Robust estimation of a high-dimensional integrated covariance matrix

In this article, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent articles in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances, that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy–Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.     

Blind deconvolution model in periodic setting with fractional Gaussian noise

We consider the problem of estimating the response function in a deconvolution model under fractional Gaussian noise and noisy kernel. A preliminary threshold is used to stabilize the inversion. Our estimator is adaptive and attains minimax optimal or near-optimal rates in a wide range of Besov balls.     

频率综合器中电荷泵相位噪声参数模型

在深亚微米互补金属氧化物半导体工艺制造的频率综合器中,电荷泵产生的噪声成为输出频率信号相位噪声的重要来源.以往用于电荷泵噪声的导通比估算模型比较粗糙,已经无法满足设计低噪声频率综合器的需要,通过引入电荷泵导通时间,提出了频率综合器中电荷泵的采样噪声等效模型,能更加精确地估计电荷泵噪声对频率综合器输出相位噪声的贡献.本文提出的电荷泵噪声模型为设计频率综合器提供了仿真相位噪声更为准确的方法.     

论我国运用BOT方式进行机场建设的法律障碍及对策

BOT方式在我国基础设施建设的项目中运用范围比较广泛,但是在中国大陆的机场建设项目中却迟迟没有得以运用。法律障碍是阻碍机场建设项目运用BOT方式进行的主要原因之一。本文从多个法律角度出发,找出造成我国未能运用BOT方式进行机场建设的主要法律障碍,对其进行深入的分析,并提出了合理化建议。     

Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.     

基于半鞅过程的中国股市随机波动、跳跃和微观结构噪声统计特征研究

本文基于半鞅过程和非参数统计推断方法,利用已实现幂变差的渐进统计特性,构造检验统计量,在统一的分析框架下,对金融资产价格中随机波动、跳跃和微观结构噪声等问题进行全面系统的研究。并根据上海证券交易所不同行业的股票,上证50 股票指数及其成分股的高频数据进行实证研究。结果表明,我国A 股市场中,噪音交易显著;约43%的风险来源于资产收益过程的随机波动风险,可用股票期权交易对冲;不同来源风险的重要性程度依次为:随机波动的风险、系统性跳跃风险以及异质性跳跃风险;流动性越好的股票越显示出跳跃、尤其是无限小跳的证据。     

Effectiveness of a random compound noise strategy for robust parameter design

Robust parameter design has been widely used to improve the quality of products and processes. Although a product array, in which an orthogonal array for control factors is crossed with an orthogonal array for noise factors, is commonly used for parameter design experiments, this may lead to an unacceptably large number of experimental runs. The compound noise strategy proposed by Taguchi [30 G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, UNIPUB/Kraus International, White Plains, New York, 1987. [Google Scholar]] can be used to reduce the number of experimental runs. In this strategy, a compound noise factor is formed based on the directionality of the effects of noise factors. However, the directionality is usually unknown in practice. Recently, Singh et al. [28 J. Singh, D.D. Frey, N. Soderborg, and R. Jugulum, Compound noise: Evaluation as a robust parameter design method, Qual. Reliab. Eng. Int. 23 (2007), 387–398. doi: 10.1002/qre.812[Crossref], [Web of Science ®] , [Google Scholar]] proposed a random compound noise strategy, in which a compound noise factor is formed by randomly selecting a setting of the levels of noise factors. The present paper evaluates the random compound noise strategy in terms of the precision of the estimators of the response mean and the response variance. In addition, the variances of the estimators in the random compound noise strategy are compared with those in the n-replication design. The random compound noise strategy is shown to have smaller variances of the estimators than the 2-replication design, especially when the control-by-noise-interactions are strong.     

Least squares parameter estimation in multiplicative noise models

A simple multiplicative noise model with a constant signal has become a basic mathematical model in processing synthetic aperture radar images. The purpose of this paper is to examine a general multiplicative noise model with linear signals represented by a number of unknown parameters. The ordinary least squares (LS) and weighted LS methods are used to estimate the model parameters. The biases of the weighted LS estimates of the parameters are derived. The biases are then corrected to obtain a second-order unbiased estimator, which is shown to be exactly equivalent to the maximum log quasi-likelihood estimation, though the quasi-likelihood function is founded on a completely different theoretical consideration and is known, at the present time, to be a uniquely acceptable theory for multiplicative noise models. Synthetic simulations are carried out to confirm theoretical results and to illustrate problems in processing data contaminated by multiplicative noises. The sensitivity of the LS and weighted LS methods to extremely noisy data is analysed through the simulated examples.     

Adaptive Kalman Filtering with Multivariate Generalized Laplace System Noise

An adaptive Kalman filter is proposed to estimate the states of a system where the system noise is assumed to be a multivariate generalized Laplace random vector. In the presence of outliers in the system noise, it is shown that improved state estimates can be obtained by using an adaptive factor to estimate the dispersion matrix of the system noise term. For the implementation of the filter, an algorithm which includes both single and multiple adaptive factors is proposed. A Monte-Carlo investigation is also carried out to access the performance of the proposed filters in comparison with other robust filters. The results show that, in the sense of minimum mean squared state error, the proposed filter is superior to other filters when the magnitude of a system change is moderate or large.     

Faster Convergence to the Estimation of Quadratic Variation with Microstructure Noise

The continuous quadratic variation of asset return plays a critical role for high-frequency trading. However, the microstructure noise could bias the estimation of the continuous quadratic variation. Zhang et al. (2005 Zhang, L., Mykland, P., Ait-Sahalia, Y. (2005). A tale of two time scales: determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100(472):1394–1411.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed a batch estimator for the continuous quadratic variation of high-frequency data in the presence of microstructure noise. It gives the estimates after all the data arrive. This article proposes a recursive version of their estimator that outputs variation estimates as the data arrive. Our estimator gives excellent estimates well before all the data arrive. Both real high-frequency futures data and simulation data confirm the performance of the recursive estimator.