Testing serial correlations in high-dimensional time series via extreme value theory

2020 ◽  
Vol 216 (1) ◽  
pp. 106-117
Author(s):  
Ruey S. Tsay
Keyword(s):  
Time Series ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
High Dimensional ◽  
Serial Correlations

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.

scholarly journals Volcanic hazard assessment for the Canary Islands (Spain) using extreme value theory

2011 ◽  
Vol 11 (10) ◽  
pp. 2741-2753 ◽  
Author(s):  
R. Sobradelo ◽  
J. Martí ◽  
A. T. Mendoza-Rosas ◽  
G. Gómez
Keyword(s):  
Time Series ◽  
Poisson Process ◽  
Statistical Method ◽  
Canary Islands ◽  
Extreme Value Theory ◽  
Volcanic Hazard ◽  
Value Theory ◽  
Extreme Value ◽  
Homogeneous Poisson Process ◽  
Non Homogeneous Poisson Process

Abstract. The Canary Islands are an active volcanic region densely populated and visited by several millions of tourists every year. Nearly twenty eruptions have been reported through written chronicles in the last 600 yr, suggesting that the probability of a new eruption in the near future is far from zero. This shows the importance of assessing and monitoring the volcanic hazard of the region in order to reduce and manage its potential volcanic risk, and ultimately contribute to the design of appropriate preparedness plans. Hence, the probabilistic analysis of the volcanic eruption time series for the Canary Islands is an essential step for the assessment of volcanic hazard and risk in the area. Such a series describes complex processes involving different types of eruptions over different time scales. Here we propose a statistical method for calculating the probabilities of future eruptions which is most appropriate given the nature of the documented historical eruptive data. We first characterize the eruptions by their magnitudes, and then carry out a preliminary analysis of the data to establish the requirements for the statistical method. Past studies in eruptive time series used conventional statistics and treated the series as an homogeneous process. In this paper, we will use a method that accounts for the time-dependence of the series and includes rare or extreme events, in the form of few data of large eruptions, since these data require special methods of analysis. Hence, we will use a statistical method from extreme value theory. In particular, we will apply a non-homogeneous Poisson process to the historical eruptive data of the Canary Islands to estimate the probability of having at least one volcanic event of a magnitude greater than one in the upcoming years. This is done in three steps: First, we analyze the historical eruptive series to assess independence and homogeneity of the process. Second, we perform a Weibull analysis of the distribution of repose time between successive eruptions. Third, we analyze the non-homogeneous Poisson process with a generalized Pareto distribution as the intensity function.

A novel data-driven method for structural health monitoring under ambient vibration and high-dimensional features by robust multidimensional scaling

2021 ◽  
pp. 147592172097395
Author(s):  
Alireza Entezami ◽  
Hassan Sarmadi ◽  
Masoud Salar ◽  
Carlo De Michele ◽  
Ali Nadir Arslan
Keyword(s):  
Multidimensional Scaling ◽  
Damage Detection ◽  
Extreme Value Theory ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Data Driven ◽  
Ambient Vibration ◽  
High Dimensional ◽  
Early Damage

Dealing with the problem of large volumes of high-dimensional features and detecting damage under ambient vibration are critical to structural health monitoring. To address these challenges, this article proposes a novel data-driven method for early damage detection of civil engineering structures by robust multidimensional scaling. The proposed method consists of some simple but effective computational parts including a segmentation process, a pairwise distance calculation, an iterative algorithm regarding robust multidimensional scaling, a matrix vectorization procedure, and a Euclidean norm computation. AutoRegressive Moving Average models are fitted to vibration time-domain responses caused by ambient excitations to extract the model residuals as high-dimensional features. In order to increase the reliability of damage detection and avoid any false alarm, the extreme value theory is considered to determine a reliable threshold limit. However, the selection of an appropriate extreme value distribution is crucial and troublesome. To cope with this limitation, this article introduces the generalized extreme value distribution and its shape parameter for choosing the best extreme value model among Gumbel, Fréchet, and Weibull distributions. The main contributions of this article include developing a novel data-driven strategy for early damage detection and addressing the limitation of using high-dimensional features. Experimental data sets of two well-known civil structures are utilized to validate the proposed method along with some comparative studies. Results demonstrate that the proposed data-driven method in conjunction with the extreme value theory is highly able to detect damage under ambient vibration and high-dimensional features.

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

2010 ◽  
Vol 10 (5) ◽  
pp. 12765-12794 ◽  
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.

Extremes for high dimensional chaotic systems

2020 ◽  
Author(s):  
Tobias Kuna ◽  
Valerio Lucarini ◽  
Davide Faranda ◽  
Jerouen Wouters ◽  
Viviane Baladi
Keyword(s):  
Dynamical System ◽  
Extreme Value Theory ◽  
Chaotic Systems ◽  
Value Theory ◽  
Extreme Value ◽  
High Impact ◽  
Hitting Times ◽  
High Dimensional ◽  
Physical Measure ◽  
Extreme Distribution

<p>Extremes are related to high impact and serious hazard events and hence their study and prediction have been and continue to be highly relevant for all kind of applications in geoscience and beyond. Extreme value theory is promising to be able to predict them reliably and robustly. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to dynamical systems and has been related to properties of physical measure (statistical properties of the system), return and hitting times. We will review what one can say for highly dimensional perfectly chaotic systems.  We will concentrate on relations between the index of the extreme distribution and invariants of the underlying dynamical system which are stable, in the sense that they will continuously depend on changing parameters in the dynamics.  Furthermore, we explore whether there exists a response theory for extremes, that is, whether the change of extremes can be quantitatilvely expressed  in terms of changing parameters. </p><p> </p>

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