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通过潜在共同因子建模多元波动率AI 解读

Volatility, represented in the form of conditional heteroscedasticity, plays an important role in controlling and forecasting risks in various financial operations including asset pricing, portfolio allocation, and hedging futures. However, modeling and forecasting multi-dimensional conditional heteroscedasticity are technically challenging. As the volatilities of many financial assets are often driven by a few common and latent factors, we propose in this article a…

未知对角系数时空模型的广义 Yule–Walker 估计AI 解读

We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule–Walker estimation method which applies the least squares estimation to a Yule–Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations…

含潜在因子、内生性与非线性的高维随机回归AI 解读

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist…

相依随机变量函数的极端分位数估计AI 解读

Summary We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast with the conventional approach based on extreme value theory, we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form, and, furthermore, our estimation makes use of the full observed data. The method proposed is semiparametric as no parametric forms are assumed on the marginal…

通过分位数匹配实现分布匹配估计AI 解读

Motivated by the problem of selecting representative portfolios for backtesting counterparty credit risks, we propose a matching quantiles estimation (MQE) method for matching a target distribution by that of a linear combination of a set of random variables. An iterative procedure based on the ordinary least-squares estimation (OLS) is proposed to compute MQE. MQE can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting…

评论AI 解读

I congratulate the authors for tackling a challenging statistical problem with an important financial application, that is, estimating heavy-tailed GARCH models. The significance of the proposed th...

评论AI 解读

The authors are to be congratulated for tackling a challenging statistical problem with important financial applications, that is, modeling multivariate volatility processes via dimension-reduction...

日用电负荷曲线的建模与预测：混合方法AI 解读

We propose a hybrid approach for the modeling and the short-term forecasting of electricity loads. Two building blocks of our approach are (1) modeling the overall trend and seasonality by fitting a generalized additive model to the weekly averages of the load and (2) modeling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors.…

高维时间序列因子建模：因子个数的推断AI 解读

This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of time series is on the order of a few thousands. Asymptotic properties of the proposed method are investigated…

结合低频与高频方法的大维波动矩阵推断AI 解读

It is increasingly important in financial economics to estimate volatilities of asset returns. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. Therefore it is pertinent to reduce the effective size of volatility matrices in order to produce adequate estimates and forecasts. Furthermore, since high-frequency financial data for different assets…

曲线时间序列有限维数的识别AI 解读

The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence across different curves. The practical implementation of our method boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the determination of the dimensionality is equivalent to the identification of the nonzero…

非参数传递函数模型AI 解读

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more…

自适应变系数时空模型AI 解读

Summary We propose an adaptive varying-coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non-linearity (both in space and in time) and non-stationarity (in space) by allowing the auto-regressive coefficients to vary with both spatial location and an unknown index variable. We suggest a two-step procedure to estimate both the coefficient functions and the index variable, which is…

基于最小体积集合与逆回归的多变量波动函数检验AI 解读

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii)Â of a bathtub shape, and (iii) in a given parametric form. The…

利用条件不相关分量建模多元波动率AI 解读

Summary We propose to model multivariate volatility processes on the basis of the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that each CUC may be fitted separately with any appropriate univariate volatility model. Computationally it splits one high dimensional optimization problem into several lower dimensional subproblems. Consistency for the…

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of the innovation distribution plays an important role in determining the relative performance of the two competing estimation methods, namely the maximum quasi-likelihood estimator based…

正态、Student t与bootstrap校准可支持多少个同时假设检验？AI 解读

In the analysis of microarray data, and in some other contemporary statistical problems, it is not uncommon to apply hypothesis tests in a highly simultaneous way. The number, N say, of tests used can be much larger than the sample sizes, n, to which the tests are applied, yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate. Often the sampling distribution is quite different for each test, so there may not be an opportunity to…

无限方差 ARMA 模型的加权最小绝对偏差估计AI 解读

For autoregressive moving average (ARMA) models with infinite variance innovations, quasi-likelihood-based estimators (such as Whittle estimators) suffer from complex asymptotic distributions depending on unknown tail indices. This makes statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with heavy tailed processes. In this paper, we propose a weighted least absolute deviations estimator…

利用降维近似条件分布函数AI 解读

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y|X, but that of Y|θTX, where the unit vector θ is selected so that the approximation is optimal under a least-squares criterion. We show that θ may be estimated root-n consistently. Furthermore, estimation of the conditional distribution…

时间序列的数据倾斜方法AI 解读

Summary We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as ‘empirical…

低重复次数方差分量模型中的推断AI 解读

In components of variance models the data are viewed as arising through a sum of two random variables, representing between- and within-group variation, respectively. The former is generally interpreted as a group effect, and the latter as error. It is assumed that these variables are stochastically independent and that the distributions of the group effect and the error do not vary from one instance to another. If each group effect can be replicated a large number of times,…

自适应变系数线性模型AI 解读

Summary Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is…

重尾误差下 ARCH 与 GARCH 模型的推断AI 解读

ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy–tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In…

离散值时间序列的平滑估计AI 解读

Summary We deal with smoothed estimators for conditional probability functions of discrete-valued time series {Yt} under two different settings. When the conditional distribution of Yt given its lagged values falls in a parametric family and depends on exogenous random variables, a smoothed maximum (partial) likelihood estimator for the unknown parameter is proposed. While there is no prior information on the distribution, various nonparametric estimation methods have been…