Related papers: Estimation of L\'evy-driven CARMA models under ren…
The exponentially weighted moving average (EMWA) could be labeled as a competitive volatility estimator, where its main strength relies on computation simplicity, especially in a multi-asset scenario, due to dependency only on the decay…
Using key tools such as It\^o formula for general semi-martingales, moments estimates for L\'{e}vy-type stochastic integrals and properties of regular varying functions we find conditions under which solutions of stochastic differential…
High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node.…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
As attention to recorded data grows in the realm of automotive testing and manual evaluation reaches its limits, there is a growing need for automatic online anomaly detection. This real-world data is complex in many ways and requires the…
T-wave alternans (TWA) is a potential marker for sudden cardiac death, but its reliable analysis is often constrained to noise-free environments, limiting its utility in real-world settings. We explore model-based T-wave estimation to…
The continual evolution of autonomous driving technology requires car-following models that can adapt to diverse and dynamic traffic environments. Traditional learning-based models often suffer from performance degradation when encountering…
One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…
The reliability assessment of a machine learning model's prediction is an important quantity for the deployment in safety critical applications. Not only can it be used to detect novel sceneries, either as out-of-distribution or anomaly…
Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
Large language models (LLMs) struggle with compositional generalisation, limiting their ability to systematically combine learned components to interpret novel inputs. While architectural modifications, fine-tuning, and data augmentation…
We develop a method to perform model averaging in two-stage linear regression systems subject to endogeneity. Our method extends an existing Gibbs sampler for instrumental variables to incorporate a component of model uncertainty. Direct…
We consider a mixed moving average (MMA) process X driven by a L\'evy basis and prove that it is weakly dependent with rates computable in terms of the moving average kernel and the characteristic quadruple of the L\'evy basis. Using this…
This paper explores the duration dynamics modelling under the Autoregressive Conditional Durations (ACD) framework (Engle and Russell 1998). I test different distributions assumptions for the durations. The empirical results suggest…
Products with intermittent demand are characterized by a high risk of sales losses and obsolescence due to the sporadic occurrence of demand events. Generally, both point forecasting and probabilistic forecasting approaches are applied to…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of…