Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data.

Study on drought events in China based on time-varying nested Archimedean-copula function

Drought forecasting, which can enable contingency actions to be implemented in advance of a drought, plays a significant role in reducing the risks and impacts of drought. In this study, a simulation framework of the occurrence probability of drought events based on nested Copula function and Gibbs sampling is proposed to effectively compensate for the high-dimensional problems and lack of initial data in traditional methods. And the precipitation data of 718 meteorological stations from 1961 to 2018 in China was analyzed. The results showed that the occurrence location of drought events was mainly concentrated from 35° to 42° north latitude and 105° to 120° east longitude, with the occurrence time mainly concentrated from September to November. The Archimedean-copula function, constructed based on latitude, longitude, and occurrence time, could precisely determine the spatiotemporal joint probability distribution of drought events (RMSE:0.01). The optimal time-varying nested Archimedean-copula functions were obtained from February to May (Spring), June to September (Summer) and October to January (Autumn and Winter). Compared to the nested Archimedean-copula function, the accuracy of Gibbs sampling and simulation based on time-varying nested Archimedean-copula function was increased by 84.05% latitude and 69.76% longitude. The results provide an effective means for scientific drought forecasting, and water resource management departments can take preventive measures at an early stage.

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.