Extreme Value ◽  
Financial Time

On the Probability Distribution of Mooring Line Tensions in a Directional Environment

2011 ◽  
Author(s):  
Jan Mathisen ◽  
Siril Okkenhaug ◽  
Kjell Larsen
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Extreme Value ◽  
Mooring Line ◽  
Large Set ◽  
Short Term ◽  
Reliability Method ◽  
Line Design

A joint probabilistic model of the metocean environment is assembled, taking account of wind, wave and current and their respective heading angles. Mooring line tensions are computed in the time domain, for a large set of short-term stationary conditions, intended to span the domain of metocean conditions that contribute significantly to the probabilities of high tensions. Weibull probability distributions are fitted to local tension maxima extracted from each time series. Long time series of 30 hours duration are used to reduce statistical uncertainty. Short-term, Gumbel extreme value distributions of line tension are derived from the maxima distributions. A response surface is fitted to the distribution parameters for line tension, to allow interpolation between the metocean conditions that have been explicitly analysed. A second order reliability method is applied to integrate the short-term tension distributions over the probability of the metocean conditions and obtain the annual extreme value distribution of line tension. Results are given for the most heavily loaded mooring line in two mooring systems: a mobile drilling unit and a production platform. The effects of different assumptions concerning the distribution of wave heading angles in simplified analysis for mooring line design are quantified by comparison with the detailed calculations.

scholarly journals Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory

2010 ◽  
Vol 10 (20) ◽  
pp. 10021-10031 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Distribution ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Total Ozone ◽  
Volcanic Eruptions ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Ozone Data

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.

The Extreme Value Evolving Predictor in Multiple Time Series Learning

2021 ◽  
pp. 285-295
Author(s):  
Amanda O. C. Ayres ◽  
Fernando J. Von Zuben
Keyword(s):  
Time Series ◽  
Extreme Value ◽  
Multiple Time ◽  
Multiple Time Series

scholarly journals Selecting Time Series Length to Moderate the Impact of Nonstationarity in Extreme Rainfall Analyses

2018 ◽  
Vol 57 (10) ◽  
pp. 2285-2296 ◽  
Author(s):  
Arthur T. DeGaetano ◽  
Christopher Castellano
Keyword(s):  
Time Series ◽  
Location Parameter ◽  
Extreme Rainfall ◽  
Extreme Value ◽  
Series Length ◽  
Limited Length ◽  
Long Term Trends ◽  
Recurrence Intervals ◽  
Stationary Location ◽  
The Impact

AbstractObserved and projected increases in the frequency of extreme rainfall complicate the extreme value analyses of precipitation that are used to guide engineering design specifications, because conventional methods assume stationarity. Uncertainty in the magnitude of the trend in future years precludes directly accounting for the trend in these analyses. While previous extreme value analyses have sought to use as long a record as possible, it is shown using stochastically generated time series that this practice exacerbates the potential error introduced by long-term trends. For extreme precipitation series characterized by a trend in the location parameter exceeding approximately 0.005% yr−1, limiting the record length to fewer than 70 years is recommended. The use of longer time periods results in partial-duration series that are significantly different from their stationary counterparts and a greater percentage of rainfall extremes that exceed the 90% confidence interval corresponding to a stationary distribution. The effect is most pronounced on the shortest (i.e., 2 yr) recurrence intervals and generally becomes undetectable for recurrence intervals of more than 25 years. The analyses also indicate that the practice of including stations with records of limited length that end several decades prior to the present should be avoided. Distributions having a stationary location parameter but trended scale parameter do not exhibit this behavior.

Nonstationary Extreme-Value Predictions in the Gulf of Mexico

2007 ◽  
Author(s):  
Christos N. Stefanakos
Keyword(s):  
Time Series ◽  
Gulf Of Mexico ◽  
Wave Height ◽  
Missing Values ◽  
Extreme Value ◽  
Altimeter Data ◽  
Dependence Structure ◽  
Measured Time ◽  
Definition Of

In the present work, return periods of various level values of significant wave height in the Gulf of Mexico are given. The predictions are based on a new method for nonstationary extreme-value calculations that have recently been published. This enhanced method exploits efficiently the nonstationary modeling of wind or wave time series and a new definition of return period using the MEan Number of Upcrossings of the level value x* (MENU method). The whole procedure is applied to long-term measurements of wave height in the Gulf of Mexico. Two kinds of data have been used: long-term time series of buoy measurements, and satellite altimeter data. Measured time series are incomplete and a novel procedure for filling in of missing values is applied before proceeding with the extreme-value calculations. Results are compared with several variants of traditional methods, giving more realistic estimates than the traditional predictions. This is in accordance with the results of other methods that take also into account the dependence structure of the examined time series.

Estimation of Most Probable Maximum From Short-Duration or Undersampled Time-Series Data

2015 ◽  
Author(s):  
Puneet Agarwal ◽  
William Walker ◽  
Kenneth Bhalla
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Short Duration ◽  
Time Series Data ◽  
Extreme Value ◽  
Series Data ◽  
Sampled Data ◽  
Zero Crossing ◽  
Short Time ◽  
Undersampled Data

The most probable maximum (MPM) is the extreme value statistic commonly used in the offshore industry. The extreme value of vessel motions, structural response, and environment are often expressed using the MPM. For a Gaussian process, the MPM is a function of the root-mean square and the zero-crossing rate of the process. Accurate estimates of the MPM may be obtained in frequency domain from spectral moments of the known power spectral density. If the MPM is to be estimated from the time-series of a random process, either from measurements or from simulations, the time series data should be of long enough duration, sampled at an adequate rate, and have an ensemble of multiple realizations. This is not the case when measured data is recorded for an insufficient duration, or one wants to make decisions (requiring an estimate of the MPM) in real-time based on observing the data only for a short duration. Sometimes, the instrumentation system may not be properly designed to measure the dynamic vessel motions with a fine sampling rate, or it may be a legacy instrumentation system. The question then becomes whether the short-duration and/or the undersampled data is useful at all, or if some useful information (i.e., an estimate of MPM) can be extracted, and if yes, what is the accuracy and uncertainty of such estimates. In this paper, a procedure for estimation of the MPM from the short-time maxima, i.e., the maximum value from a time series of short duration (say, 10 or 30 minutes), is presented. For this purpose pitch data is simulated from the vessel RAOs (response amplitude operators). Factors to convert the short-time maxima to the MPM are computed for various non-exceedance levels. It is shown that the factors estimated from simulation can also be obtained from the theory of extremes of a Gaussian process. Afterwards, estimation of the MPM from the short-time maxima is explored for an undersampled process; however, undersampled data must not be used and only the adequately sampled data should be utilized. It is found that the undersampled data can be somewhat useful and factors to convert the short-time maxima to the MPM can be derived for an associated non-exceedance level. However, compared to the adequately sampled data, the factors for the undersampled data are less useful since they depend on more variables and have more uncertainty. While the vessel pitch data was the focus of this paper, the results and conclusions are valid for any adequately sampled narrow-banded Gaussian process.

scholarly journals Short-duration rainfall extremes in Sweden: a regional analysis

2019 ◽  
Vol 50 (3) ◽  
pp. 945-960 ◽  
Author(s):  
Jonas Olsson ◽  
Johan Södling ◽  
Peter Berg ◽  
Lennart Wern ◽  
Anna Eronn
Keyword(s):  
Time Series ◽  
Short Duration ◽  
Regional Analysis ◽  
Generalized Pareto Distribution ◽  
Extreme Value ◽  
Northern Region ◽  
Generalized Extreme Value Distribution ◽  
Return Periods ◽  
Station Coordinates ◽  
Rainfall Extremes

Abstract We investigate short-duration rainfall extremes in a 22-year long (1996–2017) time series of 15-min values from 128 stations in Sweden. Two different approaches are used to fit extreme value distributions (EVDs) to the data: generalized extreme value distribution with annual maximum values and generalized Pareto distribution with peak-over-threshold values. First, EVDs are fitted to the data from each station, and the extreme value parameters are used together with the station coordinates in a cluster analysis. Based on the clustering results, a division of Sweden into four regions is proposed. Following the station-year method, the time series from all stations in each cluster are pooled into regional series after which depth–duration–frequency (DDF) statistics are calculated. Averaged over durations and return periods, the highest DDF values are found in region south-west, being ∼25% higher than the lowest ones found in the northern region. A six-parameter DDF function is proposed which, together with a simple empirical expression for the associated confidence interval, allows for easy DDF estimation at arbitrary durations and return periods, including uncertainty. No tendencies of change in magnitude or frequency of the short-duration extremes are found during the period.

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