Post-Processing Ensemble Weather Forecasts for Introducing Multisite and Multivariable Correlations using Rank Shuffle and Copula Theory

Statistical methods have been widely used to post-process ensemble weather forecasts for hydrological predictions. However, most of the statistical post-processing methods apply to a single weather variable at a single location, thus neglecting the inter-site and inter-variable dependence structures of forecast variables. This study synthesized a multisite and multivariate (MSMV) post-processing framework that extends the univariate method to the MSMV version by directly rearranging the post-processed ensemble members (post-reordering strategy) or by rearranging the latent variables used in univariate method (pre-reordering strategy). Based on the univariate Generator-based Post-Processing (GPP) method, the two reordering strategies and three dependence reconstruction methods (Rank shuffle (RS), Gaussian Copula (GC), and Empirical Copula (EC)) totaling 6 MSMV methods (RS-Pre, GC-Pre, EC-Pre, RS-Post, GC-Post, and EC-Post) were evaluated in post-processing ensemble precipitation and temperature forecasts for the Xiangjiang Basin in China using the 11-member ensemble forecasts from the Global Ensemble Forecasting System (GEFS). The results showed that raw GEFS forecasts tend to be biased for both the forecast ensembles and the inter-site and inter-variable dependencies. Univariate method can improve the univariate performance of ensemble mean and spread but misrepresent the inter-site and inter-variable dependence among the forecast variables. The MSMV framework can well utilize the advantages of the univariate method and also reconstruct the inter-site and inter-variable dependencies. Among the six methods, RS-Pre, RS-Post, GC-Post, and EC-Post perform better than the others with respect to reproducing the univariate statistics and multivariable dependences. The post-reordering strategy is recommended to combine the univariate method (i.e. GPP) and reconstruction methods.

EXPRESS: Handling Endogenous Regressors using Copulas: A Generalization to Linear Panel Models with Fixed Effects and Correlated Regressors

This paper proposes a panel data generalization for a recently suggested IVfree estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common GLS transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor-error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to GMM-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.

Finite-sample properties of estimators for first and second order autoregressive processes

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like . A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying -package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model

Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed.

Revisiting Gaussian copulas to handle endogenous regressors

Marketing researchers are increasingly taking advantage of the instrumental variable (IV)-free Gaussian copula approach. They use this method to identify and correct endogeneity when estimating regression models with non-experimental data. The Gaussian copula approach’s original presentation and performance demonstration via a series of simulation studies focused primarily on regression models without intercept. However, marketing and other disciplines’ researchers mainly use regression models with intercept. This research expands our knowledge of the Gaussian copula approach to regression models with intercept and to multilevel models. The results of our simulation studies reveal a fundamental bias and concerns about statistical power at smaller sample sizes and when the approach’s primary assumptions are not fully met. This key finding opposes the method’s potential advantages and raises concerns about its appropriate use in prior studies. As a remedy, we derive boundary conditions and guidelines that contribute to the Gaussian copula approach’s proper use. Thereby, this research contributes to ensuring the validity of results and conclusions of empirical research applying the Gaussian copula approach.

Copula methods for evaluating relative tail forecasting performance

PurposeThe authors apply their method to analyze which portfolios are capable of providing superior performance to those based on the Sharpe ratio (SR).Design/methodology/approachIn this paper the authors illustrate the use of conditional copulas for identifying differences in alternative portfolio performance strategies. The authors analyze which portfolios are capable of providing superior performance to those based on the SR.FindingsThe results show that under the Gaussian copula, both expected tail ratio (ETR) and skewness-kurtosis ratio portfolios exhibit remarkably low correlations respecting the SR portfolio. This means that these two portfolios are different respecting the SR one. The authors also find that copulas which focus on either the upper tail (Gumbel) or the lower tail (Clayton) render significant differences. In short, the copula analysis is useful to understand what kind of equity-screening strategy based on its corresponding performance measure (PM) performs better in relation to the SR portfolio.Practical implicationsCopula methods for evaluating relative tail forecasting performance provide an alternative tool when forecast differences are very small or found non statistically significant through standard tests.Originality/valueOur copula methods to evaluate models' performance differences are significant because when models' performance is rather similar, conclusions on statistical differences, can be defective as they may hinge on the subsample type or size used, leading to inefficient investment decisions. Our method based in copula is novel in this research topic.

Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.