Thesis start: 2024
Thesis end: 2027
Expected defense date: October 2027
Abstract
The study of records in time series plays an essential role in statistics, with applications in various fields. A record is an observation that exceeds all previous values in a series. Classical models, notably the Linear Drift Model (LDM) and the Yang-Nevzorov model, have been developed to analyze these phenomena in a framework where observations are independent but not identically distributed.
This thesis aims to go beyond these models by developing more complex approaches to address theoretical and applied questions. It proposes to improve parameter estimation by exploiting all available data, to develop statistical tests to validate model choice, and to study the asymptotic behavior of estimators and tests. Particular attention will be paid to extending models to multivariate data and applying extreme value theory to better understand the frequency of rare events.
Finally, the theoretical results will be applied to real data to detect anomalies and estimate the probability of a future record occurring. This research will contribute to a better understanding of records and their use in various practical contexts.
Keywords
Records, time series, stochastic models, estimation, statistical tests, extreme values, asymptotic, multivariate, anomalies.
Partners and/or Funders
LIMOS
Auvergne-Rhône-Alpes
Association for Specialization and Scientific Orientation
Sustainable Development Goals concerned
Publications
- We investigate the statistical properties of upper records observed in a time series {Xt}t≥1 under four widely studied record models: the Classical Record Model, the Yang-Nevzorov Model, the Linear Drift Model, and the Discrete-Time Random Walk Model. Our study focuses on the likelihood function constructed from the pairs of record values and their occurrence indicators, […]
- The global phenomenon of climate change has become one of the most pressing challenges of our time. Amidst this complex landscape, the scientific community seeks innovative methodologies to quantify and understand the occurrence and severity of climate change. The theory of records in extreme value theory provides a promising framework for detecting and verifying climate […]
News
- En juin 2025, Jinane Jouni, doctorante à l’Institut Fayol, Mines Saint-Étienne et membre du Limos, a participé à la « 14th International Conference on Extreme Value Analysis (EVA 2025) » organisée en Caroline du Nord (États-Unis) en collaboration avec l’éditeur académique … Lire la Suite →
- Les 56ᵉ Journées de Statistique (JdS) , organisées sur le Campus Saint-Charles de l’Université Aix-Marseille du 2 au 6 juin 2025 , ont été l’occasion pour Jinane Jouni , doctorante à l’Institut Fayol, Mines Saint-Etienne, LIMOS, de présenter une communication scientifique audacieuse. … Lire la Suite →