Showing papers on "Vine copula published in 2015"
TL;DR: A novel copula-based model is proposed that allows for the non-linear and non-symmetric modeling of serial as well as between-series dependencies and exploits the flexibility of vine copulas.
Abstract: The analysis of multivariate time series is a common problem in areas like finance and economics. The classical tools for this purpose are vector autoregressive models. These however are limited to the modeling of linear and symmetric dependence. We propose a novel copula-based model that allows for the non-linear and non-symmetric modeling of serial as well as between-series dependencies. The model exploits the flexibility of vine copulas, which are built up by bivariate copulas only. We describe statistical inference techniques for the new model and discuss how it can be used for testing Granger causality. Finally, we use the model to investigate inflation effects on industrial production, stock returns and interest rates. In addition, the out-of-sample predictive ability is compared with relevant benchmark models. Copyright © 2014 John Wiley & Sons, Ltd.
77 citations
TL;DR: The use of vine copulas is explored, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of 2-dimensional copulas to incorporate all relevant dependences between the storm variables of interest.
Abstract: Copulas have already proven their flexibility in rainfall modelling. Yet, their use is generally restricted to the description of bivariate dependence. Recently, vine copulas have been introduced, allowing multi-dimensional dependence structures to be described on the basis of a stage by stage mixing of 2-dimensional copulas. This paper explores the use of such vine copulas in order to incorporate all relevant dependences between the storm variables of interest. On the basis of such fitted vine copulas, an external storm structure is modelled. An internal storm structure is superimposed based on Huff curves, such that a continuous time series of rainfall is generated. The performance of the rainfall model is evaluated through a statistical comparison between an ensemble of synthetical rainfall series and the observed rainfall series and through the comparison of the annual maxima.
71 citations
TL;DR: This paper proposed a vine-copula-based structural reliability analysis method which is an effective approach for performing a reliability analysis on complex multidimensional correlation problems and can be used to solve actual complex engineering problems.
Abstract: This paper proposed a vine-copula-based structural reliability analysis method which is an effective approach for performing a reliability analysis on complex multidimensional correlation problems. A joint probability distribution function (PDF) among multidimensional random variables was established using a vine copula function, based on which a reliability analysis model was constructed. Two solution algorithms were proposed to solve this reliability analysis model: one was based on Monte Carlo simulation (MCS) and another one was based on the first-order reliability method (FORM). The former method provides a generalized computational method for a reliability analysis based on vine copula functions and can provide so-called “precise solutions”; the latter method has high computational efficiency and can be used to solve actual complex engineering problems. Finally, three numerical examples were provided to verify the effectiveness of the method.
67 citations
TL;DR: Wang et al. as mentioned in this paper proposed a multivariate conditional model for streamflow prediction and the refinement of spatial precipitation estimates, which consists of high-dimensional vine copulas, conditional bivariate copula simulations, and a quantile-copula function.
Abstract: The effective prediction and estimation of hydro-meteorological variables are important for water resources planning and management. In this study, we propose a multivariate conditional model for streamflow prediction and the refinement of spatial precipitation estimates. This model consists of high-dimensional vine copulas, conditional bivariate copula simulations, and a quantile-copula function. The vine copula is employed because of its flexibility in modeling the high-dimensional joint distribution of multivariate data by building a hierarchy of conditional bivariate copulas. We investigate two cases to evaluate the performance and applicability of the proposed approach. In the first case, we generate one-month-ahead streamflow forecasts that incorporate multiple predictors including antecedent precipitation and streamflow records in a basin located in South China. The prediction accuracy of the vine-based model is compared with that of traditional data-driven models such as the support vector regression (SVR) and the adaptive neural-fuzzy inference system (ANFIS). The results indicate that the proposed model produces more skillful forecasts than SVR and ANFIS. Moreover, this probabilistic model yields additional information concerning the predictive uncertainty. The second case involves refining spatial precipitation estimates derived from the tropical rainfall measuring mission precipitation (TRMM) product for the Yangtze River basin by incorporating remotely sensed soil moisture data and the observed precipitation from meteorological gauges over the basin. The validation results indicate that the proposed model successfully refines the spatial precipitation estimates. Although this model is tested for specific cases, it can be extended to other hydro-meteorological variables for predictions and spatial estimations.
64 citations
TL;DR: The proposed spatial R‐vine model combines the flexibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies using the distances between the variable locations and is able to capture non‐Gaussian spatial dependencies.
Abstract: We introduce an extension of R-vine copula models for the purpose of spatial dependency modeling and model based prediction at unobserved locations. The newly derived spatial R-vine model combines the exibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies by means of the distances between the variable locations. In particular the model is able to capture non-Gaussian spatial dependencies. For the purpose of model development and as an illustration we consider daily mean temperature data observed at 54 monitoring stations in Germany. We identify a relationship between the vine copula parameters and the station distances and exploit it in order to reduce the huge number of parameters needed to parametrize a 54-dimensional R-vine model needed to t the data. The new distance based model parametrization results in a distinct reduction in the number of parameters and makes parameter estimation and prediction at unobserved locations feasible. The prediction capabilities are validated using adequate scoring techniques, showing a better performance of the spatial R-vine copula model compared to a Gaussian spatial model.
62 citations
TL;DR: In this article, a drawable vine copula is employed, along with a factorization which allows the marginal and transitional densities of the time series to be expressed analytically.
58 citations
TL;DR: In this article, an integrated framework is proposed to model and estimate relatively large dependence matrices using pair vine copulas and minimum risk optimal portfolios with respect to five risk measures within the context of the global financial crisis.
57 citations
TL;DR: In this article, a pair copula family selection procedure is proposed for regular vine copulas, which extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families.
Abstract: Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student’s t copula. This paper presents two contributions related to model selection of regular vine copulas. First, our pair copula family selection procedure extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families. Second, our method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference. The merits of our approach are established in a simulation study that benchmarks against methods suggested in current literature. A real data example about forecasting of portfolio asset returns for risk measurement and investment allocation illustrates the viability and relevance of the proposed scheme.
51 citations
TL;DR: This article discusses the use of vine copulae to build flexible semiparametric models for stationary multivariate higher‐order Markov chains, and proposes a new vine structure, the M‐vine, that is particularly well suited to this purpose.
Abstract: Vine copulae provide a graphical framework in which multiple bivariate copulae may be combined in a consistent fashion to yield a more complex multivariate copula. In this article, we discuss the use of vine copulae to build flexible semiparametric models for stationary multivariate higher-order Markov chains. We propose a new vine structure, the M-vine, that is particularly well suited to this purpose. Stationarity may be imposed by requiring the equality of certain copulae in the M-vine, while the Markov property may be imposed by requiring certain copulae to be independence copulae.
49 citations
TL;DR: A new goodness-of-fit test for regular vine (R-vine) copula models, a flexible class of multivariate copulas based on a pair-copula construction (PCC), arises from the information matrix ratio and assumes fixed margins.
48 citations
TL;DR: This method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference and is established in a simulation study that benchmarks against methods suggested in current literature.
Abstract: Regular vine copulas can describe a wider array of dependency patterns than the multivariate Gaussian copula or the multivariate Student's t copula. This paper presents two contributions related to model selection of regular vine copulas. First, our pair copula family selection procedure extends existing Bayesian family selection methods by allowing pair families to be chosen from an arbitrary set of candidate families. Second, our method represents the first Bayesian model selection approach to include the regular vine density construction in its scope of inference. The merits of our approach are established in a simulation study that benchmarks against methods suggested in current literature. A real data example about forecasting of portfolio asset returns for risk measurement and investment allocation illustrates the viability and relevance of the proposed scheme.
TL;DR: This work proposes methods to effectively explore the search space of truncated vine copulas, so that they are able to improve over previous greedy sequential approaches that optimized over one tree of the vine at each step.
TL;DR: A novel vine copula-based dependence description (VCDD) process monitoring approach is proposed, to extract the complex dependence among process variables rather than perform dimensionality reduction or other decoupling processes.
Abstract: A novel vine copula-based dependence description (VCDD) process monitoring approach is proposed. The main contribution is to extract the complex dependence among process variables rather than perform dimensionality reduction or other decoupling processes. For a multimode chemical process, the C-vine copula model of each mode is initially created, in which a multivariate optimization problem is simplified as coping with a series of bivariate copulas listed in a sparse matrix. To measure the distance of the process data from each non-Gaussian mode, a generalized local probability (GLP) index is defined. Consequently, the generalized Bayesian inference-based probability (GBIP) index under a given control limit can be further calculated in real time via searching the density quantile table created offline. The validity and effectiveness of the proposed approach are illustrated using a numerical example and the Tennessee Eastman benchmark process. The results show that the proposed VCDD approach achieves good ...
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TL;DR: A new semiparametric quantile regression method based on sequentially fitting a likelihood optimal D-vine copula to given data resulting in highly flexible models with easily extractable conditional quantiles is introduced.
Abstract: Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. The authors introduce a new semiparametric quantile regression method based on sequentially fitting a likelihood optimal D-vine copula to given data resulting in highly flexible models with easily extractable conditional quantiles. As a subclass of regular vine copulas, D-vines enable the modeling of multivariate copulas in terms of bivariate building blocks, a so-called pair-copula construction (PCC). The proposed algorithm works fast and accurate even in high dimensions and incorporates an automatic variable selection by maximizing the conditional log-likelihood. Further, typical issues of quantile regression such as quantile crossing or transformations, interactions and collinearity of variables are automatically taken care of. In a simulation study the improved accuracy and saved computational time of the approach in comparison with established quantile regression methods is highlighted. An extensive financial application to international credit default swap (CDS) data including stress testing and Value-at-Risk (VaR) prediction demonstrates the usefulness of the proposed method.
TL;DR: This study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality.
Abstract: A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that is superior to the standard generalized linear mixed model (GLMM) in this context. Here we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate GLMM as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate GLMM in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness including reflection asymmetric tail dependence, and, computational feasibility despite their three-dimensionality.
TL;DR: The partial vine copula (PVC) is introduced which provides a new multivariate dependence measure and which plays a major role in the approximation of multivariate distributions by SVCs and is elucidate why the PVC is the best feasible SVC approximation in practice.
Abstract: Simplified vine copulas (SVCs), or pair-copula constructions, have become an important tool in high-dimensional dependence modeling. So far, specification and estimation of SVCs has been conducted under the simplifying assumption, i.e., all bivariate conditional copulas of the vine are assumed to be bivariate unconditional copulas. We introduce the partial vine copula (PVC) which provides a new multivariate dependence measure and which plays a major role in the approximation of multivariate distributions by SVCs. The PVC is a particular SVC where to any edge a j-th order partial copula is assigned and constitutes a multivariate analogue of the bivariate partial copula. We investigate to what extent the PVC describes the dependence structure of the underlying copula. We show that the PVC does not minimize the Kullback-Leibler divergence from the true copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-copula. However, under regularity conditions, step-wise estimators of pair-copula constructions converge to the PVC irrespective of whether the simplifying assumption holds or not. Moreover, we elucidate why the PVC is the best feasible SVC approximation in practice.
TL;DR: It is demonstrated that by coupling losses, dependencies can be incorporated in risk analysis, avoiding the underestimation of risk, and can be easily extended to other countries and natural hazards.
Abstract: Losses due to natural hazard events can be extraordinarily high and difficult to cope with. Therefore, there is considerable interest to estimate the potential impact of current and future extreme events at all scales in as much detail as possible. As hazards typically spread over wider areas, risk assessment must take into account interrelations between regions. Neglecting such interdependencies can lead to a severe underestimation of potential losses, especially for extreme events. This underestimation of extreme risk can lead to the failure of riskmanagement strategies when they are most needed, namely, in times of unprecedented events. In this article, we suggest a methodology to incorporate such interdependencies in risk via the use of copulas. We demonstrate that by coupling losses, dependencies can be incorporated in risk analysis, avoiding the underestimation of risk. Based on maximum discharge data of river basins and stream networks, we present and discuss different ways to couple loss distributions of basins while explicitly incorporating tail dependencies. We distinguish between coupling methods that require river structure data for the analysis and those that do not. For the later approach we propose a minimax algorithm to choose coupled basin pairs so that the underestimation of risk is avoided and the use of river structure data is not needed. The proposed methodology is especially useful for large-scale analysis and we motivate and apply our method using the case of Romania. The approach can be easily extended to other countries and natural hazards.
TL;DR: In this paper, a vine copula based composite likelihood approach is proposed to model spatial dependencies, which allows to perform prediction at arbitrary locations, by combining established methods to model (spatial) dependencies.
TL;DR: The proposed conditional estimator has three main advantages: it applies to both iid and time series data, it is automatically monotonic across quantiles, and it can be directly applied to the multiple covariates case without introducing any extra complications.
Abstract: We consider a new approach in quantile regression modeling based on the copula function that defines the dependence structure between the variables of interest. The key idea of this approach is to rewrite the characterization of a regression quantile in terms of a copula and marginal distributions. After the copula and the marginal distributions are estimated, the new estimator is obtained as the weighted quantile of the response variable in the model. The proposed conditional estimator has three main advantages: it applies to both iid and time series data, it is automatically monotonic across quantiles, and, unlike other copula-based methods, it can be directly applied to the multiple covariates case without introducing any extra complications. We show the asymptotic properties of our estimator when the copula is estimated by maximizing the pseudo-log-likelihood and the margins are estimated nonparametrically including the case where the copula family is misspecified. We also present the finite sample performance of the estimator and illustrate the usefulness of our proposal by an application to the historical volatilities of Google and Yahoo.
TL;DR: In this paper, convex combinations of parametric copulas are used as pair-copulas in high-dimensional vine copula models to circumvent the error-prone need to choose and estimate a parametriccopula for each paircopula in a vine model.
Abstract: We propose the use of convex combinations of parametric copulas as pair-copulas in high-dimensional vine copula models. By doing so, we circumvent the error-prone need to choose and estimate a parametric copula for each pair-copula in a vine model. We show in simulations that our proposed model fits the dependence structure in a given data sample significantly better than a competing benchmark. In our empirical study on the models’ accuracy for forecasting the Value-at-Risk of financial portfolios, we show that our proposed mixture pair-copula construction yields significantly better results in backtesting while the benchmark overestimates portfolio risk.
TL;DR: This article forms multivariate models of housing price comovements using vine copulas, which not only fit the data better, but also uncover far stronger correlations between housing price movements, especially during extreme market swings.
Abstract: I. INTRODUCTION When housing prices were rapidly appreciating from 1999 to 2006, investment firms created structured securities by combining mortgages from houses located in different parts of the country, and then traders bought and sold those securities, and also pieces of those securities called "tranches," in secondary markets. The most familiar of those structured securities was the collateralized debt obligation (CDO). The main appeal of CDOs rested in the belief that, due to the localized nature of housing markets, houses in separate geographic markets would be unlikely to simultaneously experience large decreases in prices. Credit rating agencies offered support to this thinking by awarding many CDOs the highest possible safety rating. However, it soon became clear that CDOs offered less diversified protection than originally thought when, starting in 2006, housing prices in different geographic areas, even those located far apart, simultaneously plummeted in value. As a consequence, CDOs lost much of their value, with the global CDO market shrinking from $482 billion globally in 2007 to only $8 billion in 2010. (1) In the wake of the housing crisis, financial analysts and policy makers have questioned why, compared to pre-crisis expectations, housing prices showed strong correlations across different geographic areas. In addition, a branch of research has emerged that attempts to identify sources of, and quantify magnitudes of, housing price comovements (Apergis and Payne 2012; Barros, Gil-Alana, and Payne 2012). The popular press quickly assigned blame to the statistical method used to analyze linkages between housing markets: the Gaussian copula (Li 2000). Notably, the March 2009 issue of the technology magazine Wired featured an article on the Gaussian copula entitled "Recipe for Disaster: The Formula that Killed Wall Street." Similar ideas have reached the general public through the works of Nassim Taleb (Taleb 2007). The Gaussian copula became popular due, in part, to its link to the familiar multivariate normal distribution. But the multivariate normal distribution has asymptotic independence, such that events, regardless of the strength of their correlation, become independent if one pushes far enough into the tails (Embrechts, McNeil, and Straumann 2002). Thus, in the midst of the housing crisis, which might be thought of as a lower tail event, the Gaussian copula predicted near independence in price movements across different areas, when in fact, prices plummeted simultaneously throughout most of the United States. But the Gaussian copula's link to the normal distribution was not its only appeal. Perhaps a bigger reason for its popularity was that the Gaussian copula, much like the related normal distribution, readily extends to higher dimensions. Certainly, credit rating agencies were not considering simple bivariate movements between two locations, but rather multivariate movements across many locations. Recent studies argue that alternative specifications, especially copulas that depart from normality, more accurately reflect correlations in housing price movements during extreme market swings (Ho, Huynh, and JachoChavez 2014; Zimmer 2012). However, those improved fits have been achieved only in bivariate models that compare housing price movements between two locations. It remains an open question whether non-Gaussian copulas can accurately reflect housing price movements in higher dimensional settings. Unfortunately, copulas other than the Gaussian do not readily extend to higher-than-bivariate dimensions (Nelsen 2006, 105). Attempts to develop higher dimensional copulas, some of which are discussed below, either impose unrealistic restrictions or present difficulties when applied to data. As an alternative, this article develops multivariate models of housing price comovements based on vine copulas. The approach requires marginal distributions, which financial analysts should know with some certainty, and bivariate copulas, which have well-understood statistical properties. …
TL;DR: In this article, the authors apply the Clayton canonical vine copula (CVC) to model asymmetric dependence in equities markets and find evidence of an improvement in performance across a range of risk-adjusted return measures and the indices of acceptability.
Abstract: Asymmetric dependence in equities markets have been shown to have detrimental effects on portfolio diversification as assets within the portfolio exhibit greater correlations during market downturns compared to market upturns. By applying the Clayton canonical vine copula (CVC) to model asymmetric dependence, we produce a measure of systemic risk across a portfolio of assets. In addition, we use the Clayton CVC to produce estimates of expected returns in an application to higher-moment portfolio optimization and find evidence of an improvement in performance across a range of risk-adjusted return measures and the indices of acceptability.
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TL;DR: In the empirical study on the models’ accuracy for forecasting the Value-at-Risk of financial portfolios, it is shown that the proposed mixture pair-copula construction yields significantly better results in backtesting while the benchmark overestimates portfolio risk.
Abstract: We propose the use of convex combinations of parametric copulas as pair-copulas in high-dimensional vine copula models. By doing so, we circumvent the error-prone need to choose and estimate a parametric copula for each paircopula in a vine model. We show in simulations that our proposed model fits the dependence structure in a given data sample significantly better than a competing benchmark. In our empirical study on the models’ accuracy for forecasting the Value-at-Risk of financial portfolios, we show that our proposed mixture pair-copula construction yields significantly better results in backtesting while the benchmark overestimates portfolio risk.
TL;DR: A new model is proposed using trivariate copulas and beta-binomial marginal distributions for sensitivity, specificity, and prevalence as an expansion of the bivariate model.
Abstract: In real life and somewhat contrary to biostatistical textbook knowledge, sensitivity and specificity (and not only predictive values) of diagnostic tests can vary with the underlying prevalence of disease. In meta-analysis of diagnostic studies, accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects. In this paper, a new model is proposed using trivariate copulas and beta-binomial marginal distributions for sensitivity, specificity, and prevalence as an expansion of the bivariate model. Two different copulas are used, the trivariate Gaussian copula and a trivariate vine copula based on the bivariate Plackett copula. This model has a closed-form likelihood, so standard software (e.g., SAS PROC NLMIXED) can be used. The results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model. The methods are illustrated by two examples.
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TL;DR: In this article, a simplified vine copula model is proposed to avoid the curse of dimensionality by assuming that the true density does not belong to the class of simplified vines, and an application of the estimator to a classification problem from astrophysics.
Abstract: Practical applications of multivariate kernel density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We propose an estimator that avoids the curse of dimensionality by assuming a simplified vine copula model. We prove the estimator's consistency and show that the speed of convergence is independent of dimension. Simulation experiments illustrate the large gain in accuracy compared with the classical multivariate kernel density estimator --- even when the true density does not belong to the class of simplified vines. Lastly, we give an application of the estimator to a classification problem from astrophysics.
TL;DR: In this article, a new method for estimating the extreme quantiles for a function of several dependent random variables is proposed, which does not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and furthermore makes use of the full observed data.
Abstract: We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast with the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The method proposed is semiparametric as no parametric forms are assumed on the marginal distributions. But we select appropriate bivariate copulas to model the joint dependence structure by taking advantage of the recent development in constructing large dimensional vine copulas. Consequently a sample quantile resulting from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile. This estimator is proved to be consistent under the regularity conditions on the closeness between a quantile set and its truncated set, and the empirical approximation for the truncated set. The simulation results lend further support to the reliable and robust performance of the method proposed. The method is further illustrated by a real world example in backtesting financial risk models.
01 Jan 2015
TL;DR: In this article, the dependence risk profile, investment risk and portfolio allocation features of seven 20-stock portfolios from the mining, energy, retail and manufacturing sectors of the Australian market in the context of the 2008-2009 global financial crisis (2008-2009 GFC) and full sample period scenarios revolving around it were modeled.
Abstract: This thesis models the dependence risk profile, investment risk and portfolio allocation features of seven 20-stock portfolios from the mining, energy, retail and manufacturing sectors of the Australian market in the context of the 2008-2009 global financial crisis (2008-2009 GFC) and pre-GFC, GFC, post-GFC and full sample period scenarios revolving around it. The mining and energy portfolios are the base of the study, while the retail and manufacturing are considered for benchmarking purposes. Pair vine copula models including canonical vines (c-vines), drawable vines (d-vines) and regular vines (r-vines) are fitted for the analysis of the portfolios’ multivariate dependence and their underlying sectors’ dependence risk dynamics. Besides, linear and nonlinear optimization methods threaded with the variance, mean absolute deviation (MAD), minimizing regret (Minimax), conditional Value-at-Risk (CVaR) and conditional Drawdown-at-Risk (CDaR) risk measures are implemented to examine the portfolios’ investment risk and optimal portfolio allocation features.
The vine copula modelling of dependence aims at examining the dependence risk profile of the portfolios in specific market conditions; studying the changes of the portfolios’ dependence structure between pairs of period scenarios; and recognizing the vine copula models that best account for the portfolios’ multivariate dependence. The multiple risk measure-based portfolio optimization seeks to identify the least and most investment risky portfolios, single out the portfolio that offers the best risk-return trade-off and recognize the stocks in the portfolios that are good candidates for investment.
This thesis’ main contributions stem from the “copula counting technique” and “average model convergence” perspectives proposed to handle, analyse and interpret the portfolios’ dependence structure and portfolio allocation features. The copula counting technique aside from simplifying the analysis and interpretation of the assets’ dependence structure, it enables an in-depth and comprehensive analysis of their underlying dependence risk dynamics in specific market conditions. The average model convergence addresses the optimal stock selection and investment confidence problems underlying any type of portfolio optimization, and faced by investors when having to select stocks from a wide array of optimal investment scenarios, in a more objective manner, through model convergence and model consensus. Both, the copula counting technique and average model convergence are new concepts that introduce new theory to the pair vine copula and multiple risk measure-based portfolio optimization literatures.
The research findings stemming from the vine copula modelling of dependence indicate that the each of the portfolios modelled has dependence risk features consistent with specific market conditions. Out of the seven portfolios modelled the gold mining and retail benchmark portfolios are found to have the lowest dependence risk in times of financial turbulence. The iron ore-nickel…
21 Dec 2015
TL;DR: In this paper, the dependence structure of finite block-maxima of multivariate distributions is examined and a closed form expression for the copula density of the vector of the blockmaxima is provided.
Abstract: We examine the dependence structure of finite block-maxima of multivariate distributions. We provide a closed form expression for the copula density of the vector of the block-maxima. Further, we show how partial derivatives of three-dimensional vine copulas can be obtained by only one-dimensional integration. Combining these results allows the numerical treatment of the block-maxima of any three-dimensional vine copula for finite block-sizes. We look at certain vine copula specifications and examine how the density of the block-maxima behaves for different block-sizes. Additionally, a real data example from hydrology is considered. In extreme-value theory for multivariate normal distributions, a certain scaling of each variable and the correlation matrix is necessary to obtain a non-trivial limiting distribution when the block-size goes to infinity. This scaling is applied to different three-dimensional vine copula specifications.
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TL;DR: A sample quantile resulting from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile and is proved to be consistent under the regularity conditions on the closeness between a quantile set and its truncated set, and the empirical approximation for the truncation set.
Abstract: We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast with the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The method proposed is semiparametric as no parametric forms are assumed on the marginal distributions. But we select appropriate bivariate copulas to model the joint dependence structure by taking advantage of the recent development in constructing large dimensional vine copulas. Consequently a sample quantile resulting from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile. This estimator is proved to be consistent under the regularity conditions on the closeness between a quantile set and its truncated set, and the empirical approximation for the truncated set. The simulation results lend further support to the reliable and robust performance of the method proposed. The method is further illustrated by a real world example in backtesting financial risk models.
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TL;DR: It is shown that the PVCA does not minimize the KL divergence from the true copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-copula, and how spurious conditional (in)dependencies may arise in SVCMs is demonstrated.
Abstract: In the last decade, simplified vine copula models (SVCMs), or pair-copula constructions, have become an important tool in high-dimensional dependence modeling. So far, specification and estimation of SVCMs has been conducted under the simplifying assumption, i.e., all bivariate conditional copulas of the data generating vine are assumed to be bivariate unconditional copulas. For the first time, we consider the case when the simplifying assumption does not hold and an SVCM acts as an approximation of a multivariate copula. Several results concerning optimal simplified vine copula approximations and their properties are established. Under regularity conditions, step-by-step estimators of pair-copula constructions converge to the partial vine copula approximation (PVCA) if the simplifying assumption does not hold. The PVCA can be regarded as a generalization of the partial correlation matrix where partial correlations are replaced by j-th order partial copulas. We show that the PVCA does not minimize the KL divergence from the true copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-copula. Moreover, we demonstrate how spurious conditional (in)dependencies may arise in SVCMs.