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函数型数据的极端相关系数AI 解读

Abstract We propose a coefficient that measures extremal dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in two significant ways: (i) it is designed to measure dependence between curves; and (ii) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation…

统计泛函的可诱导复杂度AI 解读

Summary A property, or statistical functional, is said to be elicitable if it minimizes the expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work has sought to identify which properties are elicitable, here we investigate a more nuanced question: how many dimensions are required to indirectly elicit a given property? This number…

多元广义双曲随机向量的二次型AI 解读

Summary This article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (Gil-Pelaez, 1951). Two numerical applications are considered: the distribution of the two-stage least squares estimator and the expected shortfall of a quadratic portfolio.

GARCH 模型中 M 估计量的自助法推断AI 解读

Summary We consider the weighted bootstrap approximation to the distribution of a class of M-estimators for the parameters of the generalized autoregressive conditional heteroscedastic model. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator, which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is useful for computing bootstrap…

高维极值依赖的分解AI 解读

Summary We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operations applied to regularly-varying random vectors preserve regular variation. We summarize tail dependence via a matrix of pairwise tail dependence metrics that is positive semidefinite; eigendecomposition allows one…

β-混合随机向量极端依赖的结构突变检验AI 解读

We derive a structural break test for extremal dependence in |$\beta$|-mixing, possibly high-dimensional random vectors with either asymptotically dependent or asymptotically independent components. Existing tests require serially independent observations with asymptotically dependent components. To avoid estimating a long-run variance, we use self-normalization, which obviates the need to estimate the coefficient of tail dependence when components are asymptotically…

含噪高频数据中误差分布的频域分析AI 解读

Data observed at a high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or smooth random function, and measurement error. Supposing that the latent component is an Itô diffusion process, we propose to estimate the measurement error density function by applying a deconvolution technique with appropriate localization. Our estimator, which does not require equally-spaced…

波动率泛函的局部非参数 bootstrapAI 解读

Volatility functionals are widely used in financial econometrics. In the literature, they are estimated with realized volatility functionals using high-frequency data. In this paper we introduce a nonparametric local bootstrap method that resamples the high-frequency returns with replacement in local windows shrinking to zero. While the block bootstrap in time series (Hall et al., 1995) aims to reduce correlation, the local bootstrap is intended to eliminate the…

近似贝叶斯计算估计量的渐近效率AI 解读

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large data limit. Our key assumption is that the data are summarized by a fixed-dimensional summary…

广义自回归条件异方差模型的稳健拟合优度检验AI 解读

Estimation of time series models with heavy-tailed innovations has been widely discussed, but corresponding goodness-of-fit tests have attracted less attention, primarily because the autocorrelation function commonly used in constructing goodness-of-fit tests necessarily imposes 10 certain moment conditions on the innovations.As a bounded random variable has finite moments of all orders, we address the problem by first transforming the residuals with a bounded function.More…

大型积分协方差矩阵的非线性收缩估计AI 解读

Integrated covariance matrices arise in intraday models of asset returns, which allow volatility to change over the trading day. When the number of assets is large, the natural estimator of such a matrix suffers from bias due to extreme eigenvalues. We introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level, and enjoys a certain asymptotic efficiency…

高频数据中的共同因子数量AI 解读

In this paper, we introduce a local principal component analysis approach to determining the number of common factors of a continuous-time factor model with time-varying factor loadings using high-frequency data. The model is approximated locally on shrinking blocks using discrete-time factor models. The number of common factors is estimated by minimizing the penalized aggregated mean squared residual error over all shrinking blocks. While the local mean squared residual…

渐近依赖下的修正边际期望损失AI 解读

We propose an estimator of the marginal expected shortfall by considering a log transformation of a variable which has an infinite expectation. We establish the asymptotic normality of our estimator under general assumptions. A simulation study suggests that the estimation procedure is robust with respect to the choice of tuning parameters. Our estimator has lower bias and mean squared error than the empirical estimator when the latter is applicable. We illustrate our method…

渐近依赖下的修正边际期望损失AI 解读

We propose an estimator of the marginal expected shortfall by considering a log transformation of a variable which has an infinite expectation.We establish the asymptotic normality of our estimator under general assumptions.A simulation study suggests that the estimation procedure is robust with respect to the choice of tuning parameters.Our estimator has lower bias and mean squared error than the empirical estimator when the latter is applicable.We illustrate our…

分数布朗运动驱动的部分观测随机微分方程的贝叶斯推断AI 解读

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a nontrivial likelihood given the latent path. Due to the non-Markovian and high-dimensional nature of the latent path, estimating posterior expectations is computationally challenging. We present a reparameterization framework based on the Davies and Harte method for sampling stationary Gaussian processes and use it to construct a Markov chain Monte Carlo…

连续响应观测驱动时间序列模型的信息论最优性AI 解读

We investigate information-theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real-valued time-varying parameter in a univariate observation-driven model with continuous responses. We restrict our attention to models with updates of one lag order. The results provide theoretical justification for a class of score-driven models which includes the generalized autoregressive conditional heteroskedasticity model as a…

使用无偏似然估计时的 MCMC 高效实现AI 解读

When an unbiased estimator of the likelihood is used within a Metropolis–Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain. Using many Monte Carlo samples will typically result in Metropolis–Hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples; however, the computing time required to…

利用小波与阈值法估计高维波动率矩阵AI 解读

We propose a locally stationary linear model for the evolution of high-dimensional financial returns, where the time-varying volatility matrix is modelled as a piecewise-constant function of time. We introduce a new wavelet-based technique for estimating the volatility matrix, which combines four ingredients: a Haar wavelet decomposition, variance stabilization of the Haar coefficients via the Fisz transform prior to thresholding, a bias correction, and extra time-domain…

扩散过程的非参数估计：微分方程方法AI 解读

We consider estimation of scalar functions that determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation is ill-posed in this context. We adopt a probabilistic approach to regularize the problem by the adoption of a prior distribution for the unknown functional. A Gaussian prior measure is chosen in the function space by specifying its precision operator as an appropriate differential operator. We establish…

高维时间序列潜在因子的估计AI 解读

This paper deals with the dimension reduction of high-dimensional time series based on a lower-dimensional factor process. In particular, we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series T. The estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a N×N non-negative definite matrix. We show that when all the factors are strong in the sense that the norm of…

Student t 混合自回归模型及其在厚尾金融数据中的应用AI 解读

We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly…

条件异方差分数单整 ARMA 模型的最小绝对偏差估计AI 解读

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau…

非线性非高斯状态空间模型的蒙特卡洛估计AI 解读

We develop a proposal or importance density for state space models with a nonlinear non-Gaussian observation vector y ∼ p(y¦θ) and an unobserved linear Gaussian signal vector θ ∼ p(θ). The proposal density is obtained from the Laplace approximation of the smoothing density p(θ¦y). We present efficient algorithms to calculate the mode of p(θ¦y) and to sample from the proposal density. The samples can be used for importance sampling and Markov chain Monte Carlo methods. The…

Lévy 过程驱动的随机波动率模型：模拟与推断AI 解读

We study Ornstein-Uhlenbeck stochastic processes driven by Lévy processes, and extend them to more general non-Ornstein-Uhlenbeck models. In particular, we investigate the means of making the correlation structure in the volatility process more flexible. For one model, we implement a method for introducing quasi long-memory into the volatility model. We demonstrate that the models can be fitted to real share price returns data.