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Implicit Copulas: An Overview 隐式Copulas:综述
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2021.12.002
Michael Stanley Smith

Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew t copulas, factor copulas, time series copulas and regression copulas. The common auxiliary representation of implicit copulas is outlined, and how this makes them both scalable and tractable for statistical modeling. Issues such as parameter identification, extended likelihoods for discrete or mixed data, parsimony in high dimensions, and simulation from the copula model are considered. Bayesian approaches to estimate the copula parameters, and predict from an implicit copula model, are outlined. Particular attention is given to implicit copula processes constructed from time series and regression models, which is at the forefront of current research. Two econometric applications—one from macroeconomic time series and the other from financial asset pricing—illustrate the advantages of implicit copula models.

隐式copula是高维依赖建模中最常见的copula选择。介绍并综述了这一大类系词,包括椭圆系词、斜t系词、因子系词、时间序列系词和回归系词。概述了隐式copula的常见辅助表示,以及这如何使它们在统计建模中既可扩展又易于处理。考虑了参数识别、离散或混合数据的扩展似然性、高维简约性以及copula模型的模拟等问题。概述了估计copula参数的贝叶斯方法,以及从隐式copula模型进行预测的贝叶斯方法。特别关注由时间序列和回归模型构建的隐式copula过程,这是当前研究的前沿。两个计量经济学应用——一个来自宏观经济时间序列,另一个来自金融资产定价——说明了隐含copula模型的优势。
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引用次数: 9
Numerical Methods for Finding A-optimal Designs Analytically 分析求解A最优设计的数值方法
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2022.09.005
Ping-Yang Chen , Ray-Bing Chen , Yu-Shi Chen , Weng Kee Wong

The traditional way in statistics to find optimal designs for regression models is an analytical approach. Technical conditions that may be restrictive in practice are sometimes imposed to obtain the analytical results. Even then, the mathematical technique is invariably not amendable to find an optimal design under a different criterion or for the same criterion with a slightly changed model, suggesting that developing flexible and effective algorithms to search for the optimum is very useful. In particular, numerical results from an algorithm can be helpful to find analytical descriptions of optimal designs. As an example, particle swarm optimization has been shown to be quite effective for finding optimal designs for hard design problems and this paper demonstrates how its output can be used to find new analytic A-optimal approximate designs for the Gamma and inverse Gaussian models, each with the inverse link function. The methodology is quite general and may be applied to find analytical A-optimal designs for other models, like the Poisson model with the log link function, or other types of optimal designs.

统计学中寻找回归模型最优设计的传统方法是分析方法。为了获得分析结果,有时会施加在实践中可能具有限制性的技术条件。即便如此,数学技术总是不可修改,无法在不同的标准下找到最优设计,也无法在模型略有变化的情况下找到相同标准的最优设计,这表明开发灵活有效的算法来搜索最优设计是非常有用的。特别是,算法的数值结果有助于找到最优设计的分析描述。例如,粒子群优化已被证明在为硬设计问题寻找最优设计方面非常有效,本文演示了如何使用其输出为Gamma和逆高斯模型寻找新的解析A-最优近似设计,每个模型都具有逆链接函数。该方法非常通用,可用于寻找其他模型的分析A最优设计,如具有对数链接函数的泊松模型或其他类型的最优设计。
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引用次数: 0
Testing Heteroskedasticity in High-Dimensional Linear Regression 高维线性回归的异方差检验
Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2023.10.003
Akira Shinkyu
A new procedure that is based on the residuals of the Lasso is proposed for testing heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. The theoretical analysis demonstrates that the test statistic exhibits asymptotic normality under the null hypothesis of homoskedasticity, and the simulation results reveal that the proposed testing procedure obtains accurate empirical sizes and powers. Finally, the procedure is applied to real economic data.
提出了一种基于Lasso残差的高维线性回归检验异方差的新方法,其中协变量的数量可能大于样本量。理论分析表明,在均方差的零假设下,检验统计量呈现渐近正态性,仿真结果表明,所提出的检验方法获得了准确的经验大小和幂次。最后,将该方法应用于实际经济数据。
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引用次数: 0
Bayesian estimation of realized GARCH-type models with application to financial tail risk management 已实现GARCH型模型的贝叶斯估计及其在金融尾部风险管理中的应用
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2021.03.006
Cathy W.S. Chen , Toshiaki Watanabe , Edward M.H. Lin

Advances in the various realized GARCH models have proven effective in taking account of the bias in realized volatility (RV) introduced by microstructure noise and non-trading hours. They have been extended into nonlinear or long-memory patterns, including the realized exponential GARCH (EGARCH), realized heterogeneous autoregressive GARCH (HAR-GARCH), and realized threshold GARCH (TGARCH) models. These models with skew Student’s t-distribution are applied to quantile forecasts such as Value-at-Risk and expected shortfall of financial returns as well as volatility forecasting. Parameter estimation and quantile forecasting are built on Bayesian Markov chain Monte Carlo sampling methods. Backtesting measures are presented for both Value-at-Risk and expected shortfall forecasts and employ two loss functions to assess volatility forecasts. Results taken from the S&P500 in the U.S. market with approximately 5-year out-of-sample periods covering the COVID-19 pandemic period are reported as follows: (1) The realized HAR-GARCH model performs best in respect of violation rates and expected shortfall at the 1% and 5% significance levels. (2) The realized EGARCH model performs best with regard to volatility forecasts.

各种已实现GARCH模型的进展已被证明在考虑微观结构噪声和非交易时间引入的已实现波动率(RV)偏差方面是有效的。它们已经扩展到非线性或长记忆模式,包括已实现的指数GARCH(EGARCH)、已实现的异质自回归GARCH(HAR-GARCH)和已实现的阈值GARCH(TGARCH)模型。这些具有偏斜Student t分布的模型被应用于分位数预测,如风险价值和财务回报的预期缺口以及波动性预测。参数估计和分位数预测建立在贝叶斯马尔可夫链蒙特卡罗抽样方法的基础上。针对风险价值和预期缺口预测提出了回溯测试措施,并使用两个损失函数来评估波动性预测。从S&;美国市场的P500样本期约为5年,涵盖新冠肺炎大流行期,报告如下:(1)在1%和5%的显著性水平上,实现的HAR-GARCH模型在违规率和预期短缺方面表现最佳。(2) 所实现的EGARCH模型在波动性预测方面表现最好。
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引用次数: 8
A review of effective age models and associated non- and semiparametric methods 有效年龄模型及其相关的非参数和半参数方法综述
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2021.12.005
Eric Beutner

First an overview of a class of models for recurrent events is given. The class of models considered is known as virtual or effective age models. One of the strengths of this class of models is their ability to account for intervention effects after an event occurrence. Some of the models within this class allow to account for the effects of covariates and the impact of the number of already observed events. After having provided an overview of this class of models, non- and semiparametric inference methods for these models are reviewed. Several open problems in non- and semiparametric inference methods for these models are also described.

首先给出了一类递归事件模型的概述。所考虑的模型类别被称为虚拟或有效年龄模型。这类模型的优势之一是它们能够解释事件发生后的干预效果。该类中的一些模型允许考虑协变量的影响和已经观察到的事件数量的影响。在概述了这类模型之后,对这些模型的非参数和半参数推理方法进行了综述。还描述了这些模型的非参数和半参数推理方法中的几个悬而未决的问题。
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引用次数: 2
Change point estimation under a copula-based Markov chain model for binomial time series 基于copula的二项时间序列马尔可夫链模型下的变点估计
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2021.07.007
Takeshi Emura , Ching-Chieh Lai , Li-Hsien Sun

Estimation of a change point is a classical statistical problem in sequential analysis and process control. For binomial time series, the existing maximum likelihood estimators (MLEs) for a change point are limited to independent observations. If the independence assumption is violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood. A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data, where the proposed model gives an improved fit.

变化点的估计是序列分析和过程控制中的一个经典统计问题。对于二项式时间序列,现有的变化点的最大似然估计量(MLE)仅限于独立观测。如果违反了独立性假设,则MLE实质上会失去其效率,并且似然函数对数据的拟合较差。在基于copula的马尔可夫链模型下,针对序列相关观测,提出了一种新的变点估计器。主要的新颖性是对三态copula模型的自适应,该模型由受控状态、失控状态和过渡状态组成。在此模型下,借助轮廓似然提出了一个MLE。采用参数自举方法来计算未知变化点的置信集。仿真研究表明,当模型指定观测值的序列依赖性时,所提出的MLE比现有的估计量更有效。通过珠宝制造数据说明了所提出的方法,其中所提出的模型给出了改进的拟合。
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引用次数: 3
Partially orthogonal blocked three-level response surface designs 部分正交阻塞三电平响应面设计
IF 1.9 Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2021.08.007
Heiko Großmann , Steven G. Gilmour

When fitting second-order response surface models in a hypercuboidal region of experimentation, the variance matrices of D-optimal continuous designs have a particularly attractive structure, as do many regular unblocked exact designs. Methods for constructing blocked exact designs which preserve this structure and are orthogonal, or nearly orthogonal, are developed. Partially orthogonal designs are built using a small irregular fraction of a two- or three-level design and a regular fractional factorial design as building blocks. Results are derived which relate the properties of the blocked design to these components. Moreover, it is shown how the designs can be augmented to ensure that the model can be fitted and a method for constructing designs with small blocks is presented. Examples illustrate that partially orthogonal designs can compete with more traditional designs in terms of both efficiency and overall size of the experiment.

当在超立方体实验区域中拟合二阶响应面模型时,D最优连续设计的方差矩阵具有特别有吸引力的结构,许多规则的无阻塞精确设计也是如此。提出了保持这种结构并正交或近似正交的分块精确设计的构造方法。部分正交设计是使用两级或三级设计中的一小部分不规则部分和规则部分析因设计作为构建块来构建的。导出了将分块设计的属性与这些组件相关联的结果。此外,还展示了如何增强设计以确保模型能够拟合,并提出了一种用小块构建设计的方法。实例表明,部分正交设计可以在效率和实验的总体规模方面与更传统的设计竞争。
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引用次数: 3
Robust nonparametric multiple changepoint detection for multivariate variability 多变量变异性的鲁棒非参数多变化点检测
Q2 ECONOMICS Pub Date : 2023-10-01 DOI: 10.1016/j.ecosta.2023.09.001
Kelly Ramsay, Shojaeddin Chenouri
Two robust, nonparametric multiple changepoint detection algorithms are introduced: DWBS and MKWP. These algorithms can detect multiple changes in the variability of a sequence of independent multivariate observations, even when the number of changepoints is unknown. The algorithms DWBS and MKWP require minimal distributional assumptions and are robust to outlying observations and heavy tails. The DWBS algorithm uses a local search method based on depth-based ranks and wild binary segmentation. The MKWP algorithm estimates changepoints globally via maximizing a penalized version of the classical Kruskal–Wallis ANOVA test statistic. It is demonstrated that this objective function can be maximized via the well-known PELT algorithm. Under mild, nonparametric assumptions, both of these algorithms are shown to be consistent for the correct number of changepoints and the correct location(s) of the changepoint(s). A data driven thresholding method for multivariate data is introduced, based on the Schwartz information criteria. The robustness and accuracy of the new methods is demonstrated with a simulation study, where the algorithms are compared to several existing algorithms. These new methods can estimate the number of changepoints and their locations accurately when the data are heavy tailed or skewed and the sample size is large. Lastly, the proposed algorithms are applied to a four-dimensional sequence of European daily stock returns.
介绍了两种鲁棒的非参数多变点检测算法:DWBS和MKWP。这些算法可以检测到一系列独立的多变量观测的可变性中的多个变化,即使在变化点的数量未知的情况下也是如此。DWBS和MKWP算法需要最小的分布假设,并且对外围观测值和重尾具有鲁棒性。DWBS算法采用基于深度的秩和野二值分割的局部搜索方法。MKWP算法通过最大化经典Kruskal-Wallis ANOVA检验统计量的惩罚版本来全局估计变化点。结果表明,该目标函数可以通过著名的PELT算法实现最大化。在温和的非参数假设下,这两种算法对于变化点的正确数量和变化点的正确位置都是一致的。介绍了一种基于Schwartz信息准则的多变量数据的数据驱动阈值分割方法。通过仿真研究证明了新方法的鲁棒性和准确性,并将算法与几种现有算法进行了比较。这些新方法可以在数据重尾或偏态且样本量较大的情况下准确地估计出变化点的数量和位置。最后,将提出的算法应用于欧洲股票日收益的四维序列。
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引用次数: 0
Vine Copula based Portfolio Level Conditional Risk Measure Forecasting 基于Vine Copula的组合水平条件风险度量预测
Q2 ECONOMICS Pub Date : 2023-08-01 DOI: 10.1016/j.ecosta.2023.08.002
Emanuel Sommer, Karoline Bax, Claudia Czado
Accurately estimating risk measures for financial portfolios and validating their robustness is critical for both financial institutions and regulators. However, many existing models operate at the aggregate portfolio level, hence they fail to capture the complex cross-dependencies between portfolio components and particularly provide no methodology to perform a sensitivity analysis on the estimates. To address both aspects, a new approach is presented that uses vine copulas in combination with univariate ARMA-GARCH models for marginal modelling to compute conditional portfolio-level risk measure estimates by simulating portfolio-level forecasts conditioned on a stress factor. A quantile-based approach is then presented to observe the behaviour of risk measures given a particular state of the conditioning asset(s). In an illustrative case study of Spanish equities with different stress factors, the results show that the portfolio is quite robust to a sharp downturn in the American market. At the same time, there is no evidence of this behaviour with respect to the European market. The novel algorithms presented are ready for use through the R package portvine, which is publicly available on CRAN.
准确估计金融投资组合的风险指标并验证其稳健性对金融机构和监管机构都至关重要。然而,许多现有的模型在总体投资组合级别上操作,因此它们不能捕获投资组合组件之间复杂的交叉依赖关系,特别是没有提供对估计执行敏感性分析的方法。为了解决这两个问题,本文提出了一种新的方法,该方法使用vine copulas结合单变量ARMA-GARCH模型进行边际建模,通过模拟以压力因子为条件的投资组合水平预测来计算有条件的投资组合水平风险度量估计。然后提出了基于分位数的方法来观察给定条件资产的特定状态的风险度量的行为。在对不同压力因素的西班牙股票进行的说明性案例研究中,结果表明,该投资组合对美国市场的急剧下滑相当稳健。与此同时,没有证据表明欧洲市场存在这种行为。提出的新算法可以通过R包门户使用,该门户在CRAN上公开可用。
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引用次数: 0
A Computationally Efficient Mixture Innovation Model for Time-Varying Parameter Regressions 一个计算效率高的时变参数回归混合创新模型
IF 1.9 Q2 ECONOMICS Pub Date : 2023-08-01 DOI: 10.1016/j.ecosta.2023.08.001
Zhongfang He
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引用次数: 0
期刊
Econometrics and Statistics
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