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状态价格密度的动态变化AI 解读

State price densities (SPDs) are an important element in applied quantitative finance. In a Black-Scholes world they are lognormal distributions, but in practice volatility changes and the distribution deviates from log-normality. In order to study the degree of this deviation, we estimate SPDs using EUREX option data on the DAX index via a nonparametric estimator of the second derivative of the (European) call pricing function. The estimator is constrained so as to satisfy…

利用时变Copula刻画非齐次依赖关系AI 解读

Measuring dependence in multivariate time series is tantamount to modeling its dynamic structure in space and time. In risk management, the nonnormal behavior of most financial time series calls for non-Gaussian dependences. The correct modeling of non-Gaussian dependences is, therefore, a key issue in the analysis of multivariate time series. In this article we use copula functions with adaptively estimated time-varying parameters for modeling the distribution of returns.…

具有半参数因子动态的时间序列建模AI 解读

High-dimensional regression problems, which reveal dynamic behavior, are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such high-dimensional problems occur frequently in many different fields of science. In this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modeling…

共同函数主成分AI 解读

Functional principal component analysis (FPCA) based on the Karhunen–Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the log-returns of…

基于广义双曲分布的非参数风险管理AI 解读

In this article we propose the generalized hyperbolic adaptive volatility (GHADA) risk management model based on the generalized hyperbolic (GH) distribution and on a nonparametric adaptive methodology. Compared with the normal distribution, the GH distribution has semiheavy tails and represents the financial risk factors more appropriately. Nonparametric adaptive methodology has the desirable property of being able to estimate homogeneous volatility over a short time…

用边际积分估计和检验加性模型中的变系数AI 解读

We propose marginal integration estimation and testing methods for the coefficients of varying-coefficient multivariate regression models. Asymptotic distribution theory is developed for the estimation method, which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (β-mixing). Application of the…

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响应随机缺失时的半参数回归分析AI 解读

We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases a semiparametric regression imputation estimator, a marginal average estimator, and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal. The three special estimators have the same asymptotic variance. They achieve the semiparametric…

半参数广义可加模型中的 Bootstrap 推断AI 解读

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric…

时间序列的经验似然拟合优度检验AI 解读

Summary Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α-mixing process to formulate a test statistic that…

分量具有参数联系时的加性模型估计AI 解读

Motivated by a nonparametric GARCH model we consider nonparametric additive autoregression models in the special case that the additive components are linked parametrically. We show that the parameter can be estimated with parametric rate and give the normal limit. Our procedure is based on two steps. In the first step nonparametric smoothers are used for the estimation of each additive component without taking into account the parametric link of the functions. In a second…

加性回归中的结构检验AI 解读

We consider the component analysis problem for a regression model with an additive structure. The problem is to test whether some of the additive components are of polynomial structure (e.g., linear) without specifying the structure of the remaining components. A particular case is the problem of selecting the significant covariates. The method that we present is based on the wavelet transform using the Haar basis, which allows for applications under mild conditions on the…

半参数部分线性测量误差模型的估计AI 解读

We consider the partially linear model relating a response $Y$ to predictors ($X, T$) with mean function $X^{\top}\beta + g(T)$ when the $X$’s are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter $\beta$ and the function $g(\cdot)$ when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric…

广义线性模型中参数与半参数设定的检验AI 解读

We consider a generalized partially linear model E(Y|X, T) = G{X T β + m(T)}, where G is a known function, β is an unknown parameter vector, and m is an unknown function. We introduce a test statistic that allows one to decide between a parametric and a semiparametric model: (a) m is linear (i.e., m(t) = t T γ for a parameter vector γ), and (b) m is a smooth (nonlinear) function. Under linearity (a), we show that the test statistic is asymptotically normal. Moreover, we…

德国东西部迁移意向的半参数分析：事实与理论AI 解读

East–West migration in Germany peaked at the beginning of the 1990s although the average wage gap between Eastern and Western Germany continues to average about 25%. We analyse the propensity to migrate using microdata from the German Socioeconomic Panel. Fitting a parametric Generalized Linear Model (GLM) yields non-linear residual behavior. This finding is not compatible with classical Marshallian theory of migration and motivates the semiparametric analysis. We estimate a…

德国东西部迁移意向的半参数分析：事实与理论AI 解读

East–West migration in Germany peaked at the beginning of the 1990s although the average wage gap between Eastern and Western Germany continues to average about 25%. We analyse the propensity to migrate using microdata from the German Socioeconomic Panel. Fitting a parametric Generalized Linear Model (GLM) yields non-linear residual behavior. This finding is not compatible with classical Marshallian theory of migration and motivates the semiparametric analysis. We estimate a…

加性模型中低维分量的直接估计AI 解读

Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this…

加性非参数回归中的因变量变换分析AI 解读

We consider a nonparametric regression model with a parametric family of dependent variable transformations, one of which induces additive covariate effects. We estimate the additive regression effects using the integration method and estimate the transformation parameter from a profiled instrumental variable and pseudolikelihood criterion. The asymptotic distributions of the parameter and regression estimates are given. The practical performance is investigated via an…

含离散协变量单指标模型的直接半参数估计AI 解读

Others have developed average derivative estimators of the parameter β in the model E(Y|X = x) = G(xβ), where G is an unknown function and X is a random vector. These estimators are noniterative and easy to compute but require that X be continuously distributed. This article develops a noniterative, easily computed estimator of β for models in which some components of X are discrete. The estimator is n ½ consistent and asymptotically normal. An application to data on product…

针对半参数备择检验参数模型AI 解读

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional…

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收入效应矩阵正定性的 Bootstrap 检验AI 解读

Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of…

概率密度导数估计的带宽选择AI 解读

SUMMARY An adaptation of least squares cross-validation is proposed for bandwidth choice in the kernel estimation of the derivatives of a probability density. The practicality of the method is demonstrated by an example and a simulation study. Theoretical justification is provided by an asymptotic optimality result.