We examine a linear regression model applied to the components of a time series, aiming to identify time-varying, constant as well as zero conditional beta coefficients. To address the non-identifiability of parameters when a conditional beta is constant, we employ a lasso-type estimator. This penalized estimator simplifies the model by shrinking the estimates in favor of natural constant beta...
Dans cet exposé, nous étudions le problème d’estimation non paramétrique d’une fonction dans un modèle autorégressif pour un risque quadratique. À cet effet, nous développons une méthode adaptative de sélection de modèles séquentielle basée sur les estimateurs séquentiels efficaces à noyaux proposés par Arkoun et Pergamenshchikov (2016). De plus, nous obtenons des inégalités d’oracle non...
On considère des processus autorégressifs pour lesquels on crée un pont entre un comportement stable et un comportement instable à l’aide d’une matrice compagne $A_n$ dépendant du temps et dont le rayon spectral$\rho(A_n) < 1$ est tel que $\rho(A_n) \to 1$. Ce cadre de travail est particulièrement pertinent pour comprendre les problématiques de racines unitaires en se focalisant sur la...
In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption on the innovation process to extend considerably the range of application of the Markov-switching AR...
The automotive industry is undergoing a major transformation driven by stringent regulations, particularly within the European Union (EU). The EU’s directive to ban the sale of combustion engine vehicles by 2035 is accelerating the shift towards electric and hybrid vehicles, reshaping the industry’s landscape. This regulation has a significant impact on the automotive industry, particularly in...
Based on Godambe’s theory of estimating functions, we propose a class of cumulative sum (CUSUM) statistics to detect breaks in the dynamics of time series under weak assumptions. First, we assume a parametric form for the conditional mean, but make no specific assumption about the data-generating process (DGP) or even about the other conditional moments. The CUSUM statistics we consider depend...
We consider robust deep learning from strongly mixing observations, with unbounded loss function and unbounded input/output. It is only assumed that the output variable has a finite $r$ order moment, with $r > 1$. Non asymptotic bounds for the expected excess risk of the deep neural network estimator is established under subexponential strong mixing assumptions on the observations. We derive a...
Auteur : Eugen Ursu
Affiliation : BSE, Université de Bordeaux.
Résumé : Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the parameters to vary with seasons. Selecting PAR time-series models can be computationally expensive, and the results are not always satisfactory. In this presentation, we propose an automatic procedure for identifying PAR...
Consider the trajectory of a time series with time-varying coefficients. The aim of this talk is to test the adequacy of these parameters at a finite and fixed number of instants of the trajectory. For this purpose, a Wald test is constructed from point estimates of the parameters obtained by minimization of a kernel contrast. This can take the form of a localized near-maximum likelihood...
In this talk I will talk about non-asymptotic PAC-like theoretical guarantees for learning dynamical systems. For the sake of simplicity, we will concentrate on linear and linear-parameter varying systems. We will mainly consider systems in discrete-time with stochastic noise, and then we will discuss some extension of these results to continuous-time systems. Learning linear...
We consider an observed subcritical Galton Watson process $\{Y_n, n \in \mathbb{Z}\}$ with correlated stationary immigration process $\{\epsilon_n, n \in \mathbb{Z}\}$. Two situations are presented. The first one is when $cov(\epsilon_0, \epsilon_k) = 0$ for $k$ larger than some $k_0$ : a consistent estimator for the reproduction and mean immigration rates is given, and a central limit theorem...
