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

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.

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.

Extreme Value Theory and Archimedean Copulas

2004 ◽  
Vol 2004 (3) ◽  
pp. 211-228 ◽  
Author(s):  
Mario V. Wüthrich
Keyword(s):  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Archimedean Copulas
Sign in / Sign up

Export Citation Format

Share Document