Vines--a new graphical model for dependent random variables

Bedford, Tim; Cooke, Roger M.

doi:10.1214/aos/1031689016

Cited by 1,108 publications

(699 citation statements)

References 10 publications

Supporting

Mentioning

681

Contrasting

Unclassified

Order By: Relevance

“…They are based on conditional bivariate copulas, which can be coupled by the concept of vines (Bedford and Cooke, 2002). Figure 1 shows the popular D-Vine.…”

Section: Estimation Of Multivariate Return Periods Via 3-dand Pair-comentioning

confidence: 99%

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Schulte

Schumann

2015

Proc. IAHS

View full text Add to dashboard Cite

Abstract. Although the consequences of floods are strongly related to their peak discharges, a statistical classification of flood events that only depends on these peaks may not be sufficient for flood risk assessments. In many cases, the flood risk depends on a number of event characteristics. In case of an extreme flood, the whole river basin may be affected instead of a single watershed, and there will be superposition of peak discharges from adjoining catchments. These peaks differ in size and timing according to the spatial distribution of precipitation and watershed-specific processes of flood formation. Thus, the spatial characteristics of flood events should be considered as stochastic processes. Hence, there is a need for a multivariate statistical approach that represents the spatial interdependencies between floods from different watersheds and their coincidences. This paper addresses the question how these spatial interdependencies can be quantified. Each flood event is not only assessed with regard to its local conditions but also according to its spatio-temporal pattern within the river basin. In this paper we characterise the coincidence of floods by trivariate Joe-copula and pair-copulas. Their ability to link the marginal distributions of the variates while maintaining their dependence structure characterizes them as an adequate method. The results indicate that the trivariate copula model is able to represent the multivariate probabilities of the occurrence of simultaneous flood peaks well. It is suggested that the approach of this paper is very useful for the risk-based design of retention basins as it accounts for the complex spatio-temporal interactions of floods.

show abstract

“…They are based on conditional bivariate copulas, which can be coupled by the concept of vines (Bedford and Cooke, 2002). Figure 1 shows the popular D-Vine.…”

Section: Estimation Of Multivariate Return Periods Via 3-dand Pair-comentioning

confidence: 99%

Extensive spatio-temporal assessment of flood events by application of pair-copulas

Schulte

Schumann

2015

Proc. IAHS

View full text Add to dashboard Cite

show abstract

“…An elegant way of constructing more general multivariate distributions through conditioning using bivariate copulas was first introduced by [58,59] based on earlier work of [60] (see also [55] for a recent summary). The resulting so-called pair copula construction (PCC) which has been investigated in detail by [61,62] can be neatly illustrated in three dimensions by the following example: Let f be the continuous density function of a 3-dimensional distribution function F with marginals F 1 , F 2 and F 3 .…”

Section: Regular Vine Copulasmentioning

confidence: 99%

Regime Switching Vine Copula Models for Global Equity and Volatility Indices

et al. 2017

View full text Add to dashboard Cite

For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature that correlations and higher moments between different indices tend to vary in time. However, to the best of our knowledge, no one has yet considered a global setup including both equity and implied volatility indices of various continents, and allowing for a changing dependence structure. We aim to close this gap by applying Markov-switching R-vine models to investigate the existence of different, global dependence regimes. In particular, we identify times of "normal" and "abnormal" states within a data set consisting of North-American, European and Asian indices. Our results confirm the existence of joint points in a time at which global regime switching between two different R-vine structures takes place.

show abstract

“…Such an approximation, when copulas are applied to one another like a vine, are known as vine copulas; see, e.g., [1,7,8,10,13,14,15,18,19,21,24].…”

Section: Possible Application To Copulasmentioning

confidence: 99%