WALSH-FOURIER ANALYSIS OF DISCRETE-VALUED TIME SERIES

Abstract. An approach to the analyses of discrete-valued time series is discussed. The analyses are accomplished in the spectral domain using the Walsh-Fourier transform which is based on Walsh functions. This approach will enable an investigator of discrete systems to analyse the data in terms of square waveforms and sequency rather than sine waves and frequency.
We develop a general signal-plus-noise type model for discrete-valued time series in which Walsh-Fourier spectral analysis is of interest. We consider the problems of detecting whether a common signal exists in repeated measures on discrete-valued time series and in discrete-valued processes collected in an experimental design. We show that these models may depend on unknown regression parameters and we develop consistent estimates of these parameters based on the finite Walsh-Fourier transform. Applications to certain Markov models are given; however, the methods presented also apply to non-Markov cases.     

A NOTE ON A CENTRAL LIMIT THEOREM FOR STATIONARY PROCESSES

Abstract. In this paper we prove a central limit theorem for the finite Walsh-Fourier transform of a stationary sequence under a mixing condition, involving higher order cumulants of the process.     

CENTRAL LIMIT THEOREMS FOR FINITE WALSH-FOURIER TRANSFORMS OF WEAKLY STATIONARY TIME SERIES

Abstract. In this paper we utilize martingale theorems to obtain central limit theorems for the finite Walsh-Fourier transforms of various second-order stationary processes.     

Estimating the Rank of the Spectral Density Matrix

Abstract. The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix the rank of which is known.     

SOME PROPERTIES OF AUTOREGRESSIVE ESTIMATES FOR PROCESSES WITH MIXED SPECTRA

Abstract. A formal justification for the use of the method of autoregressive spectral estimation for time series consisting of a sinusoidal signal in additive noise is given in this paper. The analytical properties of the autoregressive approximation to the generalized spectral density of the process are presented, and the operational characteristics of the statistical estimation procedure are discussed. In particular, strong convergence of the autoregressive parameters and the autoregressive transfer function approximation is shown.     

Analysis of low count time series data by poisson autoregression

Abstract.  This study provides new methods of assessing the adequacy of the Poisson autoregressive time-series model for count data. New expressions are given for the score function and the information matrix and these lead to the construction of new types of residuals for this model. However, these residuals often need to be supplemented by formal statistical procedures and an overall test of the model adequacy is given via the information matrix equality that holds for correctly specified models. The techniques are applied to a monthly count data set of claimants for wage loss benefit, in order to estimate the the expected duration of claimants in the system.     

A Modified Nonparametric Prewhitened Covariance Estimator

Abstract. This paper proposes a fully modified version of the spectral matrix estimator (and the long‐run variance estimator as a special case) proposed originally by Xiao and Linton [Journal of Time Series Analysis (2002) Vol. 23, pp. 215–250], and derives its asymptotic results. A striking feature of the modified spectral matrix estimator is to achieve the convergence rate of O(T ^?8/9) in the mean squared error (MSE), which is usually achieved under the fourth‐order spectral window. However, this estimator does not sacrifice the positive definiteness of the resulting estimate for the rate improvement; it is Hermitian and positive definite in finite samples by construction. The faster convergence rate is established by a multiplicative bias correction of the crude spectral estimator under the second‐order spectral window. The approximations to some sensible definitions of the MSE of the estimator and the bandwidths that minimize the asymptotic MSEs are also derived. Monte Carlo results indicate that for a wide variety of processes the modified spectral matrix estimator reduces the bias without inflating the variance and thus improves the MSE, compared with the crude, bias‐uncorrected estimator.     

Influencing parameters in the accelerated weathering of pigmented plastics and paints – new findings and possible progress

A report is given of recent studies into the influence of spectral energy distribution, irradiation intensity, moisture, oxygen pressure and specimen temperature on the results obtained during the accelerated weathering of unpigmented and pigmented polymers. In particular, a “radiation-related spectral energy absorption” is defined and its possibilities for providing information on the sequence of the degradation processes that take place during weathering is discussed; in this respect it is possible to differentiate between the degradation of the polymer matrix by UV-degradation, degradation by photocatalytic oxidation of the polymer when photoactive pigments are used and the protective action of high-grade inorganic pigments. Finally, the possibilities for improving the process and equipment used in accelerated weathering are discussed.     

Integer programming for optimal reduction of calibration targets

Calibration targets are widely used to characterize imaging devices. The question addressed in this article is that of how many surfaces in a calibration target are needed to account for the performance of the whole target. Different to previous research where the problem of reducing calibration charts is addressed independently of the calibration problem; in this article we tackle the reduction question based on the calibration performance. We argue that the outcome of both spectral and colorimetric calibration is dependent on the properties of the cross‐product matrix encompassing the color‐signals. Further, we show that by careful mathematical manipulation it is possible to write the cross‐product matrix as a linear sum of the submatrices corresponding to each individual color signal. This formulation allows us to cast the reduction problem as a quadratic minimization where we ask: given the spectral properties of the available color signals, what is the minimum number of surfaces needed to emulate the global cross‐product matrix. To reduce the number of surfaces we impose an integer constraint on the minimization, where the weight of each surface can only assume a value of 1 or 0. Our results show that around 13 surfaces are sufficient to account of the 24 surfaces of the Macbeth color checker. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 212–220, 2008     

Recent Advances in Light Scattering Calculations for Nonspherical Particles

Methods for calculating the light scattering properties of nonspherical particles are reviewed, and applications to particle characterization are considered. Angular scattering results are given for particles in fixed and random orientations. These include the Mueller matrix representation and quasi-three-dimensional computer generated plots. Spectral (wavelength-dependent) scattering results are shown for spheres, a spheroid, and a glass fiber. Applications of spectral scattering to characterizing polydisperse suspensions are discussed.     

A regularization approach to the reconciliation of constrained data sets

A new iterative solution to the statistical adjustment of constrained data sets is derived in this paper. The method is general and may be applied to any weighted least squares problem containing nonlinear equality constraints. Other methods are available to solve this class of problem, but are complicated when unmeasured variables and model parameters are not all observable and the model constraints are not all independent. Of notable exception, however, are the methods of Crowe (1986) and Pai and Fisher (1988), although these implementations require the determination of a matrix projection at each iteration which may be computationally expensive. An alternative solution which makes the pragmatic assumption that the unmeasured variables and model parameters are known with a finite but equal uncertainty is proposed. We then re-formulate the well known data reconciliation solution in the absence of these unknowns to arrive at our new solution; hence the regularization approach. Another procedure for the classification of observable and redundant variables which does not require the explicit computation of the matrix projection is also given. The new algorithm is demonstrated using three illustrative examples previously used in other studies.     

Reconsideration of the results of the two dimensional correlation infrared spectroscopic study on water diffusion process in poly(?-caprolactone) matrix

Two dimensional correlation spectroscopy (2DCOS) is a powerful technique which can enhance spectral resolution and probe a certain sequential order of spectral variations under external perturbation. However, in asynchronous 2D contour maps which provide richer valuable information than synchronous ones, some effects other than real asynchronicity (called spectral effects), such as position shift, band width change and band overlapping, may generate interfering cross peaks. In this paper, we performed a simulation in the region of OH stretching vibration of water to evaluate the contributions of spectral effects on a highly overlapped band and study the dynamic changes of water during diffusion process in poly(?-caprolactone) (PCL) matrix. From the comparison between experimental and simulated asynchronous 2D correlation spectra, the detailed information on water diffusion process in PCL film can be extracted. It is demonstrated that artificial asynchronous cross peaks in the region of 3670-3570 cm⁻¹ are induced by band overlapping and the bound and free water in PCL matrix change simultaneously.     

基于稀疏性非负矩阵分解的故障监测方法

提出了基于稀疏性非负矩阵分解(SNMF)的故障监测方法。非负矩阵分解(NMF)是一种新的降维方法,可以得到原始数据的低秩近似矩阵。与传统的多元统计过程监控方法如主成分分析(PCA)相比,NMF对潜变量的性质没有假设,除了非负性的要求。将稀疏编码和非负矩阵分解方法结合在一起,因为施加了稀疏性的约束,稀疏性非负矩阵分解方法可以得到对数据更稀疏的表示。在分解时对低秩近似矩阵进行正交化处理,从而在降维时除去变量中的冗余信息,将信息集中到更少的投影方向上。然后,用SNMF方法来提取过程的潜变量,并定义新的监测指标来进行故障监测。使用核密度估计(KDE)方法来计算新定义的监测指标的控制上限。最后,将提出的基于SNMF的监测方法应用于TE过程来评估其监测性能,并与基于传统NMF和PCA的方法进行比较。仿真实验结果表明了所提出新方法的可行性。     

Testing non‐parametric hypotheses for stationary processes by estimating minimal distances

In this article, new tests for non‐parametric hypotheses in stationary processes are proposed. Our approach is based on an estimate of the L²‐distance between the spectral density matrix and its best approximation under the null hypothesis. We explain the main idea in the problem of testing for a constant spectral density matrix and in the problem of comparing the spectral densities of several correlated stationary time series. The method is based on direct estimation of integrals of the spectral density matrix and does not require the specification of smoothing parameters. We show that the limit distribution of the proposed test statistic is normal and investigate the finite sample properties of the resulting tests by means of a small simulation study.     

过程系统中波动传播辨识及源定位的集成方法研究(英文)

An integrated method for identifying the propagation of multi-loop process oscillations and their source location is proposed in this paper. Oscillatory process loop variables are automatically selected based on the component-related ratio index and a mixing matrix, both of which are obtained in data preprocessing by spectral independent component analysis. The complex causality among oscillatory process variables is then revealed by Granger causality test and is visualized in the form of causality diagram. The simplification of causal connectivity in the diagram is performed according to the understanding of process knowledge and the final simplest causality diagram, which represents the main oscillation propagation paths, is achieved by the automated cutting-off thresh-old search, with which less significant causality pathways are filtered out. The source of the oscillation disturbance can be identified intuitively through the final causality diagram. Both simulated and real plant data tests are presented to demonstrate the effectiveness and feasibility of the proposed method.     

ICP-MS法同时测定食用级碳酸钙中Ba、AS、Pb、Hg、Cd、Cr

本文采用电感耦合等离子体质谱仪（ICP—MS）直接测定食用级碳酸钙中Ba、As、Pb、Hg、Cd、Cr有害重金属元素的含量。用硝酸低温溶解碳酸钙样品,加入内标元素1n,采用内标法,有效地补偿了基体效应所带来的测量偏差。该方法的加标回收率为：95％-110％,测定精度（RSD）为：0．7％-4．3％。本文所研究的方法具有简便、快速、准确等特点,可用于食用级碳酸钙样品有害元素的分析。     

MAXIMUM LIKELIHOOD ESTIMATION OF AUTOCOVARIANCE MATRICES FROM REPLICATED SHORT TIME SERIES

Abstract. The maximum likelihood estimation of an autocovariance matrix based on replicated observations of stationary times series is considered. A sufficient condition for the existence of the estimate, when the sample covariance matrix is singular, is given. An iterative method for its computation is proposed: it is based on some spectral decompositions of Toeplitz matrices. Simulation results show the superiority of the estimate over the usual empirical sample autocovariance matrix.     

树脂基复合材料在雷达结构中的应用

本文介绍了树脂基复合材料的性能和成型工艺特点及其结构件的设计方法；阐述了树脂基复合材料在雷达结构中的应用；分析了目前树脂基复合材料在雷达结构中应用存在的问题，并给出了一些建议。     

Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

When considering two or more time series of functional data objects, for instance those derived from densely observed intraday stock price data of several companies, the empirical cross‐covariance operator is of fundamental importance due to its role in functional lagged regression and exploratory data analysis. Despite its relevance, statistical procedures for measuring the significance of such estimators are currently undeveloped. We present methodology based on a functional central limit theorem for conducting statistical inference for the cross‐covariance operator estimated between two stationary, weakly dependent, functional time series. Specifically, we consider testing the null hypothesis that the two series possess a specified cross‐covariance structure at a given lag. Since this test assumes that the series are jointly stationary, we also develop a change‐point detection procedure to validate this assumption of independent interest. The most imposing technical hurdle in implementing the proposed tests involves estimating the spectrum of a high dimensional spectral density operator at frequency zero. We propose a simple dimension reduction procedure based on functional principal component analysis to achieve this, which is shown to perform well in a simulation study. We illustrate the proposed methodology with an application to densely observed intraday price data of stocks listed on the New York stock exchange‐20.40     

Parameter Estimation of Stochastic Processes with Long-range Dependence and Intermittency

This paper considers the case where a stochastic process may display both long-range dependence and second-order intermittency. The existence of such a process is established in Anh, Angulo and Ruiz-Medina (1999). We systematically study the estimation of parameters involved in the spectral density function of a process with long-range dependence and second-order intermittency. An estimation procedure for the parameters is given. Numerical results are presented to support the estimation procedure proposed in this paper.