This article presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for ...relatively high-dimensional applications, involving 50 or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied tail dependence using extreme value theory, and we verify that simulation-based estimation using rank statistics is reliable even in high dimensions. We consider "scree" plots to aid the choice of the number of factors in the model. The model is applied to daily returns on all 100 constituents of the S&P 100 index, and we find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that factor copula models provide superior estimates of some measures of systemic risk. Supplementary materials for this article are available online.
Several approximations of copulas have been proposed in the literature. By using empirical versions of checker-type copulas approximations, we propose non parametric estimators of the copula. Under ...some conditions, the proposed estimators are copulas and their main advantage is that they can be sampled from easily. One possible application is the estimation of quantiles of sums of dependent random variables from a small sample of the multivariate law and a full knowledge of the marginal laws. We show that estimations may be improved by including in an easy way in the approximated copula some additional information on the law of a sub-vector for example. Our approach is illustrated by numerical examples.
•We study downside and upside risk spillovers between currency and stock prices.•Downside and upside VaR and conditional VaR are computed using copulas.•Currency values and stock prices in emerging ...countries are positively related.•There is downside and upside spillover risk effects between stock and currency markets.•Upside and downside risk spillovers are asymmetric.
We examined downside and upside risk spillovers from exchange rates to stock prices and vice versa for a set of emerging economies. We characterized the dependence structure between currency and stock returns using copulas and computed downside and upside value-at-risk and conditional value-at-risk. We documented a positive relationship between stock prices and currency values in emerging economies with respect to the US dollar and the euro, with downside and upside spillover risk effects transmitted both ways. Finally, we also documented asymmetries in upside and downside risk spillovers and asymmetric differences in the size of risk spillovers when the domestic currency values against the US dollar and the euro. Our results, consistent with flight-to-quality phenomena, have implications for downside and upside risk management of international investor portfolios in emerging markets.
•Novel joint behavioral model for AV carsharing and AV ride sourcing is presented.•Impacts of built environment & sustainable travel behaviors are analyzed.•Copula-based generalized additive discrete ...choice model is specified.•Identifies environmental & behavioral interventions to accelerate AV-C & AV-R adoption.•Important to consider systematic & random heterogeneity.
Rapid advancements in vehicle automation and a shift towards collaborative consumption trends will disrupt future urban mobility systems. We present a joint model of consumers’ affinity towards shared automated vehicles (SAVs) with two distinct yet related configurations: automated vehicle (AV) carsharing and AV ride sourcing. Compact and walkable built environment is known to support active travel and shared mobility but the potential impacts of built environment on adoption of automated shared mobility are largely unknown. Besides sociodemographic, sustainable travel, and technology-related factors, we examine the role of neighborhood-level walkability (composite measure of land-use, pedestrian-oriented urban design, and transit accessibility) in shaping public’s opinion about AV carsharing and AV ride sourcing technologies. Detailed travel behavior and stated preference/taste data for over 2700 individuals from the most recent 2019 Puget Sound Travel Survey are complemented with neighborhood-level high-resolution data on built environment fabric. Two dependent variables of interest include individual’s level of interest in AV carsharing and AV ride sourcing programs. A novel and comprehensive geo-additive heterogeneous copula-based joint behavioral model is developed - revealing complex stochastic dependence patterns between users’ interest in AV ride sourcing and carsharing programs and different layers of systematic and random taste heterogeneity. Results show that improving neighborhood walkability can be an effective way to increase public’s interest in using automated ride sourcing and carsharing services. Findings also highlight the opportunity to enable SAV adoption by harnessing the synergies between green (transit) travel, technology use for work/non-work purposes, use of existing mobility-on-demand (MOD) services, and affinity towards automated MOD services. Results are translated to potential policies for designing proactive behavioral and built environment interventions for accelerating SAV adoption with an enhanced sensitivity towards the needs of distinct and more vulnerable population groups (e.g., older, unemployed, and/or less educated individuals). The study methodologically contributes by presenting a comprehensive behavioral model for SAV adoption by differentiating ride sourcing and carsharing.
Studying the multivariate extension of copula correlation yields a dimension reduction principle, which turns out to be strongly related with the ‘simple measure of conditional dependence’ T recently ...introduced by Azadkia and Chatterjee (2021). In the present paper, we identify and investigate the dependence structure underlying this dimension reduction principle, provide a strongly consistent estimator for it, and demonstrate its broad applicability. For that purpose, we define a bivariate copula capturing the scale-invariant extent of dependence of an endogenous random variable Y on a set of d≥1 exogenous random variables X=(X1,…,Xd), and containing the information whether Y is completely dependent on X, and whether Y and X are independent. The dimension reduction principle becomes apparent insofar as the introduced bivariate copula can be viewed as the distribution function of two random variables Y and Y′ sharing the same conditional distribution and being conditionally independent given X. Evaluating this copula uniformly along the diagonal, i.e., calculating Spearman’s footrule, leads to an unconditional version of Azadkia and Chatterjee’s ‘simple measure of conditional dependence’ T. On the other hand, evaluating this copula uniformly over the unit square, i.e., calculating Spearman’s rho, leads to a distribution-free coefficient of determination (also known as ‘copula correlation’). Several real data examples illustrate the importance of the introduced methodology.
On non-central squared copulas Nasri, Bouchra R.
Statistics & probability letters,
June 2020, 2020-06-00, Volume:
161
Journal Article
Peer reviewed
The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing ...copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula (Nasri, 2019) can be used to estimate the parameters for several copula families.
A new class of hierarchical copulas is introduced based on joint survival functions of multivariate exponential mixture distributions. The key element of this construction is the mixing random vector ...defined by convolutions associated to a Lévy subordinator, and leading to hierarchical copulas with Archimedean within-block copulas and asymmetric between-block pair-copulas. For the specific case of two-level trees, dependence properties of pairs are investigated, and a full estimation procedure is proposed for the tree structure and parameters of the hierarchical copulas. The efficiency of the procedure is illustrated through three simulation examples and a study with two real datasets.
In this study, we introduce a novel concept of a copula dependence structure termed the stochastic monotone wing property and investigate its associated properties. This concept is closely related to ...the monotone conditional variance property, which describes the behavior of the conditional variance of V given U=u as either an increasing or a decreasing function of u for a given random vector (U,V) with a certain distribution function. The need for such a dependence structure arises in various fields, including insurance, where a copula family with the monotone conditional variance property is needed for the joint distribution of frequency and average severity in the collective risk model. Beyond insurance, its applications extend to economics and climatology. Furthermore, this study proposes a new parametric copula family that exhibits the stochastic monotone wing property and provides a method for constructing copulas with this characteristic.
Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, ...and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a given Archimedean generator is presented. Sampling this copula involves sampling an exponentially tilted stable distribution. A fast rejection algorithm is developed for the more general class of tilted Archimedean generators. It is proven that this algorithm reduces the complexity of the standard rejection algorithm to logarithmic complexity. As an application it is shown that the fast rejection algorithm outperforms existing algorithms for sampling exponentially tilted stable distributions involved, e.g., in nested Clayton copulas. Third, with the additional help of randomization of generator parameters, explicit sampling algorithms for several nested Archimedean copulas based on different Archimedean families are found. Additional results include approximations and some dependence properties, such as Kendall’s tau and tail dependence parameters. The presented ideas may also apply in the more general context of sampling distributions given by their Laplace–Stieltjes transforms.
•Vine copulas were employed to forecast spring seasonal precipitation at Australia’s agro-ecological zones (AEZ).•Influence of SOI and IPO Tripole Index on precipitation forecasting were assessed ...using bi- and trivariate copula models.•Except the western AEZ, indices had a major role in precipitation forecasting.•Trivariate models showed greater accuracy for three out of four AEZs, particularly in the tail dependence.
Vine copulas are employed to explore the influence of multi-synoptic-scale climate drivers – El Niño Southern Oscillation (ENSO) and Inter-decadal Pacific Oscillation (IPO) Tripole Index (TPI) – on spring precipitation forecasting at Agro-ecological Zones (AEZs) of the Australia’s wheat belt. To forecast spring precipitation, significant seasonal lagged correlation of ENSO and TPI with precipitation anomalies in AEZs using data from Australian Water Availability Project (1900–2013) was established. Most of the AEZs exhibit statistically significant dependence of precipitation and climate indices, except for the western AEZs. Bivariate and trivariate copula models were applied to capture single (ENSO) and dual predictor (ENSO & TPI) influence, respectively, on seasonal forecasting. To perform a comprehensive evaluation of the developed copula-statistical models, a total of ten one- and two-parameter bivariate copulas ranging from elliptical to Archimedean families were examined. Stronger upper tail dependence is visible in the bivariate model, suggesting that the influence of ENSO on precipitation forecasting during a La Niña event is more evident than during an El Niño event. In general, while the inclusion of TPI as a synoptic-scale driver into the models leads to a notable reduction in the mean simulated precipitation, it depicts a general improvement in the median values. The forecasting results showed that the trivariate forecasting model can yield a better accuracy than the bivariate model for the east and southeast AEZs. The trivariate forecasting model was found to improve the forecasting during the La Niña and negative TPI. This study ascertains the success of copula-statistical models for investigating the joint behaviour of seasonal precipitation modelled with multiple climate indices. The forecasting information and respective models have significant implications for water resources and crop health management including better ways to adapt and implement viable agricultural solutions in the face of climatic challenges in major agricultural hubs, such as Australia’s wheat belt.
