Convergence rates for density estimators of weakly dependent time series

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. We consider different methods of estimation of the density as kernel, projection or wavelets ones. Various cases of weakly dependent series are investigated including the Doukhan & Louhichi (1999)'s $\eta$-weak dependence condition, and the $\tilde \phi$-dependence of Dedecker & Prieur (2005). We thus obtain results for Markov chains, dynamical systems, bilinear models, non causal Moving Average... From a moment inequality of Doukhan & Louhichi (1999), we provide convergence rates of the term of error for the estimation with the \L^q loss or almost surely, uniformly on compact subsets

Dependent Lindeberg central limit theorem and some applications

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal or non causal time series: Gaussian, associated, linear, ARCH($\infty$), bilinear, Volterra processes,$...$, enter this frame

L’énigme de la croissance du PIB irlandais en 2015 : tentatives de réponse / Irish GDP Growth in 2015: A Puzzle and Propositions for a Solution

In July 2016, the Irish statistical institute significantly revised GDP annual growth in 2015 from 7% to 26%. This revision does not correspond to a similar increase in employment nor in the accumulation of new physical capital, but to the relocation of preexisting intangible assets by multinationals to Ireland. This article provides a comprehensive depiction of the effects of these relocations on the Irish GDP and balance of payments in 2015. We question the need to change the accounting standards defining the macroeconomic aggregates and the framework for economic analysis. We conclude that an effort to adapt and revamp the standards of national accounts is thus necessary to achieve a consistent recording of multinationals’ transactions, crucially by clarifying the concept of economic ownership over production and intellectual property and then by facilitating its implementation.En juillet 2016, l’institut de statistique irlandais a revu fortement à la hausse la croissance annuelle du PIB pour l’année 2015, de 7% à 26%. Cette révision ne correspond pas à une hausse de l’emploi ni à une accumulation de capital physique, mais à la relocalisation d’actifs immatériels existants en Irlande par des multinationales. L’article présente de façon détaillée l’effet de ces relocalisations sur le PIB et la balance des paiements irlandais en 2015. Nous questionnons la nécessité de modifier les normes comptables qui définissent les agrégats macroéconomiques ou le cadre de l’analyse économique. Nous concluons à la nécessité d’un effort pour adapter et réviser les normes de la comptabilité nationale afin d’appréhender les transactions internationales des multinationales, particulièrement en clarifiant le concept de propriété économique de la production et des produits de la propriété intellectuelle, puis en facilitant sa mise en oeuvre.Khder Marie-Baïanne, Montornès Jérémi, Ragache Nicolas. L’énigme de la croissance du PIB irlandais en 2015 : tentatives de réponse / Irish GDP Growth in 2015: A Puzzle and Propositions for a Solution. In: Economie et Statistique / Economics and Statistics, n°517-519, 2020. Numéro spécial : Au-delà et autour du PIB : questions à la comptabilité nationale / Special Issue : Beyond and Around GDP: Questions to National Accounting pp. 185-203