A Nonparametric Test for Weak Dependence Against Strong Cycles and its Bootstrap Analogue

Abstract. We examine a test for the hypothesis of weak dependence against strong cyclical components. We show that the limiting distribution of the test is a Gumbel distribution, denoted G(·). However, since G(·) may be a poor approximation to the finite sample distribution, being the rate of the convergence logarithmic [see Hall Journal of Applied Probability (1979) , Vol. 16, pp. 433–439], inferences based on G(·) may not be very reliable for moderate sample sizes. On the other hand, in a related context, Hall [Probability Theory and Related Fields (1991) , Vol. 89, pp. 447–455] showed that the level of accuracy of the bootstrap is significantly better. For that reason, we describe an approach to bootstrapping the test based on Efron's [Annals of Statistics (1979) , Vol. 7, pp. 1–26] resampling scheme of the data. We show that the bootstrap principle is consistent under very mild regularity conditions.     

TESTING FOR GAUSSIANITY AND LINEARITY OF A STATIONARY TIME SERIES

Abstract. Stable autoregressive (AR) and autoregressive moving average (ARMA) processes belong to the class of stationary linear time series. A linear time series { } is Gaussian if the distribution of the independent innovations {ε( t )} is normal. Assuming that E ε( t ) = 0, some of the third-order cumulants c_xxx= Ex ( t ) x ( t + m ) x ( t + n ) will be non-zero if the ε( t ) are not normal and E ε³( t )≠O. If the relationship between { x ( t )} and {ε( t )} is non-linear, then { x ( t )} is non-Gaussian even if the ε( t ) are normal. This paper presents a simple estimator of the bispectrum, the Fourier transform of { c _xxx( m, n )}. This sample bispectrum is used to construct a statistic to test whether the bispectrum of { x ( t )} is non-zero. A rejection of the null hypothesis implies a rejection of the hypothesis that { x ( t )} is Gaussian. Another test statistic is presented for testing the hypothesis that { x ( t )} is linear. The asymptotic properties of the sample bispectrum are incorporated in these test statistics. The tests are consistent as the sample size N →-∞     

Recursive estimation of quantitles using recursive kernel density estimators

Recursive estimation of quantiles may be obained via adaptive stochastic approximation

approximation theorms can be used to obtained the asympotic properties when the obervation are independent. for dependent sequences matingale theory cannot be applied straight forwardly as the tool for asympototic analysis.In this paper we consider both the case when the observation are i.i.d. and when they form a stationary and strongly regular process.the main result is sufficient condition for almost sure convergence in the strongly regular case.     

Fractional Invariance Principle

Abstract. The paper presents a central limit theorem and an allied invariance theorem related to what Marinucci and Robinson [Journal of Statistics, Planning and Inference (1999) Vol. 21, pp. 111–122] termed type II fractional Brownian motion. To widen the applicability, their independent and identically distributed (i.i.d.) assumption for the innovation process is relaxed, allowing it to be mildly conditionally heteroscedastic and requiring the Martingale‐difference property only asymptotically. Additionally, the paper presents, for contrast, the weak convergence of the conventional partial sum process in a related set‐up.     

LONG-RANGE DEPENDENCE, NON-LINEARITY AND TIME IRREVERSIBILITY

Abstract. A rather general class of stationary processes with long-range dependence is introduced by mixing independent processes with short-range dependence. The class is used to study the relation between non-linearity and time irreversibility of the long-range dependence process and the corresponding features of the component processes.     

Adaptive genetic programming for steady-state process modeling

Genetic programming is one of the computer algorithms in the family of evolutionary-computational methods, which have been shown to provide reliable solutions to complex optimization problems. The genetic programming under discussion in this work relies on tree-like building blocks, and thus supports process modeling with varying structure. This paper, which describes an improved GP to facilitate the generation of steady-state nonlinear empirical models for process analysis and optimization, is an evolution of several works in the field. The key feature of the method is its ability to adjust the complexity of the required model to accurately predict the true process behavior. The improved GP code incorporates a novel fitness calculation, the optimal creation of new generations, and parameter allocation. The advantages of these modifications are tested against the more commonly used approaches.     

DIELECTRIC PROPERTIES OF MATERIALS AND MEASUREMENT TECHNIQUES

The dielectric properties of materials are defined, and the nature of their dependence on moisture content, frequency of the applied electric field, temperature of the material, and density of particulate materials is discussed. Dielectric properties of liquid water are summarized. The influence of moisture content, frequency, temperature, and density on the values of the dielectric constant and loss factor, real and imaginary parts of the relative complex permittivity, respectively, are illustrated for several different kinds of materials. Examples include dielectric properties for the cereal grains corn and wheat, pecans, and pulverized coal. Techniques for the measurement of dielectric properties of materials at high frequencies and microwave frequencies useful for dielectric heating and drying applications are discussed briefly, and numerous publications describing these methods in greater detail are cited for reference.     

AUTOREGRESSIVE MOVING AVERAGE PROCESSES WITH NON-NORMAL RESIDUALS

Abstract. ARMA processes with non-normal residuals have applications in surface metrology and have recently been shown by Nelson and Granger (1979) to occur in modelling economic time series. In this paper we obtain the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and consider some of the implications of these results. Simulation methods for any ARMA process with given skewness and kurtosis, using Johnson transformations are briefly discussed.     

Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate

Abstract. We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a strong law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general weak‐dependence assumptions, the strong consistency and asymptotic normality of Whittle's estimate are established for a large class of models. For instance, the causal θ‐weak dependence property allows a new and unified proof of those results for autoregressive conditionally heteroscedastic (ARCH)(∞) and bilinear processes. Non‐causal η‐weak dependence yields the same limit theorems for two‐sided linear (with dependent inputs) or Volterra processes.     

聚丙烯腈基离子交换纤维制备研究进展

因聚丙烯腈具有易改性的功能基团及优良的力学性能,故对聚丙烯腈纤维进行化学改性制备离子交换纤维已成为当前研究的热点。对以聚丙烯腈为基体通过化学改性来合成螯合、弱酸、弱碱、两性离子交换纤维的制备方法进行了综述,分析了制备方法的优缺点,并展望其发展前景。     

Potential, Temperature and Doping Dependence for Macropore Formation on n-Si with Backside-Illumination

Applying an anodic bias on a silicon HF contact and illuminating the backside of a n-type silicon wafer allows to create macropores. The formation of random macropores is studied in this paper by determination of the influences of the potential, the temperature and the doping level. A statistical approach is used to evaluate the micrographs. The formation of the macroporous layer consists of two phases. Beginning with a plane surface and homogeneous dissolution of silicon, first pores occur after some time. In this nucleation phase the thickness of the homogeneously dissolved Si depends strongly on the doping level and the temperature but only weakly on the applied bias. In a second phase of stable pore growth the density of pores is investigated as a function of temperature and anodic potential. For low doped material we find a strong stabilisation influence of the deep space charge region (SCR) in the nucleation as well as in the stable pore growth phase. Thus an increased anodic bias decreases the density of pores. For highly doped silicon no stabilisation influence of the SCR is found. The pore growth is dominated by the electrochemical dissolution rate, i.e. increasing the potential increases the density of the macropores.