Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case

Abstract Given a d-dimensional random vector X = (X 1, . . ., X d ), if the standard uniform vector U obtained by the component-wise probability integral transform (PIT) of X has the same distribution of its point reflection through the center of the unit hypercube, then X is said to have copula radial symmetry. We generalize to higher dimensions the bivariate test introduced in [11], using three different possibilities for estimating copula derivatives under the null. In a comprehensive simulation study, we assess the finite-sample properties of the resulting tests, comparing them with the finite-sample performance of the multivariate competitors introduced in [17] and [1]

Combining permutation tests to rank systemically important banks

In this work we propose the use of a nonparametric procedure to investigate the relationship between the Regulator’s Global Systemically Important Banks (G-SIBs) classification and the equity-based systemic risk measures. The proposed procedure combines several permutation tests to investigate the equality of the multivariate distribution of two groups and assumes only the hypothesis of exchangeability of variables. In our novel approach, the weights used in the combination of tests are obtained using the Particle Swarm Optimization heuristic and quantify the informativeness about the selection. Finally, the p value of the combined test measures the reliability of the result. Empirical results about the selection of G-SIBs show how considering the systematic ( ), stress ( CoVaR) and connectedness components (in–out connection) of systemic risk cover more than 70% of weight in all the considered years

Empirical Projected Copula Process and Conditional Independence An Extended Version

C - Mathematical and Quantitative Methods/C1 - Econometric and Statistical Methods and Methodology: General/C10 - General <br> URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2013.68 - ISSN : 1955-611XConditional dependence is expressed as a projection map in the trivariate copula space. The projected copula, its sample counterpart and the related process are defined. The weak convergence of the projected copula process to a tight centered Gaussian Process is obtained under weak assumptions on copula derivatives.La dépendence conditionnelle est exprimée comme une projection dans l'espace copule trivarié. La copule projections, la copule empirique et le processus associés sont définis. La convergence faible du processus vers un processus gaussien centré est obtenu sous des hypothèses faibles portant sur les dérivés des copules

Living on the Edge: An Unified Approach to Antithetic Sampling

We identify recurrent ingredients in the antithetic sampling literature leading to a unified sampling framework. We introduce a new class of antithetic schemes that includes the most used antithetic proposals. This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback--Leibler sense; ii) closed-form multivariate Kendall's $\tau$ and Spearman's $\rho$; iii) ranking in concordance order and iv) a central limit theorem that characterizes stochastic behaviour of Monte Carlo estimators when the sample size tends to infinity. The proposed simulation framework inherits the simplicity of the standard antithetic sampling method, requiring the definition of a set of reference points in the sampling space and the generation of uniform numbers on the segments joining the points. We provide applications to Monte Carlo integration and Markov Chain Monte Carlo Bayesian estimation

Random projection ensemble classification

We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one special case that we study in detail, the random projections are divided into disjoint groups, and within each group we select the projection yielding the smallest estimate of the test error. Our random projection ensemble classifier then aggregates the results of applying the base classifier on the selected projections, with a data-driven voting threshold to determine the final assignment. Our theoretical results elucidate the effect on performance of increasing the number of projections. Moreover, under a boundary condition implied by the sufficient dimension reduction assumption, we show that the test excess risk of the random projection ensemble classifier can be controlled by terms that do not depend on the original data dimension and a term that becomes negligible as the number of projections increases. The classifier is also compared empirically with several other popular high-dimensional classifiers via an extensive simulation study, which reveals its excellent finite-sample performance.Both authors are supported by an Engineering and Physical Sciences Research Council Fellowship EP/J017213/1; the second author is also supported by a Philip Leverhulme prize

Do we need a stochastic trend in cay estimation? Yes.

The paper investigates the importance of modeling in cay estimations from a statistical and economic perspective by observing the stochastic trend, a thus far neglected component. In order to do this, we perform an empirical analysis on US secular annual data from 1900 to 2015 considering the cay with non-durables and services and the cay with total consumption expenditure. Findings show the usefulness of including the stochastic trend in cay estimation. Furthermore, out-of-sample statistical and economic significance tests show the ability of the cay model with trend to outperform the traditional cay measure

Hedge fund tail risk: An investigation in stressed markets

The financial industry has witnessed several crises in the past, some of which have had a major global impact. Although hedge funds are expected to have the capability to at least avoid the impact of such crises by hedging against market movements, the long-term capital management crisis in 1998 and the global meltdown in 2008 showed otherwise. In both cases, most hedge funds suffered large losses; In fact, almost all Dow Jones Credit Suisse hedge fund indexes experienced huge losses. These systemic losses have been associated mostly with large, simultaneous liquidation by market participants, causing a liquidity freeze that crippled hedge funds and spilled over to the general economy (see Brown et al. [2009]; Buraschi, Kosowski, and Trojani [2014]; and Lo, Getmansky, and Lee [2015]). The experiences from these crises have motivated investors, academics, and regulators to better understand systemic risk in hedge funds and these funds' contribution to the overall risk of a portfolio (see Billio et al. [2012a, b])

Multivariate Reflection Symmetry of Copula Functions

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail-du-ces/Documents de travail du Centre d'Economie de la Sorbonne 2017.33 - ISSN : 1955-611XWe propose a multivariate nonparametric copula test of reflection symmetry. The test is valid in any number of dimensions, extending previous results that cover the bivariate case. Furthermore, the asymptotic theory for the test relies on recent results on the dependent multiplier bootstrap, valid for sub-exponentially strongly mixing data. Consequently to the introduction of those two features, the procedure is suitable for financial time series whose asymmetric dependence, in distressed periods, has already been documented elsewhere. We conduct an extensive simulation study of empirical size and power and provide several examples of applications. In particular, we investigate the use of the statistic as a financial stress indicator by comparing it with the CISS, the leading ECB indicator