Mixed‐Norm Spaces and Prediction of SαS Moving Averages

Suppose that is an i.i.d. symmetric α‐stable noise, 1 < α < 2, and consider the moving average process given by . Conditions are obtained for the convergence rate of the moving average series, as well as that of the inverted (autoregressive) representation . These conditions are expressed in terms of the associated function and its reciprocal belonging to certain mixed‐norm spaces of functions on the open unit disc. Properties of these spaces are explored. Criteria are also derived for the rate of mixing in a certain sense.     

Kernel Entropy Estimation for Linear Processes

Let {X _n :n∈N}be a linear process with bounded probability density function f(x). We study the estimation of the quadratic functional ∫ _R f ²(x)dx. With a Fourier transform on the kernel function and the projection method, it is shown that, under certain mild conditions, the estimator has similar asymptotical properties as the i.i.d. case studied in Giné and Nickl 2008 if the linear process {X _n :n∈N}has the defined short range dependence. We also provide an application to divergence and the extension to multi‐variate linear processes. The simulation study for linear processes with Gaussian and α‐stable innovations confirms our theoretical results. As an illustration, we estimate the divergences among the density functions of average annual river flows for four rivers and obtain promising results.     

A New Covariance Function and Spatio‐Temporal Prediction (Kriging) for A Stationary Spatio‐Temporal Random Process

Consider a stationary spatio‐temporal random process and let be a sample from the process. Our object here is to predict, given the sample, for all t at the location s _o. To obtain the predictors, we define a sequence of discrete Fourier transforms using the observed time series. We consider these discrete Fourier transforms as a sample from the complex valued random variable . Assuming that the discrete Fourier transforms satisfy a complex stochastic partial differential equation of the Laplacian type with a scaling function that is a polynomial in the temporal spectral frequency ω, we obtain, in a closed form, expressions for the second‐order spatio‐temporal spectrum and the covariance function. The spectral density function obtained corresponds to a non‐separable random process. The optimal predictor of the discrete Fourier transform is in terms of the covariance functions. The estimation of the parameters of the spatio‐temporal covariance function is considered and is based on the recently introduced frequency variogram method. The methods given here can be extended to situations where the observations are corrupted by independent white noise. The methods are illustrated with a real data set.     

Detecting at‐Most‐m Changes in Linear Regression Models

In this article, we provide a new procedure to test for at‐most‐ changes in the time‐dependent regression model , that is, β ₁ =  β ₂ = ? =  β _T under the no‐change null hypothesis against the alternative if and β ^(j) ≠  β ^(?) for some with . Our procedure is based on weighted sums of the residuals, incorporating the possibility of changes. The weak limit of the proposed test statistic is the sum of two double‐exponential random variables. A small Monte Carlo simulation illustrates the applicability of the limit results in case of small and moderate sample sizes. We compare the new method to the cumulative sum control chart (CUSUM) and standardized (weighted) CUSUM procedures and obtain the power curves of the test statistics under the alternative. We apply our method to find changes in the unconditional four‐factor capital asset pricing model.     

CONTEMPORANEOUS AGGREGATION OF TRIANGULAR ARRAY OF RANDOM‐COEFFICIENT AR(1) PROCESSES

We discuss contemporaneous aggregation of independent copies of a triangular array of random‐coefficient processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated process is shown to exist, under general assumptions on W and the mixing distribution, and is represented as a mixed infinitely divisible moving average in (4). Partial sums process of is discussed under the assumption EW² < ∞ and a mixing density regularly varying at the ‘unit root’ x = 1 with exponent β > 0. We show that the previous partial sums process may exhibit four different limit behaviors depending on β and the Lévy triplet of W. Finally, we study the disaggregation problem for in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of ϕ(x) in a suitable L₂ space.     

Gaussian inference in general AR(1) models based on difference

This article develops a simple difference transformation for estimation and inference in general AR(1) models. As in Paparoditis and Politis (2000, Test 9, 487–509) and Phillips and Han (2008, Econometric Theory 24, 631–650), a Gaussian limit theory with a convergence rate of is available, whether a unit root is present in the process. Yet the novelty of our limit results is that the same weak convergence applies to the models with or without a trend, unlike those established in the literature. The merits promise usefulness of the difference transformation in applications to dynamic panels.     

Cointegrated Linear Processes in Hilbert Space

We extend the notion of cointegration for multivariate time series to a potentially infinite‐dimensional setting in which our time series takes values in a complex separable Hilbert space. In this setting, standard linear processes with nonzero long‐run covariance operator play the role of processes. We show that the cointegrating space for an process may be sensibly defined as the kernel of the long‐run covariance operator of its difference. The inner product of an process with an element of its cointegrating space is a stationary complex‐valued process. Our main result is a version of the Granger–Johansen representation theorem: we obtain a geometric reformulation of the Johansen I(1) condition that extends naturally to a Hilbert space setting, and show that an autoregressive Hilbertian process satisfying this condition, and possibly also a compactness condition, admits an representation.     

NON‐STATIONARITY AND QUASI‐MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL

This article first studies the non‐stationarity of the first‐order double AR model, which is defined by the random recurrence equation , where γ₀ > 0, α₀ ≥ 0, and {η_t}is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition . Based on this, it is shown that the quasi‐maximum likelihood estimator of (φ₀,α₀) is consistent and asymptotically normal so that the unit root problem does not exist in the double AR(1) model. Simulation studies are carried out to assess the performance of the quasi‐maximum likelihood estimator in finite samples.     

The Slow Convergence of Ordinary Least Squares Estimators of α, β and Portfolio Weights under Long‐Memory Stochastic Volatility

We consider inference for the market model coefficients based on simple linear regression under a long memory stochastic volatility generating mechanism for the returns. We obtain limit theorems for the ordinary least squares (OLS) estimators of α and β in this framework. These theorems imply that the convergence rate of the OLS estimators is typically slower than if both the regressor and the predictor have long memory in volatility, where T is the sample size. The traditional standard errors of the OLS‐estimated intercept () and slope (), which disregard long memory in volatility, are typically too optimistic, and therefore the traditional t‐statistic for testing, say, α = 0 or β = 1, will diverge under the null hypothesis. We also obtain limit theorems (which imply slow convergence) for the estimated weights of the minimum variance portfolio and the optimal portfolio in the same framework. In addition, we propose and study the performance of a subsampling‐based approach to hypothesis testing for α and β. We conclude by noting that analogous results hold under more general conditions on long‐memory volatility models and state these general conditions which cover certain fractionally integrated exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models.     

Sampling,Embedding and Inference for CARMA Processes

A CARMA(p,q) process Y is a strictly stationary solution Y of the pth‐order formal stochastic differential equation a(D)Y_t = b(D)DL_t, where L is a two‐sided Lévy process, a(z) and b(z) are polynomials of degrees p and q respectively, with p > q, and D denotes differentiation with respect to t. Since estimation of the coefficients of a(z) and b(z) is frequently based on observations of the Δ‐sampled sequence , for some Δ > 0, it is crucial to understand the relation between Y and Y^Δ. If then Y^Δ is an ARMA sequence with coefficients depending on those of Y and the crucial problems for estimation are the determination of the coefficients of Y^Δ from those of Y (the sampling problem) and the determination of the coefficients of Y from those of Y^Δ (the embedding problem). In this article we consider both questions and use the results to determine the asymptotic distribution, as n→∞, with Δ fixed, of , where is the quasi‐maximum‐likelihood estimator of the vector of coefficients of a(z) and b(z), based on n consecutive observations of Y^Δ.     

Nonparametric regression with rescaled time series errors

We consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p. The heteroscedasticity is incorporated using a scaling function defined at uniformly spaced design points on an interval [0,1]. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is consistent and asymptotically normal for a sample size T. Explicit asymptotic variance covariance matrix is obtained as well. Finally, the finite sample performance of the proposed method is tested in simulations.     

On Asymptotic Theory for ARCH (∞) Models

Autoregressive conditional heteroskedasticity (ARCH)() models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH( ) class of models and develops the theory for consistency and asymptotic normality of the quasi‐maximum likelihood estimator.     

Asymptotic Distribution of the Bias Corrected Least Squares Estimators in Measurement Error Linear Regression Models Under Long Memory

This article derives the consistency and asymptotic distribution of the bias corrected least squares estimators (LSEs) of the regression parameters in linear regression models when covariates have measurement error (ME) and errors and covariates form mutually independent long memory moving average processes. In the structural ME linear regression model, the nature of the asymptotic distribution of suitably standardized bias corrected LSEs depends on the range of the values of where d _X ,d _u , and d _ε are the LM parameters of the covariate, ME and regression error processes respectively. This limiting distribution is Gaussian when and non‐Gaussian in the case . In the former case some consistent estimators of the asymptotic variances of these estimators and a log(n)‐consistent estimator of an underlying LM parameter are also provided. They are useful in the construction of the large sample confidence intervals for regression parameters. The article also discusses the asymptotic distribution of these estimators in some functional ME linear regression models, where the unobservable covariate is non‐random. In these models, the limiting distribution of the bias corrected LSEs is always a Gaussian distribution determined by the range of the values of d _ε ? d _u .     

Removal of ammonium‐nitrogen from aqueous solution using chitosan‐coated bentonite: Mechanism and effect of operating parameters

Wastewater containing high concentration of ammonium‐nitrogen ( ) is not effectively addressed by biological treatment and when released into water bodies can cause eutrophication. In this study, the removal of from simulated wastewater using chitosan‐coated bentonite (CCB) was investigated. The effects of salt used, pH, CCB dosage, agitation rate, and temperature on the removal of were studied. The highest removal of 67.5% was attained at the following conditions: initial pH 4.0, CCB dose of 8.0 g, agitation rate of 150 rpm, and temperature of 35 °C. Fourier transform infrared analysis indicated two mechanisms: adsorption onto CCB involving hydrogen bonding with hydroxyl groups ( OH) and ion exchange between and cations present in the interlayer of bentonite. Experimental data follows the pseudo‐second‐order kinetic model (R² = 0.9964) and Koble–Corrigan isotherm (R² = 0.9705). Thermodynamic studies showed that the adsorption process is spontaneous (ΔG⁰ < 0), endothermic (ΔH⁰ > 0) in nature, and leads to an increase in randomness at the solid–solution interface (ΔS⁰ > 0). © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45924.     

Harmonically Weighted Processes

We discuss a model for long memory and persistence in time series that amounts to harmonically weighting short memory processes, . A non-standard rate of convergence is required to establish a Gaussian functional central limit theorem. Theoretically, the harmonically weighted (HW) process displays less persistence and weaker memory than the classical competitor, fractional integration (FI) of order d. Still, we establish that a test rejects the null hypothesis of d = 0 if the process is HW. Similarly, a bias approximation shows that estimators of d will fail to distinguish between HW and FI given realistic sample sizes. The difficulties to disentangle HW and FI are illustrated experimentally and with USA inflation data.     

Convective condensation in a stator–rotor–stator spinning disc reactor

Centrifugal intensification of condensation heat transfer in the rotor–stator cavities of a stator–rotor–stator spinning disc reactor (srs‐SDR) is studied, as a function of rotational velocity ω, volumetric throughflow rate , and average temperature driving force . For the current range of ω, heat transfer from the vapor bubbles to the condensate liquid is limiting, due to a relatively low gas–liquid interfacial area a_GL. For rad s^?1, a strong increase of a_GL, results in increasing the reactor‐average condensation heat transfer coefficient h_c from 1600 to 5600 W m^?2 K^?1, for condensation of pure dichloromethane vapor. Condensation heat transfer in the srs‐SDR is enhanced by rotation, independent of the vapor velocity. The intensified condensation comes at the cost of relatively high energy dissipation rates, indicating condensation in the srs‐SDR is more suited as a means to supply heat (e.g. in an intensified reactor‐heat exchanger), rather than for bulk cooling purposes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3784–3796, 2016     

Estimation of Stress Exponent and Activation Energy for Rapid Densification of 8 mol% Yttria‐Stabilized Zirconia Powder

The rapid densification behavior of 8 mol% Y₂O₃‐stabilized ZrO₂ polycrystalline (8Y‐SZP) powder compacts at the initial stage of pressure sintering (relative density () below 0.92) has been investigated using an electric current‐activated/assisted sintering (ECAS) system. Data points corresponding to a fixed heating rate were extracted from the densification rate () versus ρ and versus temperature (T) curves. These curves were obtained experimentally by consolidation at a fixed current. Under fixed current ECAS, the heating rate () decreases continuously over sintering time. Using a quasi‐ constant heating rate (CHR) method, data points were extracted to plot vs. ρ, vs. T, and ρ vs. T curves at a fixed . The stress exponent (n), estimated from a log‐log plot of grain size (d)‐corrected /ρ and effective stress (σ_eff) at 1300–1400 K, shows an almost constant value of 1. In addition, the activation energy (Q) for rapid densification, estimated from an Arrhenius plot of d‐corrected /ρ also shows an almost constant value of 350 kJ/mol, which is considerably lower than the previously reported value of the activation energy for Zr⁴⁺ lattice diffusion of about 440 kJ/mol. These results suggest that rapid densification of 8Y‐SZP by ECAS seems to proceed by diffusional creep controlled by grain‐boundary diffusion of Zr⁴⁺ ions.     

Heat transfer coefficient for condensation of steam on freely formed falling liquid jets

This article presents the research results of direct contact condensation of steam on freely formed falling liquid jets. After the comparison of experimental data and open literature correlations it was concluded that published correlations does not provide accurate coverage of experimental data. A new correlation was established in the following form © 2016 American Institute of Chemical Engineers AIChE J, 62: 2579–2584, 2016     

Electrical properties and the role of inhomogeneities at the polyvinyl alcohol/n‐inp schottky barrier interface

In this work, we have investigated the electrical properties of Au/n‐InP contacts with a thin layer of polyvinyl alcohol (PVA) as an interlayer. The current–voltage (I–V) and capacitance–voltage (C–V) measurements are carried out in the temperature range of 175–425 K. The Au/PVA/n‐InP Schottky structure show nonideal behaviors and indicates the presence of a nonuniform distribution of interface states. The temperature dependent interface states densities (N_SS), ideality factor and barrier height are obtained. An abnormal decrease in zero‐bias barrier height (BH) and increase in the ideality factor ( ) with decreasing temperature have been explained on the basis of the thermionic emission theory with Gaussian distribution (GD) of the BHs due to the BH inhomogeneities. The experimental I–V characteristics of Au/PVA/n‐InP Schottky diode has revealed the existence of a double GD with mean BH values of ( ) of 1.246 and 0.899 eV and standard deviation ( ) of 0.176 and 0.137 V, respectively. Consequently, the modified conventional activation energy versus plot gives and Richardson constants ( ) and the values are 1.17 and 0.71 eV and 9.9 and 6.9 A/cm² K², respectively, without using the temperature coefficient of the BH. The effective Richardson constant value of 9.9 A/cm² K² is very close to the theoretical value of 9.4 A/cm² K² for n‐InP. The discrepancy between Schottky barrier heights estimated from I–V and C–V measurements is also discussed. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 39773.     

The Limiting Distribution of a Non-Stationary Integer Valued GARCH(1,1) Process

We consider the integer valued GARCH(1,1) process defined by the two equation system and λ_{n + 1} = ω + αY_n + βλ_n. When α + β < 1 this process has a stationary solution and properties are well understood. In this note we find the limiting distribution of λ_n and Y_n for the case of α + β = 1.