Sensitivity Analysis of Values at Risk

The aim of this paper is to analyze the sensitivity of Value at Risk (VaR) with respect to portfolio allocation. We derive analytical expressions for the first and second derivatives of the Value at Risk, and explain how they can be used to simplify statistical inference and to perform a local analysis of the Value at Risk. An empirical illustration of such an analysis is given for a portfolio of French stocks.

Inference for Noisy Long Run Component Process

This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out in Fama-French (1988). Moreover in the presence of a long run component, spurious regressions arise and misleading long run predictions are obtained when standard statistical approaches are applie

Structural Modelling of Dynamic Networks and Identifying Maximum Likelihood

This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of nonzero elements (sparsity), or by considering a reduced rank approach for nonnegative matrix factorization (NMF). We follow the latter approach and develop a new probabilistic NMF method. We introduce a new Identifying Maximum Likelihood (IML) method for consistent estimation of the identified set of admissible NMF's and derive its asymptotic distribution. Moreover, we propose a maximum likelihood estimator of the parameter matrix for a given non-negative rank, derive its asymptotic distribution and the associated efficiency bound

Nonlinear Impulse Response Functions and Local Projections

The goal of this paper is to extend the method of estimating Impluse Response Functions (IRFs) by means of Local Projection (LP) in a nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for a Markov process, and explain how their Impulse Response Functions are directly linked to the nonlinear Local Projection, as in the case for the linear setting. We then present a nonparametric LP estimator, and compare its asymptotic properties to that of IRFs obtained through direct estimation. We also explore issues of identification for the nonlinear IRF in the multivariate framework, which remarkably differs in comparison to the Gaussian linear case. In particular, we show that identification is conditional on the uniqueness of deconvolution. Then, we consider IRF and LP in augmented Markov models.Comment: 44 pages, 4 figure

Inference for Noisy Long Run Component Process

This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out in Fama-French (1988). Moreover in the presence of a long run component, spurious regressions arise and misleading long run predictions are obtained when standard statistical approaches are applie

Nonlinear Persistence and Copersistence

In a nonlinear framework, temporal dependence of time series is sensitive to transformations. The aim of this paper is to examine in detail the relationships between various forms of persistence and nonlinear transformations of stationary and nonstationary processes. We introduce the concept of persistence space and use it to define the degrees of persistence of univariate or multivariate processes. For illustration, we examine and compare the persistence structure of a fractionally integrated process and a beta mixture of AR(1) processes. The study of multivariate processes is focused on nonlinear comovements between the components, called the copersistence directions, or cointegration directions in the nonstationary case. We nd that, in general, there is a multiplicity of such directions, causing an identication problem in the analysis of nonlinear cointegration.Nonlinear Autocorrelogram, Canonical Analysis, Persistence, Chaos, Unit Root, Cointegration

Aspects statistiques de la méthode d’évaluation contingente

La théorie classique du consommateur se révèle insuffisante lorsque les biens considérés sont de nature complexe et que leur utilisation ne peut se résumer à la seule donnée de la quantité consommée. C’est le cas général des services, où des caractéristiques de qualité ont un rôle important et où de nouveaux produits peu connus des individus sont continuellement introduits. Il existe deux approches pour déterminer les comportements face à un nouveau produit ou des changements de qualité. La méthode hédonique repose sur l’étude des comportements passés et extropole de ces comportements observés la demande du nouveau produit. La méthode d’évaluation contingente repose sur des enquêtes faites auprès des consommateurs. Le but de cet article est de préciser la conception de telles enquêtes et les analyses statistiques qui en résultent.The standard consumer theory is not appropriate when the goods which are considered are complex, and their use cannot be well summarized by the consumed quantity only. This question is crucial for the services where quality characterisitcs are important and where new services are permanently introduced, which are not well known by the consumers. There exist two main aproaches to analyse the behaviour’s modification, when a new service is introduced, or a quality characteristic is changed. The hedonic methodology is based on the observation of past behaviours and tries to extrapolate these behaviours to the new situation. The contingent valuation method is based on opinion polls, containing appropriate questions. The aim of this article is to explain how to construct the questionaries and how to perform the statistical analysis of the corresponding answers