Trend Detection in the Presence of Positive and Negative Serial Correlation: A Comparison of Block Maxima and Peaks‐Over‐threshold Data

2021 ◽  
Vol 57 (4) ◽  
Author(s):  
N. L. O’Brien ◽  
D. H. Burn ◽  
W. K. Annable ◽  
P. J. Thompson
Keyword(s):  
Serial Correlation ◽  
Trend Detection ◽  
Peaks Over Threshold ◽  
Threshold Data ◽  
Block Maxima

Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

2014 ◽  
Vol 46 (02) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather
Keyword(s):  
Stable Process ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Shape Functions ◽  
Peaks Over Threshold ◽  
New Methods ◽  
Convergence Results ◽  
Block Maxima ◽  
Threshold Approach ◽  
Mixed Moving Maxima

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

scholarly journals Evaluation of classical spatial-analysis schemes of extreme rainfall

2012 ◽  
Vol 12 (11) ◽  
pp. 3229-3240 ◽  
Author(s):  
D. Ceresetti ◽  
E. Ursu ◽  
J. Carreau ◽  
S. Anquetin ◽  
J. D. Creutin ◽  
...  
Keyword(s):  
Cross Validation ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Optimal Interpolation ◽  
Peaks Over Threshold ◽  
Model Block ◽  
Block Maxima ◽  
Extreme Value Model ◽  
Value Model

Abstract. Extreme rainfall is classically estimated using raingauge data at raingauge locations. An important related issue is to assess return levels of extreme rainfall at ungauged sites. Classical methods consist in interpolating extreme-value models. In this paper, such methods are referred to as regionalization schemes. Our goal is to evaluate three classical regionalization schemes. Each scheme consists of an extreme-value model (block maxima, peaks over threshold) taken from extreme-value theory plus a method to interpolate the parameters of the statistical model throughout the Cévennes-Vivarais region. From the interpolated parameters, the 100-yr quantile level can be estimated over this whole region. A reference regionalization scheme is made of the couple block maxima/kriging, where kriging is an optimal interpolation method. The two other schemes differ from the reference by replacing either the extreme-value model block maxima by peaks over threshold or kriging by a neural network interpolation procedure. Hyper-parameters are selected by cross-validation and the three regionalization schemes are compared by double cross-validation. Our evaluation criteria are based on the ability to interpolate the 100-yr return level both in terms of precision and spatial distribution. It turns out that the best results are obtained by the regionalization scheme combining the peaks-over-threshold method with kriging.

scholarly journals Extreme value theory in emerging markets: Evidence from the Montenegrin stock exchange

2015 ◽  
Vol 60 (206) ◽  
pp. 87-116 ◽  
Author(s):  
Julija Cerovic ◽  
Vesna Karadzic
Keyword(s):  
At Risk ◽  
Stock Market ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Emerging Market ◽  
Value Theory ◽  
Extreme Value ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

The concept of Value at Risk(VaR) estimates the maximum loss of a financial position at a given time for a given probability. This paper considers the adequacy of the methods that are the basis of extreme value theory in the Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether the peaks-over-threshold method outperforms the block maxima method in evaluation of Value at Risk in emerging stock markets such as the Montenegrin market. The daily return of the Montenegrin stock market index MONEX20 is analyzed for the period January 2004 - February 2014. Results of the Kupiec test show that the peaks-over-threshold method is significantly better than the block maxima method, but both methods fail to pass the Christoffersen independence test and joint test due to the lack of accuracy in exception clustering when measuring Value at Risk. Although better, the peaks-over-threshold method still cannot be treated as an accurate VaR model for the Montenegrin frontier stock market.

A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

2007 ◽  
Vol 10 (06) ◽  
pp. 1043-1075 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Value Theory ◽  
Extreme Value ◽  
Expected Shortfall ◽  
Stable Laws ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Block Maxima

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Detecting climate-related trends in streamflow data

2002 ◽  
Vol 45 (8) ◽  
pp. 89-104 ◽  
Author(s):  
Paul J. Pilon ◽  
Sheng Yue
Keyword(s):  
Local Knowledge ◽  
Serial Correlation ◽  
Selection Criteria ◽  
Spatial Scales ◽  
High Density ◽  
Global Network ◽  
Trend Detection ◽  
Testing Procedures ◽  
Stable Conditions ◽  
Streamflow Data

This paper reviews the results of a number of studies that have investigated streamflow data for the existence of trend. These studies provide evidence that trends in various, but not all, streamflow regimes are occurring at rates that are higher than one might attribute to chance alone. Results of different studies using different approaches were compared and were shown, at times, to have dramatic differences. These differences might potentially be due to pre-conditioning of data prior to trend detection in attempts to minimize the impacts of serial correlation on testing procedures. It was also evident that patterns of trend can vary over small spatial scales and that a relatively high-density network is required to effectively comprehend trend and how it might be altering across an area. A global network of streamflow sites representing pristine or stable conditions is needed to assess patterns of change. Selection criteria for sites within such a network are provided, and it is highlighted that local knowledge is required to perform this selection.

scholarly journals Data Geometry and Extreme Value Distribution

2021 ◽  
Vol 2 (2) ◽  
pp. 06-15
Author(s):  
Mamadou Cisse ◽  
Aliou Diop ◽  
Souleymane Bognini ◽  
Nonvikan Karl-Augustt ALAHASSA
Keyword(s):  
Weibull Distribution ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Data System ◽  
Peaks Over Threshold ◽  
Stochastic Graphs ◽  
Block Maxima ◽  
Extreme Values Theory

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

Threshold selection for regional peaks-over-threshold data

2015 ◽  
Vol 43 (7) ◽  
pp. 1291-1309 ◽  
Author(s):  
M. Roth ◽  
G. Jongbloed ◽  
T.A. Buishand
Keyword(s):  
Threshold Selection ◽  
Peaks Over Threshold ◽  
Threshold Data ◽  
Selection For

Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

2014 ◽  
Vol 46 (2) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather
Keyword(s):  
Stable Process ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Shape Functions ◽  
Peaks Over Threshold ◽  
New Methods ◽  
Convergence Results ◽  
Block Maxima ◽  
Threshold Approach ◽  
Mixed Moving Maxima

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

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