论文检索

主特征值与主特征向量的检验AI 解读

We establish central limit theorems for principal eigenvalues and eigenvectors under divergent spiked covariance models, and develop three two-sample tests for testing (1) the equality of principal eigenvalues, (2) the stability of eigenvalue proportions, and (3) the invariance of principal eigenvectors. One important application of our results is to understand structural breaks in large factor models. That is, when a structural break is suspected or detected, these tests…

波动率的乘法因子模型AI 解读

Facilitated with high-frequency observations, we introduce a remarkably parsimonious one-factor volatility model that offers a novel perspective for comprehending daily volatilities of a large number of stocks. Specifically, we propose a multiplicative volatility factor (MVF) model, where stock daily variance is represented by a common variance factor and a multiplicative idiosyncratic component. We demonstrate compelling empirical evidence supporting our model and provide…

动态波动率模型下高维协方差矩阵的渐近理论与收缩估计AI 解读

We study the estimation of high-dimensional covariance matrices and their empirical spectral distributions under dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We establish the condition under which the limiting spectral distribution (LSD) of the sample covariance matrix under scalar BEKK models is different from the i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample covariance matrix and…

多因子资产定价模型的样本内与样本外夏普比率AI 解读

Using available return data, many multi-factor asset pricing models present impressive in-sample Sharpe ratios, significantly surpassing that of the market portfolio. Such a performance, however, contradicts the conventional wisdom in finance. Investors cannot realistically attain the in-sample Sharpe ratios. They obtain the out-of-sample Sharpe ratios, which are significantly lower. Estimation risk is one reason for this performance deterioration. We theoretically study the…

股票共同跳跃网络AI 解读

We propose a Degree-Corrected Block Model with Dependent Multivariate Poisson edges (DCBM-DMP) to study stock co-jump dependence. To estimate the community structure, we extend the SCORE algorithm in Jin (2015) and develop a Spectral Clustering On Ratios-of-Eigenvectors for networks with Dependent Multivariate Poisson edges (SCORE-DMP) algorithm. We prove that SCORE-DMP enjoys strong consistency in community detection. Empirically, using high-frequency data of S&P 500…

统计因子模型下的高维最小方差组合估计AI 解读

We propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Our approach relies on properly integrating ℓ1 constraint on portfolio weights with an appropriate covariance matrix estimator. In terms of covariance matrix estimation, we extend the theoretical results of POET (Fan et al., 2013) to a setting that is coherent with principal component analysis. Simulation and…

椭圆分布及其推广下的高维协方差矩阵检验AI 解读

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume specific parametric distributions nor involve the kurtosis of data. More generally, we can test against any non-negative definite matrix that can even be not invertible. As an…

基于高频数据的高维最小方差组合估计AI 解读

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which…

基于逐笔观测的积分波动率估计AI 解读

We develop a volatility estimator that can be directly applied to tick-by- tick data. More specifically, we consider a model that allows for (i) irregular observation times that can be endogenous, (ii) dependent noise that can have diurnal features and be dependent on the latent price process, and (iii) jumps in the latent price process. We show that our estimator yields consistent estimates and enjoys the optimal rate of convergence. Simulation as well as empirical studies…

基于含噪高频观测的高维协方差矩阵谱分布推断AI 解读

In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (signal) sample covariance matrices depends on that of signal-plus-noise-type sample covariance matrices. As an…

微观结构噪声的统计性质AI 解读

We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In…

纳入交易信息的积分波动率有效估计AI 解读

We consider a setting where market microstructure noise is a parametric function of trading information, possibly with a remaining noise component. Assuming that the remaining noise is Op(1/n), allowing irregular times and jumps, we show that we can estimate the parameters at rate n, and propose a volatility estimator which enjoys n convergence rate. Simulation studies show that our method performs well even with model misspecification and rounding. Empirical studies…

采样时点可能内生时的已实现波动率AI 解读

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the realized volatility in a general endogenous time setting. We also establish a central limit theorem for the tricity under the hypothesis that there is no endogeneity, based on which we propose a test and document that this…

高维扩散过程积分协方差矩阵的估计AI 解读

We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting spectral distribution (LSD) of RCV depends on the covolatility process not only through the targeting ICV, but…