Generalized information matrix tests for copulas

We propose a family of goodness-of-fit tests for copulas. The tests use generalizations of the information matrix (IM) equality of White and so relate to the copula test proposed by Huang and Prokhorov. The idea is that eigenspectrum-based statements of the IM equality reduce the degrees of freedom of the test’s asymptotic distribution and lead to better size-power properties, even in high dimensions. The gains are especially pronounced for vine copulas, where additional benefits come from simplifications of score functions and the Hessian. We derive the asymptotic distribution of the generalized tests, accounting for the nonparametric estimation of the marginals and apply a parametric bootstrap procedure, valid when asymptotic critical values are inaccurate. In Monte Carlo simulations, we study the behavior of the new tests, compare them with several Cramer–von Mises type tests and confirm the desired properties of the new tests in high dimensions.     

四棱豆营养器官化感潜力的比较

以萝卜和菜心种子为受体,采用生物检测方法,对四棱豆根、茎和叶水浸液的化感潜力进行比较研究,结果表明：四棱豆根、茎和叶水浸液对萝卜和菜心种子萌发的抑制作用随水浸液处理浓度的增加呈增强趋势.根和茎水浸液对萝卜和菜心的根长均有抑制作用,且根的抑制效果高于茎,而叶表现为促进作用.水浸液对萝卜和菜心胚轴生长均有不同程度的促进作用.四棱豆叶水浸液对提高萝卜根冠比的效果明显,而茎和根水浸液对其影响较小.经四棱豆根、茎和叶水浸液处理后,均能明显降低菜心的根冠比,其中根水浸液的作用效果更为明显.     

Modeling multivariate cybersecurity risks

Modeling cybersecurity risks is an important, yet challenging, problem. In this paper, we initiate the study of modeling multivariate cybersecurity risks. We develop the first statistical approach, which is centered at a Copula-GARCH model that uses vine copulas to model the multivariate dependence exhibited by real-world cyber attack data. We find that ignoring the due multivariate dependence causes a severe underestimation of cybersecurity risks. Both simulation and empirical studies show that the proposed approach leads to accurate predictions of multivariate cybersecurity risks.     

Bayesian model selection for D‐vine pair‐copula constructions

In recent years analyses of dependence structures using copulas have become more popular than the standard correlation analysis. Starting from Aas et al. ( 2009 ) regular vine pair‐copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence present in data can simplify and reduce them significantly. In this paper the authors detect (conditional) independence in a particular vine PCC model based on bivariate t copulas by deriving and implementing a reversible jump Markov chain Monte Carlo algorithm. However, the methodology is general and can be extended to any regular vine PCC and to all known bivariate copula families. The proposed approach considers model selection and estimation problems for PCCs simultaneously. The effectiveness of the developed algorithm is shown in simulations and its usefulness is illustrated in two real data applications. The Canadian Journal of Statistics 39: 239–258; 2011 © 2011 Statistical Society of Canada     

不同pH值对裂叶牵牛种子萌发和幼苗生长的影响

研究了pH值对裂叶牵牛种子萌发和幼苗生长的影响,结果表明：pH值为3～4的酸性水溶液可缩短裂叶牵牛的种子萌发时间,并促进种子萌发.随着pH值的降低,裂叶牵牛幼苗的根长、苗高及鲜质量受到的抑制作用增大;pH值对裂叶牵牛叶绿素b的影响高于叶绿素a;随着pH值的降低,叶绿素a/b增大.pH值对裂叶牵牛幼苗根、茎、叶的可溶性糖和MDA（丙二醛）含量的影响存在差异.pH值降低使裂叶牵牛的茎及根中的可溶性糖和MDA含量增加.当pH值为4时,裂叶牵牛叶中的可溶性糖和MDA含量均最高;当pH值高于或低于4时,裂叶牵牛叶的可溶性糖和MDA含量均下降.     

国际油价与中美股价的相依关系研究——基于不同行业数据的分析

石油市场和股票市场作为现代经济中两个重要的市场，在经济活动中发挥着重要的作用。二者之间的关系对研究市场间的价格波动和风险传递有着重要的意义，本文通过vine copula模型对国际油价和中美两国股价之间相依关系进行分析，并将得到的相依关系运用到风险管理中。利用国际油价和中美各十个行业股票价格指数进行相依关系建模，得到相应的相依结构和相依关系，选择出与油价相依关系较强的行业股票价格指数和油价构建投资组合，利用相依关系模拟出收益率数据，度量投资组合的风险。实证研究结果表明中美两国的行业股票价格指数与国际油价的相依关系存在着显著的不同，中国行业股票价格指数与国际油价之间的相依关系要弱于美国行业股票价格指数与国际油价的相依关系；同时利用相依关系组成投资组合，对两组投资组合进行风险度量，风险度量的结果显示vine copula-GARCH能对具有较强的相依关系的变量组成的投资组合风险有很好的估计。     

A multivariate volatility vine copula model

This article proposes a dynamic framework for modeling and forecasting of realized covariance matrices using vine copulas to allow for more flexible dependencies between assets. Our model automatically guarantees positive definiteness of the forecast through the use of a Cholesky decomposition of the realized covariance matrix. We explicitly account for long-memory behavior by using fractionally integrated autoregressive moving average (ARFIMA) and heterogeneous autoregressive (HAR) models for the individual elements of the decomposition. Furthermore, our model incorporates non-Gaussian innovations and GARCH effects, accounting for volatility clustering and unconditional kurtosis. The dependence structure between assets is studied using vine copula constructions, which allow for nonlinearity and asymmetry without suffering from an inflexible tail behavior or symmetry restrictions as in conventional multivariate models. Further, the copulas have a direct impact on the point forecasts of the realized covariances matrices, due to being computed as a nonlinear transformation of the forecasts for the Cholesky matrix. Beside studying in-sample properties, we assess the usefulness of our method in a one-day-ahead forecasting framework, comparing recent types of models for the realized covariance matrix based on a model confidence set approach. Additionally, we find that in Value-at-Risk (VaR) forecasting, vine models require less capital requirements due to smoother and more accurate forecasts.     

Structured Coupling of Probability Loss Distributions: Assessing Joint Flood Risk in Multiple River Basins

Losses due to natural hazard events can be extraordinarily high and difficult to cope with. Therefore, there is considerable interest to estimate the potential impact of current and future extreme events at all scales in as much detail as possible. As hazards typically spread over wider areas, risk assessment must take into account interrelations between regions. Neglecting such interdependencies can lead to a severe underestimation of potential losses, especially for extreme events. This underestimation of extreme risk can lead to the failure of riskmanagement strategies when they are most needed, namely, in times of unprecedented events. In this article, we suggest a methodology to incorporate such interdependencies in risk via the use of copulas. We demonstrate that by coupling losses, dependencies can be incorporated in risk analysis, avoiding the underestimation of risk. Based on maximum discharge data of river basins and stream networks, we present and discuss different ways to couple loss distributions of basins while explicitly incorporating tail dependencies. We distinguish between coupling methods that require river structure data for the analysis and those that do not. For the later approach we propose a minimax algorithm to choose coupled basin pairs so that the underestimation of risk is avoided and the use of river structure data is not needed. The proposed methodology is especially useful for large‐scale analysis and we motivate and apply our method using the case of Romania. The approach can be easily extended to other countries and natural hazards.     

Predictive assessment of copula models

Copulas are powerful explanatory tools for studying dependence patterns in multivariate data. While the primary use of copula models is in multivariate dependence modelling, they also offer predictive value for regression analysis. This article investigates the utility of copula models for model‐based predictions from two angles. We assess whether, where, and by how much various copula models differ in their predictions of a conditional mean and conditional quantiles. From a model selection perspective, we then evaluate the predictive discrepancy between copula models using in‐sample and out‐of‐sample predictions both in bivariate and higher‐dimensional settings. Our findings suggest that some copula models are more difficult to distinguish in terms of their overall predictive power than others, and depending on the quantity of interest, the differences in predictions can be detected only in some targeted regions. The situations where copula‐based regression approaches would be advantageous over traditional ones are discussed using simulated and real data. The Canadian Journal of Statistics 47: 8–26; 2019 © 2018 Statistical Society of Canada     

基于藤Copula方法的持续期自相依结构估计及预测

本文基于Copula方法对由高频分笔数据得到的交易量持续期进行了研究。应用多元藤Copula方法对连续几个交易量持续期之间的自相依结构进行估计,在此基础上提出了一种新的条件密度函数估计方法,进而给出了交易量持续期的预测。对中国石化高频分笔数据进行实证分析的结果表明,本文模型对持续期的预测能力要明显优于EACD模型,在密度函数预测检验方面,本文模型也有更好的表现。