Past studies have shown considerable differences between equity markets in conventional and Islamic financial systems, in terms of financial products and principles. Using a copula approach, this ...study shows that the global Islamic equity market index (represented by the Dow Jones Islamic Market Index) exhibits significant dependence with three major global conventional equity indices (Asia, Europe, and United States) and the global factors (oil prices, stock market implied volatility (VIX), the U.S. 10-year Treasury bond interest rate, and the 10-year European Monetary Union government bond index) which are common to the world financial system and pertinent to contagion risks in the case of financial crises. Moreover, this dependence varies over time for all cases except the S&P 500 index and is also asymmetric between bear and bull markets in some cases. Our findings thus suggest that the Sharia-compliance rules are not restrictive enough to make the global Islamic equity market index very different from the conventional indices. In addition, the decoupling hypothesis of the Islamic equity universe from the conventional financial system is not well supported by our empirical evidence.
•Dependence of the Islamic equity index with major global markets and factors is studied.•The copula approaches capture both average and extreme dependence structures.•Significant dependence between Islamic markets and global markets and factors is found.•Dependence structure also varies over time for almost all cases and is asymmetric.•Sharia-compliant rules are not restrictive enough to make the Islamic investments different.
In this work, we are interested in the nonparametric estimation of the copula function in the presence of bivariate twice censored data. Assuming that the copula functions of the right and the left ...censoring variables are known, we propose an estimator of the joint distribution function of the variables of interest, then we derive an estimator of their copula function. Using a representation of the proposed estimator of the joint distribution function as a sum of independent and identically distributed variables, we establish the weak convergence of the empirical copula that we introduce.
Understanding future river flood risk is a prerequisite for developing climate change adaptation strategies and enhancing disaster resilience. Previous flood risk assessments can barely take into ...account future changes of fine‐scale hydroclimatic characteristics and hardly quantify multivariate interactions among flood variables, thereby resulting in an unreliable assessment of flood risk. In this study, for the first time, we develop probabilistic projections of multidimensional river flood risks at a convection‐permitting scale through the Weather Research and Forecasting (WRF) climate simulations with 4‐km horizontal grid spacing. Vine copula has been widely used to assess the multidimensional dependence structure of hydroclimate variables, but the commonly used frequentist approach may fail to identify the correct vine model and to obtain the uncertainty interval. Thus, a Bayesian vine copula approach is proposed to explicitly address the multidimensional dependence of flood characteristics (i.e., flood peak, volume, and duration) and underlying uncertainties. The proposed approach enables a robust assessment of return periods of future floods for Guadalupe and Mission river basins located in South Texas of the United States. Our findings reveal that the South Texas region is projected to experience more flood events with longer duration and greater discharge volume. The flood peak, however, will not necessarily increase even though precipitation extremes are expected to become more frequent. The projected flood return periods over the Guadalupe river basin do not show an obvious increase while the Mission river basin is projected to face a dramatic increase in flood risk with exposed to 100‐year and even severer floods nearly every 2 years, on average, when considering the combined effects of flood peak, volume, and duration.
Key Points
Probabilistic projections of multidimensional flood risks were developed at a convection‐permitting scale
High‐resolution climate projections with the 4‐km horizontal grid spacing were developed using the convection‐permitting Weather Research and Forecasting model
Bayesian vine copula approach was proposed to uncover potential interactions among flood variables and associated uncertainties
The ongoing decarbonisation of modern electricity systems has led to a substantial increase of operational uncertainty, particularly due to the large-scale integration of renewable energy generation. ...However, the expanding space of possible operating points renders necessary the development of novel security assessment approaches. In this paper we focus on the use of security rules where classifiers are trained offline to characterize previously unseen points as safe or unsafe. This paper proposes a novel deep learning-based feature extraction framework for building security rules. We show how deep autoencoders can be used to transform the space of conventional state variables (e.g., power flows) to a small number of dimensions where we can optimally distinguish between safe and unsafe operation. The proposed framework is data-driven and can be useful in multiple applications within the context of security assessment. To achieve high accuracy, a novel objective-based loss function is proposed to address the issue of imbalanced safe/unsafe classes that characterize electricity system operation. Furthermore, an R-vine copula-based model is proposed to sample historical data and generate large populations of anticipated system states for training. The superior performance of the proposed framework is demonstrated through a series of case studies and comparisons using the load and wind generation data from the French transmission system, which have been mapped to the IEEE 118-bus system.
In this study, the accuracy of the copula-based model in the simulation of the dew point temperature in various climates of Iran was investigated, using simulations based on vine copulas such as C-, ...D-, and R-vine copulas. By examining the various vine copulas and their tree sequences, the best copula and best tree sequence based on AIC, BIC, and log-likelihood were selected. The results show that based on the complete similarity in our case between C-, D- and R-vine copulas, the selected best C-vine copulas fit well the dependence between the minimum and maximum air temperatures and dew point temperature. The simulation results were analyzed using root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE) coefficient, and violin plots. The results show that the copula-based model has high accuracy at all stations. The min (max) RMSE is related to Kerman (Ahvaz) station with RMSE = 0.396 oC (0.617 oC). Also, the min (max) NSE is related to Ahvaz (Urmia) station with NSE = 0.925 (0.955). Also, according to the violin plot, it is possible to appreciate the acceptable certainty of the copula-based model. Due to the diversity of the tree sequences of vine copulas and the use of the rotated states of the internal vine copulas, as well as the possibility of interfering with the effective parameters in high dimensions, the simulation results are reliable and have no restrictions. This model can be used as the best model to estimate dew point temperature due to the full coverage of the range of changes in data.
•A new approach for Ensemble Post-Processing based on copula functions was developed (COP-EPP).•The proposed approach proves to be more precise and accurate in generating the ensemble precipitation ...forecast.•A better representation of extremes is provided.•The method is not limited to the normal distribution assumption between the observation and forecast.
Recently, ensemble post-processing (EPP) has become a commonly used approach for reducing the uncertainty in forcing data and hence hydrologic simulation. The procedure was introduced to build ensemble precipitation forecasts based on the statistical relationship between observations and forecasts. More specifically, the approach relies on a transfer function that is developed based on a bivariate joint distribution between the observations and the simulations in the historical period. The transfer function is used to post-process the forecast. In this study, we propose a Bayesian EPP approach based on copula functions (COP-EPP) to improve the reliability of the precipitation ensemble forecast. Evaluation of the copula-based method is carried out by comparing the performance of the generated ensemble precipitation with the outputs from an existing procedure, i.e. mixed type meta-Gaussian distribution. Monthly precipitation from Climate Forecast System Reanalysis (CFS) and gridded observation from Parameter-Elevation Relationships on Independent Slopes Model (PRISM) have been employed to generate the post-processed ensemble precipitation. Deterministic and probabilistic verification frameworks are utilized in order to evaluate the outputs from the proposed technique. Distribution of seasonal precipitation for the generated ensemble from the copula-based technique is compared to the observation and raw forecasts for three sub-basins located in the Western United States. Results show that both techniques are successful in producing reliable and unbiased ensemble forecast, however, the COP-EPP demonstrates considerable improvement in the ensemble forecast in both deterministic and probabilistic verification, in particular in characterizing the extreme events in wet seasons.
Copulas and Histogram-Valued Data Jin, Honghe; Billard, Lynne
Journal of computational and graphical statistics,
04/2023, Letnik:
32, Številka:
2
Journal Article
Recenzirano
Histogram-valued data are emerging increasingly often as a consequence of the aggregation of large datasets. One statistic that underpins many methodologies especially regression and principal ...component analyses is the covariance function. To date, no method exists for calculating these functions directly from the marginal histogram observations. This article develops techniques through copula functions to develop a parametric distribution for multivariate histogram-valued data. In particular, maximum likelihood, inference function for margins, and canonical maximum likelihood estimation methods are proposed. A numerical study helps to ascertain which copulas are best to use in various cases, and thence to calculate the covariances. The results are applied to a real dataset.
This paper presents a new copula‐based methodology for Gaussian and non‐Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on ...the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non‐Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Key Points
Flexible to several conditioning constraints
Inverse problem transformed to a continuous optimization problem
Extensions to non‐Gaussian spatial structures
A novel copula-based probabilistic model is proposed to establish the temperature difference analysis model for a long-span suspension bridge’s steel box girder. The key idea is to express a ...two-dimensional function of the temperature difference in flat steel box girder by using copulas. The maximum and minimum values of daily temperature difference model was developed using long-terms structural health monitoring data. Then, the correlation between adjacent temperature differences is investigated using five types of copulas. Akaike information criterion (AIC) is used to select an optimal model from five types of copulas, and the optimal joint function (two-dimensional function) for steel box girder’s temperature difference is established. Finally, the structure’s temperature gradient model is extrapolated for the service life of the structure by using Monte Carlo method. Moreover, this paper discusses the temperature gradient models using five types of common copulas and four types of time-varying copulas. The result shows that the t-copula is the optimal function to build the two-dimensional functions for steel box girder’s temperature difference, and the temperature model along the transverse direction can offer useful information that is not available in the design codes.
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