Forecasting and prequential validation for time varying meta-elliptical distributions

We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameter problems. Results rely on the structure of meta-elliptical distributions and we allow for discontinuities in the marginals and time varying parameters. We illustrate the ideas of the paper using a large data set of 16 commodity prices

Dependence of stock returns in bull and bear markets

Pearson's correlation coefficient is typically used for measuring the dependence structure of stock returns. Nevertheless, it has many shortcomings often documented in the literature. We suggest to use a conditional version of Spearman's rho as an alternative dependence measure. Our approach is purely nonparametric and we avoid any kind of model misspecification. We derive hypothesis tests for the conditional Spearman's rho in bull andbearmarkets and verify the tests by Monte Carlo simulation.Further, we study the daily returns of stocks contained in the German stock index DAX 30. We find some significant differences in dependence of stock returns in bull and bear markets. On the other hand the differences are not so strong as one might expect. --bear market,bootstrapping,bull market,conditional Spearman's rho,copulas,Monte Carlo simulation,stock returns

Statistical Significance Testing in Information Retrieval: An Empirical Analysis of Type I, Type II and Type III Errors

Statistical significance testing is widely accepted as a means to assess how well a difference in effectiveness reflects an actual difference between systems, as opposed to random noise because of the selection of topics. According to recent surveys on SIGIR, CIKM, ECIR and TOIS papers, the t-test is the most popular choice among IR researchers. However, previous work has suggested computer intensive tests like the bootstrap or the permutation test, based mainly on theoretical arguments. On empirical grounds, others have suggested non-parametric alternatives such as the Wilcoxon test. Indeed, the question of which tests we should use has accompanied IR and related fields for decades now. Previous theoretical studies on this matter were limited in that we know that test assumptions are not met in IR experiments, and empirical studies were limited in that we do not have the necessary control over the null hypotheses to compute actual Type I and Type II error rates under realistic conditions. Therefore, not only is it unclear which test to use, but also how much trust we should put in them. In contrast to past studies, in this paper we employ a recent simulation methodology from TREC data to go around these limitations. Our study comprises over 500 million p-values computed for a range of tests, systems, effectiveness measures, topic set sizes and effect sizes, and for both the 2-tail and 1-tail cases. Having such a large supply of IR evaluation data with full knowledge of the null hypotheses, we are finally in a position to evaluate how well statistical significance tests really behave with IR data, and make sound recommendations for practitioners.Comment: 10 pages, 6 figures, SIGIR 201

Goodness-of-fit Tests For Elliptical And Independent Copulas Through Projection Pursuit

Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets.Comment: 31 page