1,720,969 research outputs found
Identifiability and estimation of meta-elliptical copula generators
No full textMeta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map g, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of g are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Statistic
Financial Stock Market Modeling and the COVID-19 crisis: Has COVID-19 structurally changed the dynamics of the stock market?
No full textThe COVID-19 crisis heavily affected financial stock markets. In March 2020 stock prices dropped immensely and markets became extremely volatile. In this report we model three European stock markets before and during the COVID-19 crisis to determine whether the dynamics of financial markets changed structurally compared to previous periods. Stock markets play a big role in our economy and can cause economic disruption when they crash. Therefore, it can be very useful to understand the dynamics of the stock market. Econometricians are nowadays often asked to model the non-constant volatility (conditional heteroscedasticity) of financial time series. This report uses Generalised AutoRegressive Conditionally Heteroscedastic (GARCH) models that are known for their precise modeling of conditional heteroscedasticity. They are also known for their ability to capture the key stylised facts, the common empirical properties applicable to all types of stock markets. This report includes general definitions and characteristics of the GARCH(p, q) process and covers topics such as autocorrelation of returns, kurtosis, leptokurticity and volatility clustering. For estimating the GARCH models this report uses the statistical program R which estimates the parameters by the Quasi-Maximum Likelihood Estimation (QMLE) method. We modeled different periods before and during COVID-19 and compared the estimated parameters with the corresponding 95% confidence intervals. To test the accuracy of the estimations we performed parametric bootstrapping. Throughout the report, models for the Dutch Amsterdam Exchange (AEX) index, the French Cotation Assistée Continu (CAC 40) index and the German Deutsche Aktien (DAX) index are analysed and compared. It seems that European markets may experience the impact of stock market crashes differently. The DAX index shows significant changes in the dynamics of the stock market due to the COVID-19 crisis whereas the AEX and CAC 40 index do not.Applied Mathematic
Non-parametric dependence modeling for financial markets using conditional Kendall's tau
No full textIn this thesis, we have examined conditional dependence in a financial context using conditional Kendall’s tau (CKT). The conditional Kendall’s tau is a measure of concordance between two random variables given some covariates. This thesis covers topics related to conditional Kendall’s tau such as (conditional) copulas. We study non-parametric estimators of the conditional Kendall’s tau using kernel density estimation and kernel regression. An application of the non-parametric estimator to the returns of thirteen different financial assets is finally provided. The assets consist of stock indices, bonds, futures and exchange rates. Further, we apply Principal Component Analysis (PCA) on the conditional Kendall’s tau data matrix to increase the interpretability. In general, it seems that conditional dependence is slightly larger in the tails for all assets. Moreover, the conditional dependence for each group of assets is discussed. It seems that the degreeof the conditional dependence relates to characteristics of an asset such as geographical properties and type of asset.Applied Mathematic
Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion
No full textIn this article, we study bounds on the uniform distance between the cumulative distribution function of a standardized sum of independent centered random variables with moments of order four and its first-order Edgeworth expansion. Existing bounds are sharpened in two frameworks: when the variables are independent but not identically distributed and in the case of independent and identically distributed random variables. Improvements of these bounds are derived if the third moment of the distribution is zero. We also provide adapted versions of these bounds under additional regularity constraints on the tail behavior of the characteristic function. We finally present an application of our results to the lack of validity of one-sided tests based on the normal approximation of the mean for a fixed sample size.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Statistic
Fast Estimation of Kendall's Tau and Conditional Kendall's Tau Matrices under Structural Assumptions
No full textKendall’s tau and conditional Kendall’s tau matrices are multivariate (conditional) dependence measures between the components of a random vector. For large dimensions, available estimators are computationally expensive and can be improved by averaging. Under structural assumptions on the underlying Kendall’s tau and conditional Kendall’s tau matrices, we introduce new estimators that have a significantly reduced computational cost while keeping a similar error level. In the unconditional setting we assume that, up to reordering, the underlying Kendall’s tau matrix is block-structured with constant values in each of the off-diagonal blocks. The estimators take advantage of this block structure by averaging over (part of) the pairwise estimates in each of the off-diagonal blocks. Derived explicit variance expressions show their improved efficiency. In the conditional setting, the conditional Kendall’s tau matrix is assumed to have a constant block structure, independently of the conditioning variable. Conditional Kendall’s tau matrix estimators are constructed similarly as in the unconditional case by averaging over (part of) the pairwise conditional Kendall’s tau estimators. We establish their joint asymptotic normality, and show that the asymptotic variance is reduced compared to the naive estimators. Then, we perform a simulation study which displays the improved performance of both the unconditional and conditional estimators. Finally, the estimators are used for estimating the value at risk of a large stock portfolio; backtesting illustrates the obtained improvements compared to the previous estimators.Applied Mathematic
On the restrictions of Pair-Copula Bayesian Networks for integration-free computations
No full textThe pair-copula Bayesian network (PCBN) is a Bayesian network (BN) where the conditional probability functions are modeled using pair-copula constructions. By assigning bivariate conditional copulas to the arcs of the BN, one finds a proper joint density which can flexibly model all kinds of dependence structures. It is a known problem that the PCBN may require numerical integration to perform computations such as sampling and likelihood-inference. To address this issue we propose novel restrictions on the graphical structure and assignment of copulas such that integration will not be required. The resulting restricted PCBN offers significant computational benefits. We establish how to estimate and conduct a structure search for the restricted PCBN. A simulation study shows that a restricted PCBN is able to model non-Gaussian dependence structures more accurately than the widely used Gaussian Bayesian network.Applied Mathematics | Stochastic
Estimation of conditional CDFs using machine learning
No full textThis paper presents a novel approach for the estimation of conditional multivariate cumulative distribution functions (CDFs) within a nonparametric framework. To achieve this, we introduce a binary random variable that indirectly represents conditional CDFs and construct a dataset by pairing input vectors with the binary variables. We developed a general approach compatible with various machine learning methods.We have also developed an R package that facilitates the application of machine learning methods. This package leverages a range of machine learning models, including decision trees, neural networks, random forests, and bagging neural networks. Through systematic learning of the intricate relationships between the covariates and the binary variables, we effectively estimate conditional CDFs.To enhance the accuracy and reliability of the estimated CDFs, we incorporate a rearrangement technique which transforms the estimated functions into monotonic representations, aligning them more closely with the target CDFs and mitigating potential inconsistencies [6].Through simulations, we evaluate the performance of the estimation approach under various scenarios and assess the impact of sample size and correlation on estimation accuracy, using Mean Integrated Squared Error as a key performance metric. The results demonstrate the effectiveness and robustness of the methodology in estimating conditional CDFs, providing a valuable tool for capturing complex dependencies in multivariate data, with potential applications in risk assessment, finance, and environmental modeling.Applied Mathematic
Contributions à l'analyse statistique des modèles de dépendance en grande dimension
No full textThis thesis can be divided into three parts.In the first part, we study adaptivity to the noise level in the high-dimensional linear regression framework. We prove that two square-root estimators attains the minimax rates of estimation and prediction. We show that a corresponding median-of-means version can still attains the same optimal rates while being robust to outliers in the data.The second part is devoted to the analysis of several conditional dependence models.We propose some tests of the simplifying assumption that a conditional copula is constant with respect to its conditioning event, and prove the consistency of a semiparametric bootstrap scheme.If the conditional copula is not constant with respect to the conditional event, then it can be modelled using the corresponding Kendall's tau.We study the estimation of this conditional dependence parameter using 3 different approaches : kernel techniques, regression-type models and classification algorithms.The last part regroups two different topics in inference.We review and propose estimators for regular conditional functionals using U-statistics.Finally, we study the construction and the theoretical properties of confidence intervals for ratios of means under different sets of assumptions and paradigms.Cette thèse peut être divisée en trois parties.Dans la première partie, nous étudions des méthodes d'adaptation au niveau de bruit dans le modèle de régression linéaire en grande dimension. Nous prouvons que deux estimateurs à racine carrée, peuvent atteindre les vitesses minimax d'estimation et de prédiction. Nous montrons qu'une version similaire construite à parti de médianes de moyenne, peut encore atteindre les mêmes vitesses optimales en plus d'être robuste vis-à-vis de l'éventuelle présence de données aberrantes.La seconde partie est consacrée à l'analyse de plusieurs modèles de dépendance conditionnelle. Nous proposons plusieurs tests de l'hypothèse simplificatrice qu'une copule conditionnelle est constante vis-à-vis de son évènement conditionnant, et nous prouvons la consistance d'une technique de ré-échantillonage semi-paramétrique. Si la copule conditionnelle n'est pas constante par rapport à sa variable conditionnante, alors elle peut être modélisée via son tau de Kendall conditionnel. Nous étudions donc l'estimation de ce paramètre de dépendance conditionnelle sous 3 approches différentes : les techniques à noyaux, les modèles de type régression et les algorithmes de classification.La dernière partie regroupe deux contributions dans le domaine de l'inférence.Nous comparons et proposons différents estimateurs de fonctionnelles conditionnelles régulières en utilisant des U-statistiques. Finalement, nous étudions la construction et les propriétés théoriques d'intervalles de confiance pour des ratios de moyenne sous différents choix d'hypothèses et de paradigmes
Contributions à l'analyse statistique des modèles de dépendance en grande dimension
No full textThis thesis can be divided into three parts.In the first part, we study adaptivity to the noise level in the high-dimensional linear regression framework. We prove that two square-root estimators attains the minimax rates of estimation and prediction. We show that a corresponding median-of-means version can still attains the same optimal rates while being robust to outliers in the data.The second part is devoted to the analysis of several conditional dependence models.We propose some tests of the simplifying assumption that a conditional copula is constant with respect to its conditioning event, and prove the consistency of a semiparametric bootstrap scheme.If the conditional copula is not constant with respect to the conditional event, then it can be modelled using the corresponding Kendall's tau.We study the estimation of this conditional dependence parameter using 3 different approaches : kernel techniques, regression-type models and classification algorithms.The last part regroups two different topics in inference.We review and propose estimators for regular conditional functionals using U-statistics.Finally, we study the construction and the theoretical properties of confidence intervals for ratios of means under different sets of assumptions and paradigms.Cette thèse peut être divisée en trois parties.Dans la première partie, nous étudions des méthodes d'adaptation au niveau de bruit dans le modèle de régression linéaire en grande dimension. Nous prouvons que deux estimateurs à racine carrée, peuvent atteindre les vitesses minimax d'estimation et de prédiction. Nous montrons qu'une version similaire construite à parti de médianes de moyenne, peut encore atteindre les mêmes vitesses optimales en plus d'être robuste vis-à-vis de l'éventuelle présence de données aberrantes.La seconde partie est consacrée à l'analyse de plusieurs modèles de dépendance conditionnelle. Nous proposons plusieurs tests de l'hypothèse simplificatrice qu'une copule conditionnelle est constante vis-à-vis de son évènement conditionnant, et nous prouvons la consistance d'une technique de ré-échantillonage semi-paramétrique. Si la copule conditionnelle n'est pas constante par rapport à sa variable conditionnante, alors elle peut être modélisée via son tau de Kendall conditionnel. Nous étudions donc l'estimation de ce paramètre de dépendance conditionnelle sous 3 approches différentes : les techniques à noyaux, les modèles de type régression et les algorithmes de classification.La dernière partie regroupe deux contributions dans le domaine de l'inférence.Nous comparons et proposons différents estimateurs de fonctionnelles conditionnelles régulières en utilisant des U-statistiques. Finalement, nous étudions la construction et les propriétés théoriques d'intervalles de confiance pour des ratios de moyenne sous différents choix d'hypothèses et de paradigmes
Conditional empirical copula processes and generalized measures of association
No full textWe study the weak convergence of conditional empirical copula processes indexed by general families of conditioning events that have non zero probabilities. Moreover, we also study the case where the conditioning events are chosen in a data-driven way. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general multivariate measures of association, possibly given some fixed or random conditioning events. By applying our theoretical results, we prove the asymptotic normality of the estimators of such measures. We illustrate our results with financial data.Statistic
- …
