基于POT-GPD损失分布的农业自然灾害VAR估算

 近年来,干旱、洪涝、雪灾等极端气象灾害频发,强烈冲击农业生产和粮食安全,科学估算农业自然灾害给粮食产出带来的风险价值,对预警农业自然灾害、确保粮食安全具有重要意义。文章针对农业自然灾害大灾损失的低频高损、数据稀少的特点,采用极值理论中的POT 模型对历史观测值超阀值数据进行建模,运用GPD模型对农业自然大灾损失进行拟合,模拟计算农业自然灾害VAR值,为农业自然灾害预警和粮食安全储备提供科学依据。     

POT模型在巨灾损失预测中的应用——基于MCMC方法的估计

极值统计学主要研究随机事件极端情况的统计规律性。运用POT模型拟合中国暴雨损失数据,确定损失超出量的分布形式。实证分析表明,借助POT模型对巨灾风险损失分布进行估计是较为合理的,但当数据量较小时,使用基于Gibbs抽样的MCMC方法估计POT模型的参数,可以解决样本数据不足导致的极大似然估计中误差增大的问题。     

A new approach to investigating spatial variations of disease

Summary.  For rare diseases the observed disease count may exhibit extra Poisson variability, particularly in areas with low or sparse populations. Hence the variance of the estimates of disease risk, the standardized mortality ratios, may be highly unstable. This overdispersion must be taken into account otherwise subsequent maps based on standardized mortality ratios will be misleading and, rather than displaying the true spatial pattern of disease risk, the most extreme values will be highlighted. Neighbouring areas tend to exhibit spatial correlation as they may share more similarities than non-neighbouring areas. The need to address overdispersion and spatial correlation has led to the proposal of Bayesian approaches for smoothing estimates of disease risk. We propose a new model for investigating the spatial variation of disease risks in conjunction with an alternative specification for estimates of disease risk in geographical areas—the multivariate Poisson–gamma model. The main advantages of this new model lie in its simplicity and ability to account naturally for overdispersion and spatial auto-correlation. Exact expressions for important quantities such as expectations, variances and covariances can be easily derived.     

在岸离岸人民币利率极端风险溢出研究

本文采用递归MVMQ-CAViaR模型,对境内外人民币利率极端风险溢出效应进行实证检验。结果表明：境内外人民币利率存在极端风险溢出效应,短期品种表现出显著的双向极端风险溢出,而长期品种以在岸利率对离岸利率单向极端风险溢出为主。在极端风险层面在岸市场仍然处于利率信息的中心地位,且暂时没有旁落离岸市场的担忧。一旦离岸人民币利率发生极端变动,央行会及时进行干预并引导市场参与者预期,降低在岸利率未来的极端风险水平;但面对小的离岸市场冲击,央行更倾向于让在岸利率进行自我调节,离岸冲击会提高在岸利率未来的极端风险水平。本文构建的模型具有较好的预测能力,有助于金融监管部门对离岸利率极端风险进行动态准确地管理。     

多元极值的参数建模方法及其金融应用：最新进展述评

 由于现实中的极值事件往往倾向于同时或相继发生,因此多元极值研究正成为极值统计学的理论前沿和研究热点。本文对该领域中参数建模方法的最新进展做了系统性述评,包括经典多元极值理论、Ledford-Tawn-Ramos方法和Heffernan和Tawn条件法等,并指出了这些建模方法的优缺点以及未来可能的理论突破点。本文还全面分析了近年来多元极值分析方法在金融领域的国内外应用现状,并探讨其未来的应用前景,可能是在金融传染、组合问题和系统性风险管理等方面。     

基于点过程的极值VaR研究

风险无时不有、无处不在,风险本身并不可怕,金融机构就是通过承担风险、管理风险来获得收益的。真正可怕的是极值风险,即稀少或极端事件的发生给经济主体带来巨额损失的风险。因此对极值风险的建模就成为风险管理的重中之重。极值理论为极端事件的统计建模和极值风险测度的计算提供了坚实的理论基础,故有必要通过介绍和比较传统极值事件的建模,基于点过程构建极值风险的一般模型,并利用外汇市场的日数据和VaR的估计与检验进行实证分析。     

Disentangling the sources of variation in the survival of the European dipper

The population growth rate of the European dipper has been shown to decrease with winter temperature and population size. We examine here the demographic mechanism for this effect by analysing how these factors affect the survival rate. Using more than 20 years of capture-mark-recapture data (1974-1997) based on more than 4000 marked individuals, we perform analyses using open capture-mark-recapture models. This allowed us to estimate the annual apparent survival rates (probability of surviving and staying on the study site from one year to the next one) and the recapture probabilities. We partitioned the variance of the apparent survival rates into sampling variance and process variance using random effects models, and investigated which variables best accounted for temporal process variation. Adult males and females had similar apparent survival rates, with an average of 0.52 and a coefficient of variation of 40%. Chick apparent survival was lower, averaging 0.06 with a coefficient of variation of 42%. Eighty percent of the variance in apparent survival rates was explained by winter temperature and population size for adults and 48% by winter temperature for chicks. The process variance outweighed the sampling variance both for chick and adult survival rates, which explained that shrunk estimates obtained under random effects models were close to MLE estimates. A large proportion of the annual variation in the apparent survival rate of chicks appears to be explained by inter-year differences in dispersal rates.     

Regression‐type models for extremal dependence

We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.     

Disentangling the sources of variation in the survival of the European dipper

The population growth rate of the European dipper has been shown to decrease with winter temperature and population size. We examine here the demographic mechanism for this effect by analysing how these factors affect the survival rate. Using more than 20 years of capture-mark-recapture data (1974-1997) based on more than 4000 marked individuals, we perform analyses using open capture-mark-recapture models. This allowed us to estimate the annual apparent survival rates (probability of surviving and staying on the study site from one year to the next one) and the recapture probabilities. We partitioned the variance of the apparent survival rates into sampling variance and process variance using random effects models, and investigated which variables best accounted for temporal process variation. Adult males and females had similar apparent survival rates, with an average of 0.52 and a coefficient of variation of 40%. Chick apparent survival was lower, averaging 0.06 with a coefficient of variation of 42%. Eighty percent of the variance in apparent survival rates was explained by winter temperature and population size for adults and 48% by winter temperature for chicks. The process variance outweighed the sampling variance both for chick and adult survival rates, which explained that shrunk estimates obtained under random effects models were close to MLE estimates. A large proportion of the annual variation in the apparent survival rate of chicks appears to be explained by inter-year differences in dispersal rates.     

Trend and Return Level of Extreme Snow Events in New York City

Abstract

A major winter storm brought up to 42 inches of snow in parts of the Mid-Atlantic and Northeast states for January 22–24, 2016. The blizzard of January 2016 impacted about 102.8 million people, claiming at least 55 lives and $500 million to $3 billion in economic losses. This article studies two important aspects of extreme snowfall events: 1. trends in annual maxima and threshold exceedances and 2. return levels for extreme snowfall. Applying extreme value methods to the extreme snow data in the New York City area, we quantify linear trends in extreme snowfall and assess how severe the 2016 blizzard is in terms of return levels. To find a more realistic standard error for the extreme value methods, we extend Smith’s method to adapt to both spatial and temporal correlations in the snow data. Our results show increasing, but insignificant trends in the annual maximum snowfall series. However, we find that the 87.5th percentile snowfall has significantly increased by 0.564 inches per decade, suggesting that, while the maximum snowfall is not significantly increasing, there have been increases in the snowfall among the larger storms. We also find that the 2016 blizzard is indeed an extreme snow event equivalent to about a 40-year return level in the New York City area. The extreme value methods used in this study are thoroughly illustrated for general readers. Data and modularized programming codes are to be available online to aid practitioners in using extreme value methods in applications.     

Estimation and forecasting hospital admissions due to Influenza: Planning for winter pressure. The case of the West Midlands, UK

Winters are a difficult period for the National Health Service (NHS) in the United Kingdom (UK), due to the combination of cold weather and the increased likelihood of respiratory infections, especially influenza. In this article we present a proper statistical time series approach for modelling and analysing weekly hospital admissions in the West Midlands in the UK during the period week 15/1990 to week 14/1999. We consider three variables, namely, hospital admissions, general practitioner consultants, and minimum temperature. The autocorrelations of each series are shown to decay hyperbolically. The correlations of hospital admission and the lag of other series also decay hyperbolically but with different speed and directions. One of the main objectives of this paper is to show that each of the three series can be represented by a Fractional Differenced Autoregressive integrated moving average model, (FDA). Further, the hospital admission winter and summer residuals shows significant interdependency, which may be interpreted as hidden periodicities within the last 10-years time interval. The short-range (8 weeks) forecasting of hospital admission of the FDA model and a fourth-order AutoRegressive AR(4) model are quite similar. However, our results reveal that the long-range forecasting of FDA is more realistic. This implies that, using the FDA approach, the respective authority can plan for winter pressure properly.     

Extreme quantile estimation based on financial time series

Estimation of market risk is an important problem in finance. Two well-known risk measures, viz., value at risk and median shortfall, turn out to be extreme quantiles of the marginal distribution of asset return. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore, estimation of extreme quantiles in the presence of such features in the data seems to be of natural interest. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review these quantile estimators and compare their known properties. Their finite sample performance are compared using Monte Carlo simulation. We propose a new estimator that exhibits encouraging finite sample performance while estimating extreme quantile in the right tail region.     

Flexible Covariance Structures for Categorical Dependent Variables Through Finite Mixtures of Generalized Extreme Value Models

A new class of finite mixture discrete choice models, denoted FinMix (fīn m?ks), is introduced. These arise from the combination of a finite number of core Generalized Extreme Value (GEV) models to achieve more flexible functional forms, particularly in terms of error covariance structures. Example members of the class include combinations of (1) Multinomial Logit (MNL) models with differing scales, (2) multinomial logit with nested MNL models, (3) tree extreme value models with differing preference trees, and so on. Compatibility of FinMix models with utility maximization is easily determined, which permits empirical investigation of the suitability of specific model forms for economic evaluation exercises.     

A Case for Better Graphics: The Unclassed Choropleth Map

In recent years a number of researchers have shown a strong interest in statistical graphics. One widely used graphical method is the “statistical map,” or what is better known in cartography as the choropleth map. A factor in the use of these maps has been the need to group data into classes, raising the obvious question of defining optimum class intervals. Computer technology now makes it possible to produce unclassed choropleth maps, minimizing quantization error. An example of the two methods is given using criminal justice statistics. The unclassed maps are more accurate with regard to quantization error and appear to be of superior visual quality     

ESTIMATING BAYESIAN NETWORKS FOR HIGH‐DIMENSIONAL DATA WITH COMPLEX MEAN STRUCTURE AND RANDOM EFFECTS

The estimation of Bayesian networks given high‐dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically assume that the data consist of independent and identically distributed samples. It is often the case, however, that the available data have a more complex mean structure, plus additional components of variance, which must then be accounted for in the estimation of a Bayesian network. In this paper, score metrics that take account of such complexities are proposed for use in conjunction with score‐based methods for the estimation of Bayesian networks. We propose first, a fully Bayesian score metric, and second, a metric inspired by the notion of restricted maximum likelihood. We demonstrate the performance of these new metrics for the estimation of Bayesian networks using simulated data with known complex mean structures. We then present the analysis of expression levels of grape‐berry genes adjusting for exogenous variables believed to affect the expression levels of the genes. Demonstrable biological effects can be inferred from the estimated conditional independence relationships and correlations amongst the grape‐berry genes.     

Multigaussian models: The danger of parsimony

Summary MultiGaussian models have the intrinsic property of imposing very little continuity to extreme values. If the variable that is being modeled is hydraulic conductivity and the processes being studied are groundwater flow and mass transport, the absence of continuous paths of extreme values will have a retardation effect in the computed travel times. In the case of radionuclide release of nuclear waste from a deep geological repository, underestimation of travel times may lead to unsafe decision making. To demonstrate the impact of the low continuity of extreme value implicit to multiGaussian modes, travel times are computed in a site similar to Finnsj?n-one of the sites in crystaline rock studied in Sweden-using two stochastic models with the same histogram and covariance, one of them is multiGaussian, and the other is not and displays high connectivity of extreme high values. The results show that the multiGaussian model leads to less conservative results than the non-multiGaussian one. Invoking the parisimony principle to select a multiGaussian model as the simplest model that can be fully described by a mean value and a covariance function should not be justification enough for such selection. If there is not enough data to characterize the connectivity of the extreme values and therefore distriminate whether a multiGaussian model is appropriate or not, less parismonious models must also be considered.     

Simulation and extremal analysis of hurricane events

In regions affected by tropical storms the damage caused by hurricane winds can be catastrophic. Consequently, accurate estimates of hurricane activity in such regions are vital. Unfortunately, the severity of events means that wind speed data are scarce and unreliable, even by standards which are usual for extreme value analysis. In contrast, records of atmospheric pressures are more complete. This suggests a two-stage approach: the development of a model describing spatiotemporal patterns of wind field behaviour for hurricane events; then the simulation of such events, using meteorological climate models, to obtain a realization of associated wind speeds whose extremal characteristics are summarized. This is not a new idea, but we apply careful statistical modelling for each aspect of the model development and simulation, taking the Gulf and Atlantic coastlines of the USA as our study area. Moreover, we address for the first time the issue of spatial dependence in extremes of hurricane events, which we find to have substantial implications for regional risk assessments.     

Spatial modeling of extreme rainfall in northeast Thailand

It is well recognized that the generalized extreme value (GEV) distribution is widely used for any extreme events. This notion is based on the study of discrete choice behavior; however, there is a limit for predicting the distribution at ungauged sites. Hence, there have been studies on spatial dependence within extreme events in continuous space using recorded observations. We model the annual maximum daily rainfall data consisting of 25 locations for the period from 1982 to 2013. The spatial GEV model that is established under observations is assumed to be mutually independent because there is no spatial dependency between the stations. Furthermore, we divide the region into two regions for a better model fit and identify the best model for each region. We show that the regional spatial GEV model reflects the spatial pattern well compared with the spatial GEV model over the entire region as the local GEV distribution. The advantage of spatial extreme modeling is that more robust return levels and some indices of extreme rainfall can be obtained for observed stations as well as for locations without observed data. Thus, the model helps to determine the effects and assessment of vulnerability due to heavy rainfall in northeast Thailand.     

Extreme value analysis of actuarial risks: estimation and model validation

We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic analysis of extreme value estimators and to devise tools for the validation of the underlying model assumptions. While the focus of the paper is on univariate tail risk analysis, the basic ideas of the analysis of the extremal dependence between different risks are also outlined. Here we emphasize some of the limitations of classical multivariate extreme value theory and sketch how a different model proposed by Ledford and Tawn can help to avoid pitfalls. Finally, these theoretical results are used to analyze a data set of large claim sizes from health insurance.