Related papers: Remarks on stationary GARCH processes under heavy …
We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…
In this paper, we discuss the convergence rate of empirical processes of Gaussian processes for a large class of function families. Our main goal is to show that the tail of the uniform norm of the empirical processes can be dominated by…
Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables, and put $S_n=X_1+...+X_n$. Under some conditions on the positive sequence $\tau_n$ and the positive increasing sequence $a_n$, we give necessary…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
Let X_1,X_2,... be a sequence of independent and identically distributed random variables, and put S_n=X_1+...+X_n. Under some conditions on the positive sequence tau_n and the positive increasing sequence a_n, we give necessary and…
GARCH models are useful tools in the investigation of phenomena, where volatility changes are prominent features, like most financial data. The parameter estimation via quasi maximum likelihood (QMLE) and its properties are by now well…
We investigate asymptotics of the tail distribution of sojourn time $$ \int_0^T \mathbb{I}(X(t)> u)dt, $$ as $u\to\infty$, where $X$ is a centered stationary Gaussian process and $T$ is an independent of $X$ nonnegative random variable. The…
Multivariate GARCH models are important tools to describe the dynamics of multivariate times series of financial returns. Nevertheless, these models have been much less used in practice due to the lack of reliable software. This paper…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
We provide new, mild conditions for strict stationarity and ergodicity of a class of BEKK processes. By exploiting that the processes can be represented as multivariate stochastic recurrence equations, we characterize the tail behavior of…
In this paper, we investigate the scaling limit of heavy-tailed nearly unstable cumulative INAR($\infty$) processes. These processes exhibit a power-law tail of the form $n^{-(1+\alpha)}$ for $\alpha \in (\frac{1}{2}, 1)$, and the $\ell^1$…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives…