arXiv subjects

Ioan Scheffel

Publications and source records attributed to Ioan Scheffel.

3 recordsLinked to original sources

arXiv2026

Central limit theory for serial tail dependence estimators in heavy-tailed long memory linear time series

We prove multiple central limit theorems for serial tail dependence estimators in heavy-tailed long memory linear time series. The main theoretical tools are two novel multivariate reduction principles for partial sums of heavy-tailed long memory linear time series, subordinated over sliding windows and above a threshold growing with sample size. This requires addressing several substantial difficulties, including handling a nonlinear, sample-size dependent, and multivariate subordination mechanism, the dependence between several overlapping linear processes, and the lack of higher-order moments of the marginal distribution. Despite these obstacles, our assumptions are mild and, in particular, the innovation process is allowed to have infinite variance. A key feature of our theory is that our second reduction principle holds uniformly in the threshold, allowing central limit theory for empirical extremograms with sample quantiles as thresholds. This question has received little attention in the literature on serial extremal dependence estimation even though the version of empirical extremograms with random thresholds is ubiquitous in practice. We compare our results in several respects with those that may be obtained under short-range dependence, thereby discovering markedly different convergence rates and limit laws in our long memory setting.

math.ST↗

arXiv2026

Maxima of stationary systems of randomly time-changed L\'evy particles

In this work, we consider maxima of systems of randomly time-changed L\'evy particles. We give a general construction to obtain infinite-dimensional classes $\{Z^{\alpha}\}$ of stationary max-infinitely divisible (max-id) processes. These classes are indexed by admissible mass functions $\alpha$, which induce state-dependent time changes of the underlying L\'evy particles. This gives a generalization of the well-known (L\'evy--)Brown--Resnick process $Z^{1}$. In contrast to $\alpha\equiv 1$, the variability of non-constant mass functions $\alpha$ changes the dependence structure of the max-id process and goes beyond the max-stable setting while preserving stationarity. We then explore the extent of the so-called max-domain of attraction (MDA) of a given (L\'evy--)Brown--Resnick process $Z^1$, by studying convergence of rescaled maxima of independent copies of $Z^{\alpha}$ to $Z^1$. Thus, our work combines potential theory for Markov processes and extreme value theory to yield a novel, infinite-dimensional, and interpretable class $\{Z^{\alpha}\}$ of stationary processes in the MDA of a given (L\'evy--)Brown--Resnick process $Z^{1}$. So far, results on the extent of such domains have been scarce in the literature.

math.PR↗

arXiv2025

Central limit theory for Peaks-over-Threshold partial sums of long memory linear time series

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme value theory, is the asymptotic behavior of such partial sums when the subordination mechanism has a threshold depending on sample size, so as to focus on the right tail of the time series. This article substantially extends longstanding asymptotic techniques by allowing the subordination mechanism to depend on the sample size in this way and to grow at a polynomial rate, while permitting the innovation process to have infinite variance. The cornerstone of our theoretical approach is a tailored reduction principle, which enables the use of classical results on partial sums of long memory linear processes. In this way we obtain asymptotic theory for certain Peaks-over-Threshold estimators with deterministic or random thresholds. Applications cover both heavy- and light-tailed regimes, yielding unexpected results which, to the best of our knowledge, are new to the literature. A simulation study illustrates the relevance of our findings in finite samples.

math.PR↗