相依结构、动态系统性风险测度与后验分析

本文利用Copula相依结构理论扩展和求解了现有的系统性风险测度CoVaR,以得到适用于不同类型常参数和时变参数Copula函数及不同分布假设的动态系统性风险测度。为了验证和评估模型设定的准确性与应用价值,我们构建了适用于该动态系统性风险测度CoVaR的严谨后验分析工具。除“无条件覆盖性”、“独立性”和“条件覆盖性”外,我们首次提出了“混合独立性”检验。基于中国14家上市商业银行的实证分析表明：中国上市商业银行与中国银行业之间的相依结构呈现多样化特征;无论是样本内还是样本外预测区间,我们的动态Copula-CoVaR模型能够有效地捕捉典型系统性风险事件;严谨的后验分析不仅需要检验系统性风险测度CoVaR,也需要检验条件事件的临界值VaR。     

金融机构尾部风险溢出效应———基于改进非对称CoVaR模型的研究

为准确度量我国金融机构对金融系统的尾部风险溢出,本文改进了基于CoVaR 方法的分位数回归模型。基于极值理论和ARMA-GARCH模型拟合收益率边缘分布,构建了改进的非对称CoVaR模型,从系统性金融风险贡献绝对值(△CoVaR)和相对值(%CoVaR)两方面详细考察了2002年7月1日至2018年12月28日我国42家上市金融机构的尾部风险溢出效应。结果表明:在q=0.01的情况下,不同类型金融机构对金融市场的系统性金融风险贡献有显著差异,银行类与保险类机构的系统性金融风险值得重点关注;金融机构的系统性金融风险贡献相对值与在险价值存在显著联系,自身风险最低的银行类机构具有最大的风险溢出强度,是我国系统性金融风险防范的核心对象,尤其是国有控股银行。研究结论对于有效防范我国系统性金融风险具有重要的理论价值和现实意义。     

Semiparametric inference for the recurrent events process by means of a single-index model

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumulative mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a dimension reduction technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensionality when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results.     

Semiparametric jump-preserving estimation for single-index models

Estimation of the single-index model with a discontinuous unknown link function is considered in this paper. Existed refined minimum average variance estimation (rMAVE) method can estimate the single-index parameter and unknown link function simultaneously by minimising the average pointwise conditional variance, where the conditional variance can be estimated using the local linear fit method with centred kernel function. When there are jumps in the link function, big biases around jumps can appear. For this reason, we embed the jump-preserving technique in the rMAVE method, then propose an adaptive jump-preserving estimation procedure for the single-index model. Concretely speaking, the conditional variance is obtained by the one among local linear fits with centred, left-sided and right-sided kernel functions who has minimum weighted residual mean squares. The resulting estimators can preserve the jumps well and also give smooth estimates of the continuity parts. Asymptotic properties are established under some mild conditions. Simulations and real data analysis show the proposed method works well.     

Estimation of general semi-parametric quantile regression

Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.     

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.     

Adaptive density estimation: A curse of support?

This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we show that, exactly as a curse of dimensionality exists when the data lie in R^d, there exists a curse of support as well when the support of the density is infinite. As for the dimensionality problem where the rates of convergence deteriorate when the dimension grows, the minimax rates of convergence may deteriorate as well when the support becomes infinite. This problem is not purely theoretical since the simulations show that the support-dependent methods are really affected in practice by the size of the density support, or by the weight of the density tail. We propose a method based on a biorthogonal wavelet thresholding rule that is adaptive with respect to the nature of the support and the regularity of the signal, but that is also robust in practice to this curse of support. The threshold, that is proposed here, is very accurately calibrated so that the gap between optimal theoretical and practical tuning parameters is almost filled.     

A misspecification test for the higher order co-moments of the factor model

The traditional estimation of higher order co-moments of non-normal random variables by the sample analog of the expectation faces a curse of dimensionality, as the number of parameters increases steeply when the dimension increases. Imposing a factor structure on the process solves this problem; however, it leads to the challenging task of selecting an appropriate factor model. This paper contributes by proposing a test that exploits the following feature: when the factor model is correctly specified, the higher order co-moments of the unexplained return variation are sparse. It recommends a general to specific approach for selecting the factor model by choosing the most parsimonious specification for which the sparsity assumption is satisfied. This approach uses a Wald or Gumbel test statistic for testing the joint statistical significance of the co-moments that are zero when the factor model is correctly specified. The asymptotic distribution of the test is derived. An extensive simulation study confirms the good finite sample properties of the approach. This paper illustrates the practical usefulness of factor selection on daily returns of random subsets of S&P 100 constituents.     

Inference on semiparametric transformation model with general interval-censored failure time data

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided.     

Moment-Implied Densities: Properties and Applications

Suppose one uses a parametric density function based on the first four (conditional) moments to model risk. There are quite a few densities to choose from and depending on which is selected, one implicitly assumes very different tail behavior and very different feasible skewness/kurtosis combinations. Surprisingly, there is no systematic analysis of the tradeoff one faces. It is the purpose of the article to address this. We focus on the tail behavior and the range of skewness and kurtosis as these are key for common applications such as risk management.     

Semiparametric non-linear time series model selection

Summary.  Semiparametric time series regression is often used without checking its suitability, resulting in an unnecessarily complicated model. In practice, one may encounter computational difficulties caused by the curse of dimensionality. The paper suggests that to provide more precise predictions we need to choose the most significant regressors for both the parametric and the nonparametric time series components. We develop a novel cross-validation-based model selection procedure for the simultaneous choice of both the parametric and the nonparametric time series components, and we establish some asymptotic properties of the model selection procedure proposed. In addition, we demonstrate how to implement it by using both simulated and real examples. Our empirical studies show that the procedure works well.     

Variable selection for partially varying coefficient single-index model

In this paper, we consider the problem of variable selection for partially varying coefficient single-index model, and present a regularized variable selection procedure by combining basis function approximations with smoothly clipped absolute deviation penalty. The proposed procedure simultaneously selects significant variables in the single-index parametric components and the nonparametric coefficient function components. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Finite sample performance of the proposed method is illustrated by a simulation study and real data analysis.     

中国上市金融机构关联性度量及影响因素分析

本文结合非对称斜率模型与单指标分位数回归，构建了中国上市金融机构的尾部风险网络，从而刻画中国金融市场尾部风险关联性的时变特征，并基于金融机构层面探讨尾部风险关联性的影响因素。研究表明，中国金融系统的总关联性与部门内关联性在金融危机与股灾期间显著上升，其中保险的部门内关联性为银行、保险、证券三部门中最高，而部门间关联性远小于部门内关联性，部门间的风险传染效应较为微弱。研究还发现投资活动是金融机构形成尾部风险关联的重要渠道，投资业务占比过高的机构应予以更多监管。     

Detecting homogeneous segments in DNA sequences by using hidden Markov models

In recent years there has been a rapid growth in the amount of DNA being sequenced and in its availability through genetic databases. Statistical techniques which identify structure within these sequences can be of considerable assistance to molecular biologists particularly when they incorporate the discrete nature of changes caused by evolutionary processes. This paper focuses on the detection of homogeneous segments within heterogeneous DNA sequences. In particular, we study an intron from the chimpanzee α-fetoprotein gene; this protein plays an important role in the embryonic development of mammals. We present a Bayesian solution to this segmentation problem using a hidden Markov model implemented by Markov chain Monte Carlo methods. We consider the important practical problem of specifying informative prior knowledge about sequences of this type. Two Gibbs sampling algorithms are contrasted and the sensitivity of the analysis to the prior specification is investigated. Model selection and possible ways to overcome the label switching problem are also addressed. Our analysis of intron 7 identifies three distinct homogeneous segment types, two of which occur in more than one region, and one of which is reversible.     

Estimation of the scale parameter after a pre-test for homogeneity in a mis-specified regression model

The risk properties of estimators of the scale parameter after a pre-test for homogeneity of the error variances in the two sample linear regression model has received quite an amount of attention in the literature. This literature typically assumes normal disturbances and a properly specified model. In this paper we consider that both equations may be mis-specified by the omission of relevant regressors and that the error distributions may belong to a wider class than the normal distribution. We derive and analyse the exact risk (under quadratic loss) of the pre-test estimator of the scale parameter for the first sub-sample.     

Local quantile regression

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile curve is not a priori fixed. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimator of the conditional quantile curve requires to balance between local curvature and stochastic variability. In this paper, we suggest a local model selection technique that provides an adaptive estimator of the conditional quantile regression curve at each design point. Theoretical results claim that the proposed adaptive procedure performs as good as an oracle which would minimize the local estimation risk for the problem at hand. We illustrate the performance of the procedure by an extensive simulation study and consider a couple of applications: to tail dependence analysis for the Hong Kong stock market and to analysis of the distributions of the risk factors of temperature dynamics.     

Tail density estimation for exploratory data analysis using kernel methods

It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models.     

Composite quantile regression for varying-coefficient single-index models

ABSTRACT

The varying-coefficient single-index model (VCSIM) is a very general and flexible tool for exploring the relationship between a response variable and a set of predictors. Popular special cases include single-index models and varying-coefficient models. In order to estimate the index-coefficient and the non parametric varying-coefficients in the VCSIM, we propose a two-stage composite quantile regression estimation procedure, which integrates the local linear smoothing method and the information of quantile regressions at a number of conditional quantiles of the response variable. We establish the asymptotic properties of the proposed estimators for the index-coefficient and varying-coefficients when the error is heterogeneous. When compared with the existing mean-regression-based estimation method, our simulation results indicate that our proposed method has comparable performance for normal error and is more robust for error with outliers or heavy tail. We illustrate our methodologies with a real example.     

An Analysis of Nonlinearities,Heteroscedasticity, and Functional Form in the Market Model

Using a generalized specification of the single-index market model, this study examines the sources of statistical anomalies previously found in estimating the market model. Two generalized models are developed for juxtaposition with the traditional linear specification. The most general model is a Box–Cox model with different λ's and heteroscedastic errors. The empirical results indicate that previous findings of significant “nonlinearities” are primarily attributable to nonnormalities and unequal variance.     

Comparison of Separable Components in Different Samples

Abstract.  Imagine we have two different samples and are interested in doing semi- or non-parametric regression analysis in each of them, possibly on the same model. In this paper, we consider the problem of testing whether a specific covariate has different impacts on the regression curve in these two samples. We compare the regression curves of different samples but are interested in specific differences instead of testing for equality of the whole regression function. Our procedure does allow for random designs, different sample sizes, different variance functions, different sets of regressors with different impact functions, etc. As we use the marginal integration approach, this method can be applied to any strong, weak or latent separable model as well as to additive interaction models to compare the lower dimensional separable components between the different samples. Thus, in the case of having separable models, our procedure includes the possibility of comparing the whole regression curves, thereby avoiding the curse of dimensionality. It is shown that bootstrap fails in theory and practice. Therefore, we propose a subsampling procedure with automatic choice of subsample size. We present a complete asymptotic theory and an extensive simulation study.