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稳健的已实现积分贝塔估计及其动态分析AI 解读

In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noise, which is robust to the stylized features, such as the time-varying beta and the price-dependent and autocorrelated microstructure noise. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find a persistent autoregressive structure. To model this dynamic…

重尾高频金融观测下的因子与特异性 VAR 波动率矩阵模型AI 解读

This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts for the dynamics of the factor and idiosyncratic volatilities and includes many parameters. In addition, many empirical studies have shown that high-frequency stock returns and volatilities often exhibit heavy tails. To handle these two…

隔夜 GARCH–Itô 波动率模型AI 解读

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this article, to account for whole-day…

基于已实现GARCH–Itô模型的波动率分析AI 解读

This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump–diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in the continuous instantaneous volatility process. The key feature of the proposed model is that the corresponding conditional daily integrated volatility adopts an autoregressive structure, where both integrated volatility and jump variation…

基于高频金融数据的大维波动率矩阵自适应阈值估计AI 解读

Universal thresholding methods have been developed to estimate the large sparse integrated volatility matrix of underlying assets based on high-frequency financial data. Since the integrated volatility matrix often has entries with a wide range of variability, universal thresholding estimators do not take the varying entries into consideration and may have unsatisfactory performances. This paper investigates adaptive thresholding estimation of the large integrated volatility…

高维带状向量自回归模型AI 解读

We consider a class of vector autoregressive models with banded coefficient matrices. This setting represents a type of sparse structure for high-dimensional time series, although the implied auto-covariance matrices are not banded. The structure is also practically meaningful when the component time series are ordered appropriately. We establish the convergence rates of the estimated banded autoregressive coefficient matrices. We also propose a Bayesian information…

融合低频与高频金融数据的统一离散时间和连续时间模型AI 解读

This paper introduces a unified model, which can accommodate both continuous-time Itô processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. This model is called a unified GARCH-Itô model. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the…

基于 Pauli 测量的最优大规模量子态层析AI 解读

Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm…

量子态层析与含噪矩阵补全的渐近等价性AI 解读

Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and quantum state tomography in quantum physics and quantum information science. As quantum state tomography and trace regression share the common goal of recovering an unknown matrix, it is nature to put them in the Le Cam paradigm for…

含测量误差的高维 Itô 过程稀疏波动率矩阵最优估计AI 解读

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Itô process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a…

利用高频金融数据估计大型波动率矩阵的快速收敛率AI 解读

Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency data. Many existing estimators of a volatility matrix of small dimensions become inconsistent when the size of the matrix is close to or larger than the sample size. This paper introduces a new type of large volatility matrix estimator based on nonsynchronized high-frequency data, allowing for the presence of microstructure noise. When both the…

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…

高维数据中基于阈值化的稀疏线性判别分析AI 解读

In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is usually unknown, the rule of classification is constructed using a training sample. The well-known linear discriminant analysis (LDA) works well for the situation where the number of variables used for classification is much smaller than…

高频金融数据的大维度波动率矩阵估计AI 解读

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In…

高频金融数据的多尺度跳跃与波动率分析AI 解读

The wide availability of high-frequency data for many financial instruments stimulates an upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet existing methods are developed for either noisy data from a continuous-diffusion price model or data from a jump-diffusion price model without noise. We propose methods to cope with…

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GARCH 模型与扩散模型的渐近不等价性AI 解读

This paper investigates the statistical relationship of the GARCH model and its diffusion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's deficiency distance. To our surprise, we are able to show that the GARCH model and its diffusion limit are asymptotically equivalent only under deterministic volatility. With stochastic volatility, due to the…

基于小波的变化曲线估计AI 解读

The recently developed theory of wavelets has a remarkable ability to “zoom in” on very short-lived frequency phenomena, such as transients in signals and singularities in functions, and hence provides an ideal tool to study localized changes. This article proposes a wavelet method for estimating jump and sharp cusp curves of a function in the plane. The method involves first computing wavelet transformation of data and then estimating jump and sharp cusp curves by wavelet…

多个总体随机序关系的似然比检验AI 解读

The likelihood ratio test is often used to test hypotheses involving a stochastic ordering. Distribution theory for the likelihood ratio test has been developed only for two stochastically ordered distributions. For testing equality of distributions against a stochastic ordering in several populations, this paper derives the null asymptotic distribution of the likelihood ratio test statistic, which is characterized by minimization problems and has no closed form. A Monte…

长记忆数据的小波收缩函数估计AI 解读

In this article we study function estimation via wavelet shrinkage for data with long-range dependence. We propose a fractional Gaussian noise model to approximate nonparametric regression with long-range dependence and establish asymptotics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to 0 at rates that differ from those for data with independence or short-range dependence. Wavelet estimates with best selection…

利用小波检测跳跃与尖锐尖点AI 解读

A method is proposed to detect jumps and sharp cusps in a function which is observed with noise, by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels. Asymptotic theory is established and practical implementation is discussed. The method is tested on simulated examples, and applied to stock market return data.

利用小波检测跳跃与尖锐突点AI 解读

A method is proposed to detect jumps and sharp cusps in a function which is observed with noise, by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels. Asymptotic theory is established and practical implementation is discussed. The method is tested on simulated examples, and applied to stock market return data.