THESIS
2016
xviii, 143 pages : illustrations ; 30 cm
Abstract
Extreme value theory studies the probabilistic and statistical behaviors of tail observations.
The theory is widely applied in various areas such as finance and environmental science.
In practice, tail observations are often dependent in time, space or both. Therefore,
characterizing the dependence structure of the data plays a major role in the statistical
modeling of extremes. In this thesis, we present three studies related to finance and air
quality events observed in time and space-time. The primary goals of the studies are to
understand the extremal behaviors through the proposed models and provide predictions.
First, we propose a threshold extreme value distribution to study the tail asymmetry
between the downside risks of long and short positions for securities markets....[
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Extreme value theory studies the probabilistic and statistical behaviors of tail observations.
The theory is widely applied in various areas such as finance and environmental science.
In practice, tail observations are often dependent in time, space or both. Therefore,
characterizing the dependence structure of the data plays a major role in the statistical
modeling of extremes. In this thesis, we present three studies related to finance and air
quality events observed in time and space-time. The primary goals of the studies are to
understand the extremal behaviors through the proposed models and provide predictions.
First, we propose a threshold extreme value distribution to study the tail asymmetry
between the downside risks of long and short positions for securities markets. We handle
the temporal dependence of the financial returns by standardizing the proposed distribution
and integrating it into a generalized autoregressive conditional heteroskedasticity
(GARCH) framework. We apply our model across different asset classes to predict value-at-risk with multiple horizons and assess the evidence of tail asymmetry through Bayesian
model selection techniques. Financial and statistical implications of the empirical results
are discussed.
Second, we address the Bayesian inference for spatial extremes based on composite
likelihood under extensive simulations. Our models of interest are the max-stable processes
which are the limiting cases of infinite-dimensional extremes. We evaluate various
parametric models of max-stable processes with different priors, sample sizes and composite
weights.
Finally, we propose a novel copula-based spatial extreme value model that can handle
both the spatial dependence and interactions among multiple quantities in a unified way. The proposal addresses the surprisingly low availability of spatial extreme model in the
literature that can capture both types of dependence. We apply our model to analyze
weekly maxima of five types of air pollutants recorded in Pearl River Delta in China and
predict the levels of pollution for unmonitored regions.
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