ON M‐Estimation Under Long‐Range Dependence in Volatility

Abstract. We consider M‐estimation of a location parameter for processes with zero autocorrelations but long‐range dependence in volatility. The observed process is the product of i.i.d. Gaussian observations and a long‐memory Gaussian process. For nonlinear estimators, the rate of convergence depends on the type of the ψ‐function. For skew‐symmetric ψ‐functions, a central limit theorem with ‐rate of convergence holds, under suitable regularity assumptions. This is not true in general for M‐estimators where the ψ‐function is not skewsymmetric.     

Asymptotics for the Conditional‐Sum‐of‐Squares Estimator in Multivariate Fractional Time‐Series Models

This article proves consistency and asymptotic normality for the conditional‐sum‐of‐squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time‐series models. The model is parametric and quite general and, in particular, encompasses the multivariate non‐cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where uniform convergence fails is handled using a truncation argument.     

Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series

Abstract. Asymptotic distribution is derived for the least squares estimates (LSE) in the unstable AR(p) process driven by a non‐Gaussian long‐memory disturbance. The characteristic polynomial of the autoregressive process is assumed to have pairs of complex roots on the unit circle. In order to describe the limiting distribution of the LSE, two limit theorems involving long‐memory processes are established in this article. The first theorem gives the limiting distribution of the weighted sum, is a non‐Gaussian long‐memory moving‐average process and (c_n,k,1 ≤ k ≤ n) is a given sequence of weights; the second theorem is a functional central limit theorem for the sine and cosine Fourier transforms      

EFFICIENT ESTIMATION FOR PERIODIC AUTOREGRESSIVE COEFFICIENTS VIA RESIDUALS

A two‐step estimation method is proposed for periodic autoregressive parameters via residuals when the observations contain trend and periodic autoregressive time series. The oracle efficiency of the proposed Yule–Walker‐type estimator is established. The performance is illustrated by simulation studies and real data analysis.     

The Periodogram of fractional processes1

Abstract. We analyse asymptotic properties of the discrete Fourier transform and the periodogram of time series obtained through (truncated) linear filtering of stationary processes. The class of filters contains the fractional differencing operator and its coefficients decay at an algebraic rate, implying long‐range‐dependent properties for the filtered processes when the degree of integration α is positive. These include fractional time series which are nonstationary for any value of the memory parameter (α ≠ 0) and possibly nonstationary trending (α ≥ 0.5). We consider both fractional differencing or integration of weakly dependent and long‐memory stationary time series. The results obtained for the moments of the Fourier transform and the periodogram at Fourier frequencies in a degenerating band around the origin are weaker compared with the stationary nontruncated case for α > 0, but sufficient for the analysis of parametric and semiparametric memory estimates. They are applied to the study of the properties of the log‐periodogram regression estimate of the memory parameter α for Gaussian processes, for which asymptotic normality could not be showed using previous results. However, only consistency can be showed for the trending cases, 0.5 ≤ α < 1. Several detrending and initialization mechanisms are studied and only local conditions on spectral densities of stationary input series and transfer functions of filters are assumed.     

Progress in membrane gas–liquid reactors

Gas–liquid reactions are crucially important in chemical synthesis and industries. In recent years, membrane gas–liquid reactors have attracted great attentions due to their high selectivity, productivity and efficiency, and easy process control and scale‐up. Membrane gas–liquid reactors can be divided into three categories: dispersive membrane reactor, non‐dispersive membrane reactor and pore flowthrough reactor. The progress in membrane gas–liquid reactors, including features, applications, advantages and limits, is briefly reviewed. © 2012 Society of Chemical Industry     

Syntheses and properties of new poly(amide–imide)s based on 1,4‐bis(4‐aminophenoxy)naphthalene and various diimide–diacids

A series of new alternative poly(amide–imide)s (PAIs, III_a–j ) was synthesized by the direct polycondensation of 1,4‐bis(4‐aminophenoxy)naphthalene (1,4‐BAPON) with various aromatic diimide–diacids. These polymers were obtained in quantitative yields with inherent viscosities of 0.71–1.03 dL/g. Except for III_a, most of the polymers were soluble in aprotic polar solvents such as NMP, DMAc, DMF, and DMSO and could be solution‐cast into transparent, flexible, and tough films. The glass transition temperatures of these PAIs were in the range of 235–280°C. Thermogravimetric analyses established that these polymers were fairly stable up to 450°C, and 10% weight loss temperatures were recorded in the range of 520–569°C under nitrogen and 506–566°C under an air atmosphere. Compared with the PAIs with the 1,4‐bis(4‐aminophenoxy)benzene structure (series IV), the solubility of series III was better than that of series IV. Series III also exhibited lower crystallinity and better processability than those of series IV. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 217–225, 2000