Treatment after Pollution?

The paper considers the causal relationship about CO2 emissions, traffic density and urbanization development in China's provinces by the quantile causality test The method can capture the structural breaks under different quantiles from the nonlinear perspective. The robust results don't find the causality relationship between traffic density and CO2 emissions. Urbanization will increase CO2 emission at the high quantile level while the impact of CO2 emissions on urbanization presents a symmetric relationship. The promoting effect of transportation on urbanization only occurs at the beginning of urbanization. It shows the environmental pollution is a key factor to the whole process of urbanization. With the advancement of urbanization, the increase of traffic line density has no significant impact on the urbanization process. The results can provide references for the government in the layout of local traffic lines and the improvement of urbanization.

Optimizing Expected Shortfall under an ℓ1 Constraint—An Analytic Approach

Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N is the number of different assets in the portfolio, and T is the length of the available time series. The critical ratio depends on the confidence level α, which means we have a line of critical points on the α−r plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an ℓ1 regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e., a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric ℓ1 regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights, and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio r=N/T, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters.

A Method for Confidence Intervals of High Quantiles

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

Spatio-temporal patterns of larval fish settlement in the northwestern Mediterranean Sea

Most coastal fish species spend their early life stages in the pelagic environment, before settling in coastal habitats. The variability in the arrival of larvae to coastal habitats provides information on the species’ biology and recruitment potential. To explore the dynamics of larval fish supply to coastal habitats in the NW Mediterranean Sea, 13 sites were monitored using light-traps, from July 2012 to December 2015. Most variation in catches per unit effort (CPUE) among topographic basins and species were statistically significant for high (quantile 75%) and very high (quantile 90%) catches only. At the yearly scale, CPUE displayed strong seasonality, and 3 main species assemblages were detected in late spring-early summer, summer and late autumn-early winter. At the monthly scale, CPUE were higher around the new moon for all quantiles and temporally autocorrelated at a lag of ~28 d. Larval supply also varied spatially with site-specific associations and with riverine influence. Altogether, these results confirm that the previously described patterns of larval supply observed in tropical and subtropical environments (e.g. the high variability at all spatial and temporal scales and the strong influence of the moon) also apply to Mediterranean fish assemblages. Our quantile-based approach demonstrated that the larval supply in the NW Mediterranean Sea is a solid candidate for monitoring the state of the marine ecosystems, highlighting the need to continue such time series.

High-quantile regression for tail-dependent time series

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.

Research on the Pricing of Global Drought Catastrophe Bonds

The rapid development of catastrophe bonds provides a new idea for catastrophe risk dispersion, since its traditional means fail to afford the economic losses caused by the global drought catastrophe. With the deepening of the concept of the community with a shared future for mankind, there is an opportunity to issue global drought catastrophe bonds through international cooperation. Based on the data of global drought catastrophe losses from 1900 to 2018, this paper selects 21 countries as the primary participants of international cooperation and studies the pricing of drought catastrophe bonds by the POT model and high quantile estimation. The results show that the first-class bond has a 10% occurrence probability with the trigger point of $252.54 million, and the second-class one has a 35% occurrence probability with the trigger point being $117.13 million. In line with high quartile estimates, the one-year principal-protected catastrophe bonds with a face value of $1,000 are valued at $957.14 and $939.29, respectively. Besides, the principal portion of the lost bonds is $912.50 and $783.04, while the total of it is $867.86 and $626.79, respectively.

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation (CTE) for a loss distribution with a finite mean but infinite variance.The present work introduces a new estimator of the CTE based on the bias-reduced estimators of high quantile for heavy-tailed distributions. The asymptotic normality of the proposed estimator is established and checked, in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the known old estimator.

Impact of Foreign Direct Investment on Environmental Performance

The paper presents the results of a study that attempts to investigate the impact of foreign direct investment (FDI) on environmental performance (EP) by constructing a panel quantile regression model. Based on panel data from 1990 to 2014, this study contributes to evaluate the EP of each of the 40 countries using a directional slack-based model considering undesirable output. Our findings reveal several key conclusions: first, FDI has an insignificant influence on EP for the full sample. Second, the impact of FDI on EP between developed and developing countries exists heterogeneity. Furthermore, there is heterogeneity regarding the effect of FDI on EP at different quantiles of EP in developed countries. Specifically, in the developed countries, the effect is statistically insignificant at the lower quantile of EP, then it turns significantly positive at the middle and high quantile, and the positive effect rises with the increase of quantiles of EP. Finally, based on the conclusions of quantitative analysis, some important policy recommendations are proposed: different governments ought to enact different strategies for the introduction of FDI, according to different development situations of different countries.