Tail dependence functions and vine copulas Joe, Harry; Li, Haijun; Nikoloulopoulos, Aristidis K.
Journal of multivariate analysis,
2010, 2010-01-00, 20100101, Letnik:
101, Številka:
1
Journal Article
Recenzirano
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Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as ...well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated.
Vine Copula Based Modeling Czado, Claudia; Nagler, Thomas
Annual review of statistics and its application,
03/2022, Letnik:
9, Številka:
1
Journal Article
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With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable ...separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical (including the Gaussian and
t
-copula) and Archimedean families (such as Clayton and Gumbel copulas). Both classes are rather restrictive with regard to symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by building a multivariate model using only bivariate building blocks. This gives rise to highly flexible models that still allow for computationally tractable estimation and model selection procedures. These features made vine copula models quite popular among applied researchers in numerous areas of science. This article reviews the basic ideas underlying these models, presents estimation and model selection approaches, and discusses current developments and future directions.
Spatiotemporal dependence structures play a pivotal role in understanding the meteorological characteristics of a basin or subbasin. This further affects the hydrological conditions and, ...consequently, will provide misleading results if these structures are not taken into account properly. In this study, we modelled the spatial dependence structure of three climate variables, maximum and minimum temperature and precipitation, throughout the Monsoon‐dominated zone of Pakistan. For temperature, six meteorological stations have been considered, for precipitation we used the results of four meteorological stations. For modelling the dependence structure between temperature and precipitation at multiple sites, we utilized C‐Vine, D‐Vine and student t‐copula models. For temperature, multivariate mixture normal distributions, and for precipitation, the gamma distribution, have been used as marginals under the copula models. The models were calibrated by utilizing the 20 years daily data from 1981 to 2000, and for validation, we used the data for 10‐year period from 2001 to 2010. The simulations were performed for each variable separately, conditioned on spatial neighbours. A comparison was made between the different copula models, on the basis of observational and simulated patterns and spatial dependence structures, the performance was evaluated for the validation period. The results show that all copula models performed well; however, there are subtle differences between them. The copula models captured the patterns and spatial dependence structures between climate variables, however, the t‐copula showed poor performance in reproducing the dependence structure with respect to magnitude. It was observed that important statistics of observed data have been closely approximated except a few maximum values for maximum temperature and minimum values for minimum temperature. Probability density functions of simulated data follow closely the pattern of observational data. These methods can be combined with statistical downscaling models to improve their performance, particularly in modelling the dependence structure between climate variables at multiple sites.
Target area of this study is the Monsoon‐dominated region of Pakistan where the figure shows different climate zones. Area under study and the locations of considered meteorological stations are enlarged on the left side. The latitude and longitude are mentioned on horizontal and vertical axes, respectively.
Current practice in predicting future weather is the use of numerical weather prediction (NWP) models to produce ensemble forecasts. Despite of enormous improvements over the last few decades, they ...still tend to exhibit bias and dispersion errors and, consequently, lack calibration. Therefore, these forecasts may be improved by statistical postprocessing. In this work, we propose a D‐vine‐copula‐based postprocessing for 10 m surface wind speed ensemble forecasts. This approach makes use of quantile regression related to D‐vine copulas, which is highly data driven and allows one to adopt more general dependence structures as the state‐of‐the‐art zero‐truncated ensemble model output statistic (tEMOS) model. We compare local and global D‐vine copula quantile regression (DVQR) models to the corresponding tEMOS models and their gradient‐boosting extensions (tEMOS‐GB) for different sets of predictor variables using one lead time and 60 surface weather stations in Germany. Furthermore, we investigate which types of training periods can improve the performance of tEMOS and the D‐vine‐copula‐based method for wind speed postprocessing. We observe that the D‐vine‐based postprocessing yields a comparable performance with respect to tEMOS if only wind speed ensemble variables are included and to substantial refinements if additional meteorological and station‐specific weather variables are integrated. As our main result, we note that, in the global setting, DVQR is able to provide better scores than tEMOS‐GB in general, whereas the local DVQR is able to substantially outperform the local tEMOS‐GB at particular stations admitting nonlinear relationships among the variables. In addition, we remark that training periods capturing seasonal patterns perform the best. Last but not least, we adapt a criterion for calculating the variable importance in D‐vine copulas and we outline which predictor variables are due to this approach the most important for the correction of wind speed ensemble forecasts.
In the global postprocessing of wind speed ensemble forecasts, the D‐vine copula quantile regression (DVQR) is able to substantially outperform the boosted zero‐truncated ensemble model output statistics with gradient‐boosting extensions (tEMOS‐GB) with respect to the continuous ranked probability skill score (CRPSS), as shown in the figure. Locally, DVQR shows a similar performance to tEMOS‐GB and yields clearly better results than tEMOS‐GB at particular stations admitting nonlinear relationships among the variables.
Flexible multivariate distributions are needed in many areas. The popular multivariate Gaussian distribution is however very restrictive and cannot account for features like asymmetry and heavy ...tails. Therefore dependence modeling using copulas is nowadays very common to account for such patterns. The use of copulas is however challenging in higher dimensions, where standard multivariate copulas suffer from rather inflexible structures. Vine copulas overcome such limitations and are able to model complex dependency patterns by benefiting from the rich variety of bivariate copulas as building blocks. This article presents the R package CDVine which provides functions and tools for statistical inference of canonical vine (C-vine) and D-vine copulas. It contains tools for bivariate exploratory data analysis and for bivariate copula selection as well as for selection of pair-copula families in a vine. Models can be estimated either sequentially or by joint maximum likelihood estimation. Sampling algorithms and graphical methods are also included.
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•Adopting a novel methodology called VC-DM for multivariate drought analysis.•Developing LSSVM-SCA as a modern hybridization strategy for downscaling rainfall data.•Using ...four-dimensional vine copula-based structures (Canonical and Drawable Vines)•Considering climate change conditions in predicting future drought characteristics.
This research provides a novel methodology for modeling multivariate dependence structures of meteorological drought characteristics (severity, duration, peak, and interarrival time), based on the combination of four-dimensional Vine Copulas and Data Mining algorithm (hereinafter called VC-DM). Two flexible vine copula structures (i.e., canonical vine (C-vine) and drawable vine (D-vine)) were used for multivariate drought modeling in three climatologically different regions of Iran (i.e., Mehrabad, Semnan, and Nowshahr synoptic stations). Furthermore, data mining algorithms approach was employed for downscaling/bias correction rainfall data obtained from four General Circulation Models (GCMs) (i.e., CanESM2, BNU-ESM, CCSM4, and GFDL-CM3). The approach was based on the least square support vector machine (LSSVM), which is hybridized with two optimization algorithms (i.e., grid search (GS) and Sine Cosine algorithm (SCA)). Results indicated that LSSVM-SCA was more accurate than LSSVM-GS for all GCMs in the testing period. The uncertainty analysis results for the historical period (1977–2005) revealed that LSSVM-SCA had less uncertainty than LSSVM-GS. It was also observed that of all the selected GCMs, CanESM2 had less uncertainty for most climate change scenarios (RCP2.6, RCP4.5, and RCP8.5). So, CanESM2 as the best GCM with low uncertainty and LSSVM-SCA as the superior downscaling/bias correction method were selected for drought characteristics analysis under climate change conditions. The rainfall predictions for the 2021–2100 period were projected to decrease in Mehrabad station and increase in Semnan and Nowshahr stations under all three selected RCPs. Finally, all projected drought characteristics were analyzed by the selected and preferable vine copula-based model (C-vine model with mixed-pair copulas) to provide comprehensive insight towards future drought conditions. It can be concluded that more severe droughts will occur in 2021–2100 than the historical period, and the absolute value of drought severity decreases under RCP2.6 in all stations. All drought durations are also expected to decrease while drought peaks will not change significantly in all stations and under all scenarios.
Vine growing and production in global context Navrátilová, Miroslava; Brož, David; Beranová, Markéta
SHS Web of Conferences,
2021, Letnik:
92
Journal Article, Conference Proceeding
Recenzirano
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Research background:
The global agri-food complex changed in last years. From global scale point of view agri-food complex must face new challenges in the field of changes of natural conditions and ...in the field of social and trade relations. Vine growing is due to the specific demands on its production is a suitable representative of these global changes.
Purpose of the article:
The aim of this paper is to investigate relationship between area of vineyards and its production in context of globalization.
Methods:
Secondary data were obtained from official information sources. From the point of view of the methodological apparatus, the analysis of time series were used. Based on the selection of a suitable trend function were forecasted following two period. Furthermore, modifications to the data matrix were made. For individual variables, which were compared using appropriate statistical methods. The growth coefficient was determined. The relationship between the variables was investigated.
Findings & Value added:
Based on the data, there is an obvious degressive trend in vineyards, which could be caused by the European Union standard for maximum planting up to 2 % per year. Wine production fluctuates significantly during monitoring and it is very difficult to determine its trend. In the last decade, there is possible to see an increasing of wine consumption. In future research, the relationship between consumption and production, or the production and overall performance of agriculture as a sector, may be examined.
A widespread methodology for modeling modern day information, which consists of high-dimensional digital measurements, is to use vine copulas; they can flexibly encode the underlying dependence ...structure of the data. Here we introduce a new algorithm to encode complete and truncated vines in a matrix, and as such, storing the information content of vines in a virtual environment. The conditional independence structure encoded by a vine can be represented in graph terms. We summarize these representations, and show equivalence between them. We show a new result, namely that when a perfect elimination ordering of a vine structure is given, then it can be uniquely represented with a matrix. Nápoles has shown a way to represent vines in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences, which can also store truncated vines. Moreover, this new algorithm can directly build truncated vines by storing each level separately - without building up the entire vine, which would be necessary in Nápoles' algorithm. We calculate the runtime of these algorithms. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.
•R-statistic is used in predictor variables selection and vine structure determination.•Stochastic simulation series preserve distribution and statistical characteristics of observed records.•The ...proposed approach has low sensitivity to the number of predictor variables.•The proposed approach possesses good adaptability and robustness.
Stochastic streamflow generation is crucial for water resources planning and management as well as water conservancy project design and operation. This study proposes an accurate, reliable and parsimonious approach for stochastic streamflow generation considering temporal and spatial dependence on the basis of regular vine copula model. The emphasis is on advancing an R-statistic based strategy of vine structure determination that divide the vine copula model construction into two independent parts and avoid continuous accumulation of uncertainty in the traditional Kendall's tau based method. Two study regions (the Upper Colorado River basin and Middle Yangtze River basin) with diverse hydrology regime and available data length are selected as case studies to showcase the performance of the proposed approach in practice. The results indicate better performance than two existing models in terms of streamflow estimation, and demonstrate that stochastic simulation series can preserve distribution and statistical characteristics of observed records. R-vine copula model constructed by the proposed approach is confirmed to possess low sensitivity to the number of predictor variables as well as good adaptability and robustness to streamflow series with diverse characteristics and abundances. The enhanced capability and performance stem from the accurate identification of predictor variables and characterization of complex and diverse dependence structures among different streamflow series, on the basis of a comprehensive and precise dependence measure, R-statistic.
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