Temporal Aggregation of Seasonally Near‐Integrated Processes

We investigate the implications that temporally aggregating, either by average sampling or systematic (skip) sampling, a seasonal process has on the integration properties of the resulting series at both the zero and seasonal frequencies. Our results extend the existing literature in three ways. First, they demonstrate the implications of temporal aggregation for a general seasonally integrated process with S seasons. Second, rather than only considering the aggregation of seasonal processes with exact unit roots at some or all of the zero and seasonal frequencies, we consider the case where these roots are local‐to‐unity such that the original series is near‐integrated at some or all of the zero and seasonal frequencies. These results show, among other things, that systematic sampling, although not average sampling, can impact on the non‐seasonal unit root properties of the data; for example, even where an exact zero frequency unit root holds in the original data it need not necessarily hold in the systematically sampled data. Moreover, the systematically sampled data could be near‐integrated at the zero frequency even where the original data is not. Third, the implications of aggregation on the deterministic kernel of the series are explored.‐142     

A Plug‐in Bandwidth Selection Procedure for Long‐Run Covariance Estimation with Stationary Functional Time Series

In several arenas of application, it is becoming increasingly common to consider time series of curves or functions. Many inferential procedures employed in the analysis of such data involve the long‐run covariance function or operator, which is analogous to the long‐run covariance matrix familiar to finite‐dimensional time‐series analysis and econometrics. This function may be naturally estimated using a smoothed periodogram type estimator evaluated at frequency zero that relies on the choice of a bandwidth parameter. Motivated by a number of prior contributions in the finite‐dimensional setting, in particular Newey and West ( 1994 ), we propose a bandwidth selection method that aims to minimize the estimator's asymptotic mean‐squared normed error (AMSNE) in L²[0,1]². As the AMSNE depends on unknown population quantities including the long‐run covariance function itself, estimates for these are plugged in in an initial step after which the estimated AMSNE can be minimized to produce an empirical optimal bandwidth. We show that the bandwidth produced in this way is asymptotically consistent with the AMSNE optimal bandwidth, with quantifiable rates, under mild stationarity and moment conditions. These results and the efficacy of the proposed methodology are evaluated by means of a comprehensive simulation study, from which we can offer practical advice on how to select the bandwidth parameter in this setting.     

Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations

Abstract. Methods for parameter estimation in the presence of long‐range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long‐range dependence in the case of heavy‐tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/α for long‐range dependent FARIMA time series with symmetric α‐stable (1 < α < 2) innovations. We establish the consistency and the asymptotic normality of two types of wavelet estimators of the parameter H. We do so by exploiting the fact that the integrated series is asymptotically self‐similar with parameter H. When the parameter α is known, we also obtain consistent and asymptotically normal estimators for the fractional differencing exponent d = H ? 1/α. Our results hold for a larger class of causal linear processes with stable symmetric innovations. As the wavelet‐based estimation method used here is semi‐parametric, it allows for a more robust treatment of long‐range dependent data than parametric methods.     

Temporal Aggregation and Bandwidth selection in estimating long memory

This article aims at showing that a temporal aggregation and a specific bandwidth reduction lead to the same asymptotic properties in estimating long memory by Geweke and Porter‐Hudak's [Journal of Time Series Analysis (1983 ) vol. 4, pp. 221–237] and Robinson's [Annals of Statistics (1995b ) vol. 23, pp. 1630–1661] estimators. In other words, irrespective of the level of temporal aggregation, the asymptotic properties of the estimator are uniquely determined by the number of periodogram ordinates used in the estimation, provided some mild additional assumptions are imposed. Monte Carlo simulations show that this result is a good approximation in finite samples. A real example with the daily US Dollar/French Franc exchange rate series is also provided.     

Modelling long‐run trends and cycles in financial time series data

This article proposes a general time series framework to capture the long‐run behaviour of financial series. The suggested approach includes linear and segmented time trends, and stationary and non‐stationary processes based on integer and/or fractional degrees of differentiation. Moreover, the spectrum is allowed to contain more than a single pole or singularity, occurring at both zero but non‐zero (cyclical) frequencies. This framework is used to analyse five annual time series with a long span, namely dividends, earnings, interest rates, stock prices and long‐term government bond yields. The results based on several likelihood criteria indicate that the five series exhibit fractional integration with one or two poles in the spectrum, and are quite stable over the sample period examined.     

Efficient Phase Equilibrium Calculation in a Reduced Flash Context

A new and efficient method for phase equilibrium calculations using cubic equations of state (EOS) has been developed. The reduced flash technique presented here takes into account non‐zero binary interaction coefficients (BIC's), and requires the iterative correction of a reduced number of independent variables (2m+3, where m is the number of components with non‐zero BIC's), irrespective of the number of components in the mixture. A new extrapolation procedure, called the Direct Reduced Flash Calculation (DRFC) is formulated. Calculations performed for several hydrocarbon mixtures with emphasis to the near‐critical region prove the robustness and the efficiency of the proposed method.     

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.     

Implementing Residual‐Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies

We show how different data types (stocks and flows) and temporal aggregation affect the size and power of the dynamic ordinary least squares residual‐based Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test of the null of cointegration. Size may be more effectively controlled by setting the minimum number of leads equal to one – as opposed to zero – when selecting the lag/lead order of the dynamic ordinary least squares regression using aggregated data, but at a cost to power. If high‐frequency data for one or more series are available – that is, the model has mixed sampling frequencies – we show how to effectively utilize the high‐frequency data to increase power while controlling size.     

Statistical tests for a single change in mean against long‐range dependence

Statistical tests are introduced for distinguishing between short‐range dependent time series with a single change in mean, and long‐range dependent time series, with the former making the null hypothesis. The tests are based on estimation of the self‐similarity parameter after removing the change in mean from the series. The focus is on the GPH (Geweke and Porter‐Hudak, 1983) and local Whittle estimation methods in the spectral domain. Theoretical properties of the resulting estimators are established when testing for a single change in mean, and small sample properties of the tests are examined in simulations. The introduced tests improve on the BHKS ( Berkes et al., 2006 ) test which is the only other available test for the considered problem. It is argued that the BHKS test has a low power against long‐range dependence alternatives and that this happens because the BHKS test statistic involves estimation of the long‐run variance. The BHKS test could be improved readily by considering its R/S‐like regression version which estimates the self‐similarity parameter and which does not involve the long‐run variance. Yet better alternatives are to use more powerful estimation methods (such as GPH or local Whittle) and lead to the tests introduced here.     

A FIXED‐ b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION

In this paper, we propose a test for a break in the level of a fractionally integrated process when the timing of the putative break is not known. This testing problem has received considerable attention in the literature in the case where the time series is weakly autocorrelated. Less attention has been given to the case where the underlying time series is allowed to be fractionally integrated. Here, valid testing can only be performed if the limiting null distribution of the level break test statistic is well defined for all values of the fractional integration exponent considered. However, conventional sup‐Wald type tests diverge when the data are strongly autocorrelated. We show that a sup‐Wald statistic, which is standardized using a non‐parametric kernel‐based long‐run variance estimator, does possess a well‐defined limit distribution, depending only on the fractional integration parameter, provided the recently developed fixed‐b asymptotic framework is applied. We give the appropriate asymptotic critical values for this sup‐Wald statistic and show that it has good finite sample size and power properties.     

Assessing Persistence In Discrete Nonstationary Time‐Series Models

Abstract. The aim of this paper is to examine the application of measures of persistence in a range of time‐series models nested in the framework of Cramer (1961) . This framework is a generalization of the Wold (1938) decomposition for stationary time‐series which, in addition to accommodating the standard I(0) and I(1) models, caters for a broad range of alternative processes. Two measures of persistence are considered in some detail, namely the long‐run impulse‐response and variance‐ratio functions. Particular emphasis is given to the behaviour of these measures in a range of non‐stationary models specified in discrete time. We document the conflict that arises between different measures, applied to the same model, as well as conflict arising from the use of a given measure in different models. Precisely which persistence measures are time dependent and which are not, is highlighted. The nature of the general representation used also helps to clarify which shock the impulse‐response function refers to in the case of models where more than one random disturbance impinges on the time series.     

On the properties of the periodogram of a stationary long‐memory process over different epochs with applications

This article studies the asymptotic properties of the discrete Fourier transforms (DFT) and the periodogram of a stationary long‐memory time series over different epochs. The main theoretical result is a novel bound for the covariance of the DFT ordinates evaluated on two distinct epochs, which depends explicitly on the Fourier frequencies and the gap between the epochs. This result is then applied to obtain the limiting distribution of some nonlinear functions of the periodogram over different epochs, under the additional assumption of gaussianity. We then apply this result to construct an estimator of the memory parameter based on the regression in a neighbourhood of the zero‐frequency of the logarithm of the averaged periodogram, obtained by computing the empirical mean of the periodogram over adjacent epochs. It is shown that replacing the periodogram by its average has an effect similar to the frequency domain pooling to reduce the variance of the estimate. We also propose a simple procedure to test the stationarity of the memory coefficient. A limited Monte Carlo experiment is presented to support our findings.     

Effects of retainer frame,irradiance level and specimen thickness on cone calorimeter test results

The effects of retainer frame use, irradiance level and specimen thickness were studied as the second phase work of a round robin project on the cone calorimeter. The project was conducted in support of various U.S. building code groups, developing a system to determine the degrees of combustibility of building materials. The results of the second phase and a comparison with the corresponding round robin results conducted at 75 kW/m² according to the Board for the Coordination of the Model Codes (BCMC) protocol, are presented here. For most of the materials, no significant differences in parameters measured in the cone calorimeter were found when the retainer frame was not used, versus when the retainer frame was used. The irradiance of 50 kW/m² compared with 75 kW/m² produced significantly longer ignition times (with one exception) and lower heat‐release‐related variables as expected. The exception was gypsum board, for which heat release related values were usually higher at 50 kW/m² than at 75 kW/m². The specimen thickness effect could not be studied adequately due to the small number of tests conducted. A significant thickness effect was shown for the heat‐release‐related variables but not for time to ignition. The effect, however, was opposite for polyurethane foam in comparison with cellulosic materials. Copyright © 2004 John Wiley & Sons, Ltd.     

Intermolecular and intramolecular hydrogen bonding of poly(dimethylsiloxane)urethane‐graft–poly(methyl methacrylate) copolymers based on 2,4‐TDI and m‐XDI

In this study, poly(dimethylsiloxane)urethane–graft–poly(methyl methacrylate) (PDMS urethane–g–PMMA) copolymers with low crosslinking density were synthesized. Glass transition temperatures of the copolymers were investigated by dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). Results confirm that PDMS urethane–g–PMMA is miscible in the 2,4‐TDI (2,4‐ toluene diisocyanate) system, whereas it is partially miscible in the m‐XDI (m‐xylene diisocyanate) system. Free, intra‐ (urethane–urethane), and inter‐ (urethane–ester) association hydrogen bonding exist in the urethane group of copolymers. The inter‐association hydrogen bonding can improve the compatibility of the copolymer components. The relationship between the frequency shift and enthalpy confirm the distribution of hydrogen bonding in the macromonomer and copolymer. Ninety percent of the hydrogen bonding is by interassociation in the 2,4‐TDI system. The intra‐association hydrogen bonding in the m‐XDI system is higher than that in the 2,4‐TDI system. Consequently, aggregation may occur easily in the siloxane‐grafted chain in the m‐XDI system. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 962–972, 2002     

Reducing the size distortion of the KPSS test

This article proposes a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by Sul et al. (2005) to the autoregressive spectral density estimator and parametrically estimate the long‐run variance. We also derive the finite sample bias of the numerator of the test statistic up to the 1/T order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long‐run parameter in the model satisfies the boundary condition.     

Physical properties of poly(trimethylene terephthalate)/organoclay nanocomposites obtained via melt compounding and in situ polymerization

Two series of poly(trimethylene terephthalate) (PTT) nanocomposites, containing an organically modified montmorillonite (MMT) clay (1,2‐aminododecanoic acid (ADA)–intercalated MMT) were prepared via melt compounding and in situ polymerization methods using dimethyl terephthalate (DMT) and 1,3‐propanediol (PDO). The effect of different methods of preparation and varying organoclay contents (1−5 wt%) on the structural, morphological, thermal, and mechanical properties were investigated. The results of wide‐angle X‐ray diffraction (WAXD) and transmission electron microscope (TEM) suggested the possible existence of intercalation morphology between ADA‐MMT and the PTT matrix obtained from melt compounding, and mostly exfoliation state from in situ polymerization depending on the amount of organoclay. From DSC studies, in melt compounding case, the addition of ADA‐MMT in PTT increases melt‐crystallization (T_cm) peak temperature by 14−15°C irrespective of the clay content. However, the melting temperature (T_m) of pristine PTT remains unchanged with increasing clay content. In the case of in situ polymerization, the T_cm and T_m peaks are shifted towards lower temperature with increasing clay content. Dynamic mechanical thermal analysis (DMTA) studies on melt compounded samples revealed a marginal lowering of glass transition temperature (T_g) irrespective of clay content, and a noticeable decrease in T_g with increasing clay content for in situ polymerized samples. The PTT/ADA‐MMT nanocomposites via melt compounding showed higher initial modulus and yield stress, and lower strain at break compared with in situ polymerization with increasing clay content. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

Viscoelastic properties of dilute aqueous solution of methylcellulose at ultrasonic frequencies

The viscoelastic properties of dilute aqueous solutions of methylcellulose at ultrasonic frequencies were investigated by a torsional method using quartz crystal resonators. The concentration dependences of G′ and G″ – ωη_s increased with increasing temperature at 13 kHz, but at higher frequencies G′ and G″ – ωη_s were simply proportional to the concentration irrespective of temperature. These results may be explained by the difference of corresponding viscoelastic mechanism at measuring frequencies. In order to examine the configuration of methylcellulose in water, which changes remarkably with temperature, the intrinsic values at various temperatures were experimentally obtained by extrapolation to zero concentration, and the frequency dependence of intrinsic dynamic viscosity was examined. The values of components of the complex intrinsic viscosity at various temperatures and their frequency dependences were quantitatively compared with those calculated from the Tschoegl theory. The values of hydrodynamic strength parameter in the Tschoegl theory for an aqueous solution of methylcellulose increased with increasing temperature, and an effect of the internal viscosity due to the aggregation of methylcellulose was observed at higher temperatures. However, on the whole, the viscoelastic behavior was relatively close to Rouse-like behavior.     

Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes

Abstract. We study the autocorrelation structure and the spectral density function of aggregates from a discrete‐time process. The underlying discrete‐time process is assumed to be a stationary AutoRegressive Fractionally Integrated Moving‐Average (ARFIMA) process, after suitable number of differencing if necessary. We derive closed‐form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. These results are then used to assess the loss of forecasting efficiency due to aggregation.     

Performance of tanks in series for non-ideal mixing

The performance of tanks in series, for imperfect mixing, is evaluated by resorting to a model characterized by two parameters, m and n, describing the level of mixing and the intensity of channeling or short-circuit present in any one tank. An expression is obtained for the variation with time of the outlet concentration from the last tank, after subjecting the feed to a step change; it involves the summation of a number of terms, equal to the number of tanks in series, each term being the product of two expressions, the Binomial Probability Function and the Probability Integral of Chi-Square Distribution, for which values are readily available in statistical and mathematical tables. When no short-circuit is present, a single reading in the tables is required, whatever the number of tanks in series or the level of mixing; this includes perfect mixing, as a special case. For any given value of n, one family of curves is sufficient to correlate the variables, whatever may be the value of m or level of mixing. Five graphs depict clearly the overall influence of parameters m and n on the performance of reservoirs in series and can be used as working tools in many cases.     

Modeling of “living” free‐radical polymerization processes. I. Batch,semibatch, and continuous tank reactors

A comprehensive mathematical model is developed for “living” free‐radical polymerization carried out in tank reactors and provides a tool for the study of process development and design issues. The model is validated using experimental data for nitroxide‐mediated styrene polymerization and atom transfer radical copolymerization of styrene and n‐butyl acrylate. Simulations show that the presence of reversible capping reactions between growing and dormant polymer chains should boost initiation efficiency when using free nitroxide in conjunction with conventional initiator and also increase the effectiveness of thermal initiation. A study shows the effects of the value of the capping equilibrium constant and capping reaction rate constants for both nitroxide‐mediated styrene polymerization (using alkoxyamine as polymer chain seeds) and atom transfer radical polymerization of n‐butyl acrylate (using methyl 2‐bromopropionate as chain extension seeds). Also the effect of introducing additional conventional initiator into atom transfer radical polymerization of n‐butyl acrylate is studied. It is found that the characteristics of long chain growth are determined by the fast exchange of radicals between growing and dormant polymer chains. Polymerization results in batch, semibatch, and a series of continuous tank reactors are analyzed. The simulations also show that a semibatch reactor is most flexible for the preparation of polymers with controlled architecture. For continuous tank reactors, the residence time distribution has a significant effect on the development of chain architecture. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1630–1662, 2002