Copula-based measures of tail dependence with applications

With the advent of globalization and the recent financial turmoil, the interest for the analysis of dependencies between financial time series has significantly increased. Risk measures such as value-at-risk are heavily affected by the joint extreme comovements of associated risk factors. This thesis suggests some copula-based statistical tools which can be useful in order to have more insights into the nature of the association between random variables in the tail of their distributions. Preliminarily, an overview of important definitions and properties in copula theory is given, and some known measures of tail dependence based on the notion of tail dependence coefficients and rank correlations are introduced. A first proposal consists of a graphical tool based on the so-called tail concentration function, in order to distinguish different families of copulas in a 2D configuration. This can be used as a copula selection tool in practical fitting problems, when one wants to choose one or more copulas to model the dependence structure in the data, highlighting the information contained in the tail. The thesis mainly deals with financial time series applications, where copula functions and the related concepts of tail copula and tail dependence coefficients are used to characterize the dependence structure of asset returns. Classical cluster analysis tools are revisited by introducing suitable copula-based tail dependence measures, which are exploited in the identification of similarities or dissimilarities between the variables of interest and, in particular, between financial time series. Such an approach is designed to investigate the joint behaviour of pairs of time series when they are taking on extremely low values. Either the asymptotic and the finite behaviour are assessed. The proposed methodology is based on a suitable copula-based time series model(GARCH-copula model), in order to model the marginal behaviour of each time series separately from the dependence pattern. Moreover, non-parametric estimation procedures are adopted for describing the pairwise dependencies, thus avoiding any model assumption. Simulation studies are conducted in order to check the performances of the proposed procedures and applications to financial data are presented showing their practical implementation. The information coming from the output of the introduced clustering techniques can be exploited for automatic portfolio selection procedures in order to hedge the risk of a portfolio, by taking into account the occurrence of joint losses. A two-stage portfolio diversification strategy is proposed and empirical analysis are provided. Results show how the suggested approach to the clustering of financial time series can be used by an investor to have more insights into the relationships among different assets in crisis periods. Moreover, the application to portfolio selection framework suggests a cautious usage of standard procedures that may not work when the markets are expected to experience periods of high volatility

Clustering of time series via non-parametric tail dependence estimation

We present a procedure for clustering time series according to their tail dependence behaviour as measured via a suitable copula-based tail coefficient, estimated in a non-parametric way. Simulation results about the proposed methodology together with an application to financial data are presented showing the usefulness of the proposed approach

A Portfolio Diversification Strategy via Tail Dependence Clustering

We provide a two-stage portfolio selection procedure in order to increase the diversification benefits in a bear market. By exploiting tail dependence-based risky measures, a cluster analysis is carried out for discerning between assets with the same performance in risky scenarios. Then, the portfolio composition is determined by fixing a number of assets and by selecting only one item from each cluster. Empirical calculations on the EURO STOXX 50 prove that investing on selected assets in trouble periods may improve the performance of risk-averse investors

Copula-based measures of tail dependence with applications

With the advent of globalization and the recent financial turmoil, the interest for the analysis of dependencies between financial time series has significantly increased. Risk measures such as value-at-risk are heavily affected by the joint extreme comovements of associated risk factors. This thesis suggests some copula-based statistical tools which can be useful in order to have more insights into the nature of the association between random variables in the tail of their distributions. Preliminarily, an overview of important definitions and properties in copula theory is given, and some known measures of tail dependence based on the notion of tail dependence coefficients and rank correlations are introduced. A first proposal consists of a graphical tool based on the so-called tail concentration function, in order to distinguish different families of copulas in a 2D configuration. This can be used as a copula selection tool in practical fitting problems, when one wants to choose one or more copulas to model the dependence structure in the data, highlighting the information contained in the tail. The thesis mainly deals with financial time series applications, where copula functions and the related concepts of tail copula and tail dependence coefficients are used to characterize the dependence structure of asset returns. Classical cluster analysis tools are revisited by introducing suitable copula-based tail dependence measures, which are exploited in the identification of similarities or dissimilarities between the variables of interest and, in particular, between financial time series. Such an approach is designed to investigate the joint behaviour of pairs of time series when they are taking on extremely low values. Either the asymptotic and the finite behaviour are assessed. The proposed methodology is based on a suitable copula-based time series model(GARCH-copula model), in order to model the marginal behaviour of each time series separately from the dependence pattern. Moreover, non-parametric estimation procedures are adopted for describing the pairwise dependencies, thus avoiding any model assumption. Simulation studies are conducted in order to check the performances of the proposed procedures and applications to financial data are presented showing their practical implementation. The information coming from the output of the introduced clustering techniques can be exploited for automatic portfolio selection procedures in order to hedge the risk of a portfolio, by taking into account the occurrence of joint losses. A two-stage portfolio diversification strategy is proposed and empirical analysis are provided. Results show how the suggested approach to the clustering of financial time series can be used by an investor to have more insights into the relationships among different assets in crisis periods. Moreover, the application to portfolio selection framework suggests a cautious usage of standard procedures that may not work when the markets are expected to experience periods of high volatility.Con l'avvento della globalizzazione e la recente crisi finanziaria, l'interesse verso l'analisi delle relazioni tra serie storiche finanziarie è notevolmente aumentato. Misure di rischio come il value-at-risk sono fortemente influenzate dai movimenti estremi congiunti dei fattori di rischio associati. Nella presente tesi si suggeriscono alcuni strumenti statistici basati sulla nozione di copula, che possono essere utili al fine di ottenere informazioni sulla natura dell'associazione tra variabili casuali nella coda delle loro distribuzioni. Preliminarmente, vengono introdotte definizioni e proprietà fondamentali della teoria delle copule, e discusse alcune note misure di dipendenza basate sul concetto di coefficienti di dipendenza nella coda e correlazioni fra i ranghi. Una prima proposta consiste in uno strumento grafico basato sulla cosiddetta funzione di concentrazione di coda per distinguere tra diverse famiglie di copule in una configurazione bidimensionale. Questo strumento può essere impiegato in problemi pratici, quando si vuole scegliere tra una o più copule per modellizzare la struttura di dipendenza nei dati, evidenziando le informazioni contenute nella coda. La tesi prende in considerazione diverse applicazioni nell'analisi di serie storiche finanziarie, in cui le funzioni copula e i relativi concetti di copule di coda e coefficienti di dipendenza nelle code vengono impiegati per caratterizzare la struttura di dipendenza dei rendimenti finanziari. Gli strumenti standard per l'Analisi dei Gruppi (Cluster Analysis) vengono rivisitati attraverso l'introduzione di opportune misure di dipendenza, che permettano di identificare similarità o dissimilarità tra le quantità di interesse, nello specifico rappresentate da serie finanziarie. Tale approccio ha lo scopo di studiare il comportamento congiunto di coppie di serie finanziarie nel momento in cui esse assumono valori estremamente bassi. Vengono valutate sia la dipendenza asintotica che il comportamento finito. La metodologia proposta utilizza un modello per serie storiche basato sulle copule (GARCH-copula model), che consente di modellizzare il comportamento marginale di ogni serie temporale separatamente dalla struttura di dipendenza. Inoltre, vengono adottate procedure di stima non parametriche in relazione alla struttura di dipendenza, evitando così qualunque assunzione sul modello. Vengono condotti degli studi di simulazione per testare le procedure proposte e diverse applicazioni a dati finanziari mostrano la loro implementazione pratica. Il risultato delle tecniche introdotte precedentemente può essere utilizzato in procedure di selezione automatica di portafoglio al fine di coprire il rischio dovuto al verificarsi di perdite congiunte. Viene proposta una strategia di diversificazione di portafoglio in due fasi e illustrate le analisi empiriche. L'approccio suggerito per il raggruppamento di serie finanziarie può essere utile ad un investitore per avere una visione più approfondita delle correlazioni tra mercati finanziari in periodi di crisi. Inoltre, l'applicazione nell’ambito della selezione di portafogli suggerisce un uso prudente delle procedure standard che potrebbero non essere appropriate quando si prevede che i mercati possano attraversare periodi di alta volatilità

EUSN 2021 Book of Abstracts. 5th European Conference on Social Networks

In recent years, the analysis of ego networks has attracted a great attention and found application in many areas of the social sciences. Several studies have pointed out the crucial role played by network characteristics (such as size and composition) in the study of social relationships and their impact on many aspects of everyday life (e.g., social support, well-being, health, and mobility). In this context, the identification of network typologies has become a crucial task and a powerful tool to capture aspects of the social space or personal community in which people are embedded. Along this direction, clustering methods have been exploited to identify and characterize existent types of ego networks. In this work, we propose a distance-based clustering procedure to identify groups of similar ego networks, which are described by a small number of compositional variables. The proposed approach is motivated by the empirical study of ego networks of contacts extracted from the latest edition of “Family and Social Subjects" (FSS) Survey conducted by the Italian National Statistical Institute in 2016. In particular, we focus on elderly respondents living alone, which can be regarded as a vulnerable category, with the aim to describe their network of contacts. As the FSS Survey is not specifically oriented to network analysis, its major limitation consists in the lack of information on alter-alter ties. Coping with these limitations, we first mine relational information in FSS data in order to derive the ego networks of respondents. Then, we develop a clustering procedure in the hierarchical framework to identify a partition of ego networks according to their composition. The proposed approach has the main advantage to be particularly suitable when the involved variables are heterogeneous, in both range and type, which can easily happen if ego networks are derived from secondary data, rather than using ad-hoc designs. We discuss the choice of a suitable dissimilarity metric and the issue of the selection of the number of clusters. The prototypical units---one for each cluster---resulting from the proposed method, enhance the cluster interpretation. Results on the analysis of ego networks for the elderly people show the suitability of the proposed procedure to investigate the existing patterns in egocentric data, especially when the data are defined over heterogeneous attributes concerning the network composition, making our approach applicable to various surveys

Discrimination in machine learning algorithms

Machine learning algorithms are routinely used for business decisions which may directly affect individuals: for example, because a credit scoring algorithm refuses them a loan. It is then relevant from an ethical (and legal) point of view to ensure that these algorithms do not discriminate based on sensitive attributes (sex, race), which may occur unwittingly and unknowingly by the operator and the management. Statistical tools and methods are then required to detect and eliminate such potential biases

A clustering procedure for ego-network data: an application to Italian elders living in couple

The analysis of ego-network characteristics (especially size and composition) has become crucial in studying many aspects of everyday life. In this work, we propose a clustering procedure to find a partition of ego-networks into homogeneous groups according to their features. We use data from the \u201cFamily and Social Subjects\u201d (FSS) survey conducted by the Italian National Statistical Institute in 2009, on elderly couples with both partners aged 65 years and more. Preliminary results show the suitability of our proposal to analyze this kind of ego-network data

A spatially-weighted AMH copula-based dissimilarity measure for clustering variables: An application to urban thermal efficiency

Investigating thermal energy demand is crucial for developing sustainable cities and the efficient use of renewable sources. Despite the advances made in this field, the analysis of energy data provided by smart grids is currently a demanding challenge due to their complex multivariate structure and high dimensionality. In this article, we propose a novel copula-based dissimilarity measure suitable for analyzing district heating demand and introduce a procedure to apply it to high-temporal resolution panel data. Inspired by the characteristics of the considered data, we explore the usefulness of the Ali-Mikhail-Haq copula in defining a new dissimilarity measure to cluster variables in the hierarchical framework. We show that our proposal is particularly sensitive to small dissimilarities based on tiny differences in the strength of the dependence between the involved random variables. Therefore, the measure we introduce is able to distinguish between objects with low dissimilarity better than standard rank-based dissimilarity measures. Moreover, our proposal considers a weighted version of the copula-based dissimilarity that embeds the spatial location of the involved objects. We investigate the proposed measure through Monte Carlo studies and compare it with an analogous dissimilarity measure based on Kendall's correlation. Finally, the application to real data concerning the Italian city Bozen-Bolzano makes it possible to find clusters of buildings homogeneous with respect to their main characteristics, such as energy efficiency and heating surface. In turn, our findings may support the design, expansion, and management of district heating systems

An approach to cluster time series extremes with spatial constraints

We introduce a clustering method for time series based on tail dependence. Such a method considers spatial constraints by means of a suitable dissimilarity index that merges temporal and spatial dependence via extreme-value copulas. The proposed approach is applied to the study of rainfall extremes