Copula Estimation Research Articles

Technical Efficiency of Rice Production in the Upper North of Thailand: Clustering Copula-Based Stochastic Frontier Analysis

This study examines the efficiency of rice production in Thailand, especially major rice, which is the main crop of farmers in all regions of Thailand and is still a pressing issue. Analyzing technical efficiency by using the appropriate analytical tools inevitably brings about determining the correct production efficiency measures. In this study, we applied the K-Means algorithm and copula-based stochastic frontier model to cluster farmer groups in order to find the different factors that impact the group, and to relax the assumption of the two components of random error, which is that they are independent to each other; the correlation of the two components of random error is also represented by the estimation of copula. The findings from the K-Means clustering algorithms applied in this study indicate that the production frontiers can be divided into two frontiers, with the number of farmers under the frontiers of such production differing from the number of farmers collected in each area. The production frontiers were obtained with 591 farmers under the first production frontier and 65 farmers under the second. In addition, the results reflected a correlation between the two error components U and V. This suggests inefficiencies and zero-mean, and that the symmetric error is not independent of each other. The findings from the application of the copula-based stochastic frontier production function models indicate that land, cost of chemicals, and labor inputs have significant positive effects on the mean output of major rice in both groups of farmers. Therefore, the results of this study indicate that the financial services in rural areas should be continuously promoted by governmental policy, particularly via agricultural loans, to rural people since the utilization of inputs affects the quantity of rice produced. Timely loans should be encouraged.

Modeling the Interdependence Structure between Rain and Radar Variables Using Copulas: Applications to Heavy Rainfall Estimation by Weather Radar

In radar quantitative precipitation estimates (QPE), the progressive evolution of rainfall algorithms has been guided by attempts to reduce the uncertainties in rainfall retrieval. However, because most of the algorithms are based on the linear dependence between radar and rain variables and designed for rain rates ranging from light to moderate rainfall, they result in misleading estimations of intense or strong rainfall rates. In this paper, based on extensive data gathered during the AMMA and Megha-Tropiques data campaigns, we provided a way to improve the estimation of intense rainfall rates from radar measurements. To this end, we designed a formulation of the QPE algorithm that accounts for the co-dependency between radar observables and rainfall rate using copula simulation synthetic datasets and using the quantile regression features for a more complete picture of covariate effects. The results show a clear improvement in heavy rainfall retrieval from radar data using copula-based R(KDP) algorithms derived from a realistic simulated dataset. For a better performance, Gaussian copula-derived algorithms require a 0.8 percentile distribution to be considered. Conversely, lower percentiles are better for Student’s, Gumbel and HRT copula estimators when retrieving heavy rainfall rates (R > 30). This highlights the need to investigate the entire conditional distribution to determine the performance of radar rainfall estimators.

Measuring re-identification risk using a synthetic estimator to enable data sharing.

BackgroundOne common way to share health data for secondary analysis while meeting increasingly strict privacy regulations is to de-identify it. To demonstrate that the risk of re-identification is acceptably low, re-identification risk metrics are used. There is a dearth of good risk estimators modeling the attack scenario where an adversary selects a record from the microdata sample and attempts to match it with individuals in the population.ObjectivesDevelop an accurate risk estimator for the sample-to-population attack.MethodsA type of estimator based on creating a synthetic variant of a population dataset was developed to estimate the re-identification risk for an adversary performing a sample-to-population attack. The accuracy of the estimator was evaluated through a simulation on four different datasets in terms of estimation error. Two estimators were considered, a Gaussian copula and a d-vine copula. They were compared against three other estimators proposed in the literature.ResultsTaking the average of the two copula estimates consistently had a median error below 0.05 across all sampling fractions and true risk values. This was significantly more accurate than existing methods. A sensitivity analysis of the estimator accuracy based on variation in input parameter accuracy provides further application guidance. The estimator was then used to assess re-identification risk and de-identify a large Ontario COVID-19 behavioral survey dataset.ConclusionsThe average of two copula estimators consistently provides the most accurate re-identification risk estimate and can serve as a good basis for managing privacy risks when data are de-identified and shared.

Seismic demand analysis using environmental contours of vector-valued ground motion intensity measures

A study is presented on seismic demand analysis using environmental contours of vector-valued ground motion intensity measures. The environmental contours specify combinations of intensity measures for estimating an engineering demand parameter with a given exceedance probability. Copulas are employed to model the joint distribution of vector-valued ground motion intensity measures for developing the environmental contours. A framework is presented for copula estimation of spectral accelerations using ground motion records from stations on stratified sand and silt deposits in Mexico City. The statistical dependence between pairs of spectral accelerations at a range of periods is analyzed in terms of Kendall’s τ and used for estimating parametric copula models. Goodness of fit of the estimated copulas is examined and the Akaike information criteria is applied for selection of copula models. Environmental contours of spectral accelerations are developed adopting the inverse FORM approach and employed to estimate mean exceedance rates of maximum interstory drift of a building model. Both, the cases of deterministic and stochastic response models of interstory drift are examined. The accuracy of the environmental contour estimates is assessed by comparison with Monte Carlo simulations and estimates from long-term analyses. It is found that the approximation of the failure surface in the inverse FORM approach is quite appropriate for a range of return periods for which very precise or reasonably accurate response estimates were obtained from the environmental contours.

General strategies for modeling joint probability density function of wind speed, wind direction and wind attack angle

The joint probability density function (JPDF) of the wind field parameters is essential for wind load analysis or energy assessment, but one key parameter of the wind attack angle is often excluded in current studies. Three different methodologies are proposed, aiming to estimate the JPDF of wind speed, wind direction and wind attack angle. Strategy I consists of the vine approach with the modified binary Bernstein copula adopted for nonparametric estimation. The modified ternary Bernstein copula is recommended to estimate the ternary copula directly in Strategy II. In strategy III, the Offset Elliptical Normal mixture model is extended to evaluate the three-dimensional case, where the wind vector is resolved into three orthogonal components. A typical mountainous bridge site with strongly inhomogeneous wind characteristics is selected to inspect the performance of these strategies. Satisfactory results are given by all these strategies in which the strategy II has better goodness-of-fit. Strategy I is slightly less reliable in estimating the dependencies of higher tree variables while avoids the time-consuming nonparametric estimation of three-dimensional copula. The strategy III is based on the physical model and performs better in the conditional probability estimation when the number of samples is small.

Copula Estimation for Nonsynchronous Financial Data

Copula is a powerful tool to model multivariate data. We propose the modelling of intraday returns of multiple financial assets through copula. The problem originates due to the asynchronous nature of intraday financial data. We propose a consistent estimator of the correlation coefficient in case of elliptical copula and show that the plug-in copula estimator is uniformly convergent. For non-elliptical copulas, we capture the dependence through Kendall’s Tau (leveraging the relation between copula parameter and Kendall’s tau). We demonstrate underestimation of the copula parameter and propose an alternative method to obtain an improved estimator. In simulations, the proposed estimator reduces the bias significantly for a general class of copulas. We apply the proposed methods to real data of several stock prices.

Cryptocurrencies, Diversification and the COVID-19 Pandemic

This paper features an analysis of cryptocurrencies and the impact of the COVID-19 pandemic on their effectiveness as a portfolio diversification tool and explores the correlations between the continuously compounded returns on Bitcoin, Ethereum and the S&P500 Index using a variety of parametric and non-parametric techniques. These methods include linear standard metrics such as the application of ordinary least squares regression (OLS) and the Pearson, Spearman and Kendall’s tau measures of association. In addition, non-linear, non-parametric measures such as the Generalised Measure of Correlation (GMC) and non-parametric copula estimates are applied. The results across this range of measures are consistent. The metrics suggest that, whilst the shock of the COVID-19 pandemic does not appear to have increased the correlations between the cryptocurrency series, it appears to have increased the correlations between the returns on cryptocurrencies and those on the S&P500 Index. This suggests that investments in cryptocurrencies are not likely to offer key diversification strategies in times of crisis, on the basis of evidence provided by this crisis.

Interfuel substitution: A copula approach

We investigate interfuel substitution using the Minflex Laurent flexible demand system and a more flexible copula estimation approach. In doing so, we relax the joint normality assumption of the errors of the demand system and estimate the model without having to delete one equation as is usually the practice under the assumption of jointly normally distributed errors. The results indicate that the short-run Morishima elasticities of substitution among crude oil, natural gas, and coal are small, implying that one fuel has hardly utilized to substitute for another fuel.

Approximate Bayesian conditional copulas

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, i.e. a joint cumulative distribution function on the unit hypercube with uniform marginals, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.

On weak conditional convergence of bivariate Archimedean and Extreme Value copulas, and consequences to nonparametric estimation

Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of convergence for copulas might seem far too restrictive to be of any practical importance – in fact, given samples of a copula C the corresponding empirical copulas do not converge weakly conditional to C with probability one in general. Within the class of Archimedean copulas and the class of Extreme Value copulas, however, standard pointwise convergence and weak conditional convergence can even be proved to be equivalent. Moreover, it can be shown that every copula C is the weak conditional limit of a sequence of checkerboard copulas. After proving these three main results and pointing out some consequences, we sketch some implications for two recently introduced dependence measures and for the nonparametric estimation of Archimedean and Extreme Value copulas.

Efficiency evaluation of the microgrid for selection of common bus using copula function-based efficiency curves of the converters

Due to the increase in load growth, construction of renewable energy-based microgrids (MG) has been seen as the most economical and viable solution in the recent past. It leads to the need for feasibility investigation at the planning and design stage for appropriate selection of common bus (CB) type. One of the critical factors to determine the suitable CB is efficiency analysis. This paper proposes an efficiency evaluation method by using the copula function-based efficiency curves of the converters. The degree of association between percentage loading and efficiency of the converters is defined using best-fitted copula estimation, and a large number of iterations are performed using Monte Carlo simulations to generate the efficiency for each time instant. A variety of scenarios are simulated to determine when and which type of CB is most favourable. The efficiency of the MG is strongly dependent on the converter efficiency, number of converters in the MG, and seasonal variations, both in generation and load demand. The results indicate that DC CB has superior performance with the net efficiency gain ranging from 8.26% to 5.63% in all scenarios considered in this study. Moreover, DC CB is most advantageous in the MG with the DC load only. It will bring greater advantages in the future with the continuous development of renewable energy-based MGs and the increasing penetration of DC loads.

Simulation techniques of Archimedean Copula Estimators: Parametric and Semi-Parametric Approaches

In this paper, we look at two different approaches methodologies for copula estimation. The first is based on a parametric approach using MLE and IFM methods, while the second is entirely based on Kendall's tau and spearman's rho in a semi-parametric context, where the margins are estimated non-parametrically. Interestingly, based on R software simulation techniques, the contribution of their algorithms, approach, and illustration was our main focus for this paper. As an application, a class of Archimedean copulas was notably chosen. This particular class of copulas was also presented for censored data to show the estimator's performance even better.

The uniform CLT for the empirical estimator of countable state space semi-Markov kernels indexed by functions with applications

This paper is concerned with the uniform CLT for an empirical estimator of countable state space semi-Markov processes indexed by functions under the uniformly integrable entropy condition. The results of this paper generalise those of Limnios [(2004), ‘A Functional Central Limit Theorem for the Empirical Estimator of a Semi-Markov Kernel’, Journal of Nonparametric Statistics, 16(1–2), 13–18. The International Conference on Recent Trends and Directions in Nonparametric Statistics]. We apply our results to the following important topics: on the kernel-type estimator of the semi-Markov kernel, the weak convergence of the smoothed empirical semi-Markov processes, we introduce the copula estimators in the semi-Markov framework and we establish their limiting laws by using the functional delta methods. We prove the main results for the uniform CLT via a martingale difference sequence as in Bae et al. [(2010), ‘The Uniform CLT for Martingale Difference Arrays Under the Uniformly Integrable Entropy’, Bulletin of the Korean Mathematical Society, 47(1), 39–51].

Modelling mortality dependence: An application of dynamic vine copula

Vine copula, constructed from bivariate copulas, provides great flexibility in modelling complex high-dimensional dependence. When applied to multi-population mortality modelling, vine copula yields significant improvement over traditional multivariate copulas. In this paper, we propose to capture time-varying features in mortality dependence with dynamic regular vine (R-vine) copula which is built from bivariate copulas with time-varying dependence parameters. We develop two dependence dynamics for R-vine copulas and illustrate the selection and estimation of dynamic R-vine copulas using mortality data from eight populations. The estimated R-vine copulas using the proposed dependence dynamics are shown to yield better goodness of fit than both static and regime-switching vine copulas. We further demonstrate the simulation of mortality paths using dynamic R-vine copulas and examine the impact of vine copula choice on the assessed effectiveness of longevity hedge.

Inflating Away the Public Debt? An Empirical Assessment

Abstract This paper proposes a new method for measuring the impact of inflation on the real value of public debt. The distribution of debt debasement is based on two inputs: the distribution of privately held nominal debt by maturity, for which we provide new estimates, and the distribution of risk-adjusted inflation dynamics, for which we provide a novel copula estimator using options data. We find that inflation by itself is unlikely to lower the U.S. fiscal burden significantly because debt is concentrated at short maturities and perceived inflation shocks have little short-run persistence and are small.

Co-Movement between Tourist Arrivals of Inbound Tourism Markets in South Korea: Applying the Dynamic Copula Method Using Secondary Time Series Data

Tourism demand is severely affected by unpredicted events, which has prompted scholars to examine ways of predicting the effects of positive and negative shocks on tourism, to ensure a sustainable tourism industry. The purpose of this study was to investigate if non-linear dependence structures exist between tourist flows into South Korea from five major source countries, as South Korea has undergone fluctuations in tourist arrivals due to diverse circumstances and has complex relations with tourism source countries. Additionally, the study examines the structures of extreme tail dependence, which is indicated in the case of unexpected events, and identifies how co-movements vary over time through dynamic copula–GARCH (generalized autoregressive conditional heteroskedasticity) tests. The secondary time series data for the 2005–2019 period of tourist arrivals to Korea were derived from the Korea Tourism Knowledge and Information System for testing the copula models. The copula estimations indicate significant dependencies among all market pairs as well as the strongest dependence between China and Taiwan. Moreover, extreme tail dependence structures show co-movements for four pairs of tourism markets in only negative shocks, for five pairs in both positive and negative conditions, but no co-movement in the China–Taiwan pair. Finally, the dynamic dependence structures reveal that the China–Taiwan dependence is higher than the other time-varying dependence structures, implying that the two markets complement each other.

Dependence Structure between Tourist Arrivals of Inbound Tourism Markets inSouth Korea

Tourism demand is severely affected by unpredicted events. The purpose of this study was to investigate if non-linear dependence structures exist between tourist flows into South Korea from five major source countries, as South Korea has undergone fluctuations in tourist arrivals due to diverse circumstances and has complex relations with tourism source countries. Additionally, the study examines the structures of extreme tail dependence, which is indicated in the case of unexpected events, and identifies how co-movements vary over time through dynamic copula-GARCH (Generalized Autoregressive Conditional Heteroskedasticity) tests. The copula estimations indicate significant dependencies among all market pairs as well as the strongest dependence between China and Taiwan. Moreover, extreme tail dependence structures show co-movements for four pairs of tourism markets in only negative shocks, for five pairs in both positive and negative conditions, but no co-movement in the China-Taiwan pair. Finally, the dynamic dependence structures reveal that the China-Taiwan dependence is higher than the other time-varying dependence structures, implying that the two markets complement each other.

Modelling Financial Risks for Egyptian Insurance Market. Evidence from Insurance Investment Channels

Recently, there has been renewed interest in modelling risks especially in insurance market, there has been substantial research undertaken on the importance of copula in financial risk management field. This study aim to estimate risk measures Value-at-Risk (VaR) and Expected Shortfall (ES) based on the dependence structure between investment channels (Government bonds, Securities available for trade, Securities available for sale and Securities held to maturity) by using elliptical Gaussian copula on data collected from Egyptian insurance market from 2007/2008 to 2018/2019. The principal finding of this research is to measure the financial risk according to the copula estimation. The findings of this paper illustrate that the copula parameter ρ is simmilar to the parameter in the whole market, that is because the life insurance sector has long term conrtacts while the nonlife sector has short term contracts. Moreover, VaR and CVaR in all sectors are equevlint that reflects the stability in insurance sector.

Application of PSO Method for Archimedean Copula Parameter Estimation in Flood (Rain) and Tide Joint Distribution Analysis

Archimedean copulas are the most popular class of copulas used in hydrological statistical models. Parameter estimation of copulas is an open and complex task. A faster and computationally easier estimation procedure is needed. In this study, a particle swarm optimization (PSO) method is proposed to obtain the parameters of copulas and their corresponding marginal distributions. The proposed PSO method is illustrated on hydrological variables (i.e., flood discharge, rainfall, tide level) of four gauging sites located in Jiangsu province and Shenzhen city, China. Five commonly used marginal distributions (including Pearson Type III, lognormal, gamma, Weibull, and generalized extreme value), three symmetric Archimedean copulas (including Clayton copula, Gumbel–Hougaard copula, Frank copula), and six asymmetric Archimedean copulas are used to construct the joint distributions of selected hydrological variables. The best parameters of copulas and marginal distributions are estimated based on PSO, and the most appropriate copulas and marginal distributions are selected based on the goodness of fit between empirical and theoretical distributions. The results show that the proposed PSO-based parameter estimation method is effective in this case study.

Copula-based time series with filtered nonstationarity

Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the filtered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series. We show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation, and may be non-normal. Surprisingly, the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration, which is normal and free of marginal distribution specification. The simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas, and facilitate statistical inferences, such as hypothesis testing and model selection tests, on semiparametric copula-based dynamic models in the presence of nonstationarity. Monte Carlo studies and real data applications are presented.