Unit root testing with slowly varying trends

A unit root test is proposed for time series with a general nonlinear deterministic trend component. It is shown that asymptotically the pooled OLS estimator of overlapping blocks filters out any trend component that satisfies some Lipschitz condition. Under both fixed‐b and small‐b block asymptotics, the limiting distribution of the t‐statistic for the unit root hypothesis is derived. Nuisance parameter corrections provide heteroskedasticity‐robust tests, and serial correlation is accounted for by pre‐whitening. A Monte Carlo study that considers slowly varying trends yields both good size and improved power results for the proposed tests when compared to conventional unit root tests.     

Residuals‐based tests for the null of no‐cointegration: an Analytical comparison

Abstract. This article studies the asymptotic distribution of five residuals‐based tests for the null of no‐cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares (GLS)‐detrended variables. The local asymptotic power of the tests is shown to be a function of Brownian motion and Ornstein–Uhlenbeck processes, depending on a single nuisance parameter, which is determined by the correlation at frequency zero of the errors of the cointegration regression with the shocks to the right‐hand side variables. The tests are compared in terms of power in large and small samples. It is shown that, while no significant improvement can be achieved by using unit root tests other than the OLS detrended t‐test originally proposed by Engle and Granger (1987), the power of GLS residuals tests can be higher than the power of system tests for some values of the nuisance parameter.     

Robust and powerful serial correlation tests with new robust estimates in ARX models

Abstract. We consider robust serial correlation tests in autoregressive models with exogenous variables (ARX). Since the least squares estimators are not robust when outliers are present, a new family of estimators is introduced, called residual autocovariances for ARX (RA‐ARX). They provide resistant estimators that are less sensible to abnormal observations in the output variable of the dynamic model. Such ‘bad’ observations could be due to unexpected phenomena such as economic crisis or equipment failure in engineering, among others. We show that the new robust estimators are consistent and we can consider robust and powerful tests of serial correlation in ARX models based on these estimators. The new one‐sided tests of serial correlation are obtained in extending Hong's (1996) approach in a framework resistant to outliers. They are based on a weighted sum of robust squared residual autocorrelations and on any robust and n^1/2‐consistent estimators. Our approach generalizes Li's (1988) test statistic, that can be interpreted as a test using the truncated uniform kernel. However, many kernels deliver a higher power. This is confirmed in a simulation study, where we investigate the finite sample properties of the new robust serial correlation tests in comparison to some commonly used robust and non‐robust tests.     

Local Asymptotic Distributions of Stationarity Tests

Abstract. In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non‐stationary process in any finite sample which converges to a stationary process as T ↑ ∞. From the asymptotic distributions, we find that the stationarity tests have non‐trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704–709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.     

Local Likelihood for non‐parametric ARCH(1) models

Abstract. We propose a non‐parametric local likelihood estimator for the log‐transformed autoregressive conditional heteroscedastic (ARCH) (1) model. Our non‐parametric estimator is constructed within the likelihood framework for non‐Gaussian observations: it is different from standard kernel regression smoothing, where the innovations are assumed to be normally distributed. We derive consistency and asymptotic normality for our estimators and show, by a simulation experiment and some real‐data examples, that the local likelihood estimator has better predictive potential than classical local regression. A possible extension of the estimation procedure to more general multiplicative ARCH(p) models with p > 1 predictor variables is also described.     

Fractional cointegration in the presence of linear trends

Abstract. We consider bivariate regressions of nonstationary fractionally integrated variables dominated by linear time trends. The asymptotic behaviour of the ordinary least square (OLS) estimators in this case allows limiting normality to arise at a faster rate of convergence than if the individual series were detrended, increasing in this way the power of the tests for fractional cointegration. We also show that the limiting distribution of the t‐ratio of the slope coefficient depends upon the presence or not of a deterministic trend in the conditional regressor. We introduce the concept of local fractional trend to explain the apparently diverging asymptotic theories that apply when a trend is either present or absent in our set‐up.     

PORTMANTEAU AUTOCORRELATION TESTS UNDER Q‐DEPENDENCE AND HETEROSKEDASTICITY

We propose extensions of the Box–Pierce ( 1970 ) portmanteau autocorrelation test to allow for two generalizations: (i) time series that exhibit unconditional heteroskedasticity and (ii) to test for the presence of autocorrelation only after a fixed lag q. These extensions involve a generalized quadratic form of the Box–Pierce test that uses the heteroskedasticity autocorrelation consistent‐type estimator. While we show that this modified test is robust to unconditional heteroskedasticity, the resulting power loss may be substantial. We therefore develop feasible weighted tests that make use of nonparametric estimates of the unobserved variance process. Simulation experiments show that the weighted tests have good size and superior power properties over the unweighted tests.     

Robust Wilcoxon‐Type Estimation of Change‐Point Location Under Short‐Range Dependence

We introduce a robust estimator of the location parameter for the change‐point in the mean based on Wilcoxon statistic and establish its consistency for L₁ near‐epoch dependent processes. It is shown that the consistency rate depends on the magnitude of the change. A simulation study is performed to evaluate the finite sample properties of the Wilcoxon‐type estimator under Gaussianity as well as under heavy‐tailed distributions and disturbances by outliers, and to compare it with a CUSUM‐type estimator. It shows that the Wilcoxon‐type estimator is equivalent to the CUSUM‐type estimator under Gaussianity but outperforms it in the presence of heavy tails or outliers in the data.     

One‐pot Synthesis of N‐Formyl‐O‐acyl‐ threo‐ and erythro‐DL‐β‐phenylserine Ethyl Esters and their Antiviral Properties

A series of N‐formyl‐O‐acyl‐β‐phenylserine derivatives 1b ‐ 7b were prepared by the interaction of N‐acyl‐b‐phenylserine ethyl esters 1a ‐ 7a with formic acid in presence of 1.5% HF. One‐pot acyl group N → O migration followed N‐formylation under elaborated reaction conditions. The kinetics of the reaction was investigated. The carboxylic acid moiety in the structure of β‐phenylserine had a strong influence on the reproduction of the used test‐viruses. The toxicity and antiviral activity is dependent on the diastereomeric forms of evaluated compounds.     

On‐line monitoring of methyl methacrylate–vinyl acetate emulsion copolymerization

An adaptive calorimetric method, coupled with state estimators for emulsion copolymerization, is shown to provide accurate, on‐line information on the evolution of the composition and kinetics of an emulsion copolymerization. This method was evaluated for the emulsion copolymerization of methyl methacrylate–vinyl acetate (MMA–VAc) under nonisothermal conditions. In addition to providing on‐line estimates of the number of moles of each polymerizing species in the reactor, the state estimator provides a value for a lumped kinetic parameter proportional to the product of n N_p. This information can be combined with off‐line measurements to study the evolution of polymerization kinetics and to explain the trends observed for the molecular weight distribution and glass transition temperatures. Values of n were found to vary from 0.5 to 30 for the homopolymerization of MMA. However, the presence of VAc in the copolymerizing system drastically reduces n . This can lead to a dramatic increase in the average molecular weight of the copolymer since it alters the ratio of propagation to termination in the polymerizing particles. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1667–1683, 2000     

Effect of Conditioning Variables on Impeller Power in Anionic Conditioning of Phosphate Slurries

Abstract

The trends that promote anionic reagent adsorption and subsequent flotation were examined in a statistically designed study in an effort to determine their effect on reagent mixing during anionic conditioning on a bench scale. The impeller power was measured during conditioning, and a statistical model was developed to correlate impeller power to the various conditioning variables examined. It was observed that the impeller power was significantly affected by the conditioning variables. A range of solids loading and agitation speeds exists in which the classical power number-Reynolds number correlation was found to hold true. The impeller power was found to be influenced by the conditioning time, indicating a time-dependent variation in rheological properties of the phosphate feed slurry. It was suggested that the impeller power drawn during conditioning was an indication of the extent of mixing of the collector with the particles, which contributes to the reagentization of the phosphate particles and their subsequent flotation. Flotation recovery was found to decrease when conditioning was carried out in the regime where the impeller power deviated from the N _P-N _Re correlation.     

Persistence Heterogeneity Testing in Panels with Interactive Fixed Effects

We consider large N,T panel data models with fixed effects, a common factor allowing for cross‐section dependence, and persistent data and shocks, which are assumed fractionally integrated. In a basic setup, the main interest is on the fractional parameter of the idiosyncratic component, which is estimated in first differences after factor removal by projection on the cross‐section average. The pooled conditional‐sum‐of‐squares estimate is consistent but the normal asymptotic distribution might not be centred, requiring the time series dimension to grow faster than the cross‐section size for correction. We develop tests of homogeneity of dynamics, including the degree of integration, that have no trivial power under local departures from the null hypothesis of a non‐negligible fraction of cross‐section units. A simulation study shows that our estimates and tests have good performance even in moderately small panels.     

Local Gaussian Autocorrelation and Tests for Serial Independence

The traditional and most used measure for serial dependence in a time series is the autocorrelation function. This measure gives a complete characterization of dependence for a Gaussian time series, but it often fails for nonlinear time series models as, for instance, the generalized autoregressive conditional heteroskedasticity model (GARCH), where it is zero for all lags. The autocorrelation function is an example of a global measure of dependence. The purpose of this article is to apply to time series a well‐defined local measure of serial dependence called the local Gaussian autocorrelation. It generally works well also for nonlinear models, and it can distinguish between positive and negative dependence. We use this measure to construct a test of independence based on the bootstrap technique. This procedure requires the choice of a bandwidth parameter that is calculated using a cross validation algorithm. To ensure the validity of the test, asymptotic properties are derived for the test functional and for the bootstrap procedure, together with a study of its power for different models. We compare the proposed test with one based on the ordinary autocorrelation and with one based on the Brownian distance correlation. The new test performs well. Finally, there are also two empirical examples.     

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.     

Chitosan–Quercetin Bioconjugate as Multi‐Functional Component of Antioxidants and Dual‐Responsive Hydrogel Networks

Multifunctional hydrogels based on chitosan–quercetin (CHITQ) conjugate are prepared by a thermo‐induced radical procedure in the presence of N‐isopropylacrylamide (NIPAAm), acrylamide (AAm), and N,N′‐methylenebis(acrylamide) (MEBA). At first, quercetin (Q) is grafted onto chitosan backbone with a functionalization degree of 275 mg of Q per gram of conjugate, as calculated by ¹H‐NMR analyses to impart antioxidant properties to the polysaccharide. Then, a pH and temperature sensitive hydrogel was obtained by involving CHITQ and NIPAAm in the polymerization reaction. The accessibility of phenolic moieties is modified in response to the hydrogel swelling/deswelling, as confirmed by antioxidant tests performed at different temperatures. Dual stimuli‐responsive hydrogels are proposed for the delivery of caffeine as model drug. The release profiles of caffeine depict a system particularly performing as on/off device at acidic pH with excellent applicability prospects.     

Range Unit‐Root (RUR) Tests: Robust against Nonlinearities,Error Distributions,Structural Breaks and Outliers

Abstract. Since the seminal paper by Dickey and Fuller in 1979, unit‐root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different method to test for the type of long‐wave patterns observed not only in unit‐root time series but also in series following more complex data‐generating mechanisms. To this end, our testing device analyses the unit‐root persistence exhibited by the data while imposing very few constraints on the generating mechanism. We call our device the range unit‐root (RUR) test since it is constructed from the running ranges of the series from which we derive its limit distribution. These nonparametric statistics endow the test with a number of desirable properties, the invariance to monotonic transformations of the series and the robustness to the presence of important parameter shifts. Moreover, the RUR test outperforms the power of standard unit‐root tests on near‐unit‐root stationary time series; it is invariant with respect to the innovations distribution and asymptotically immune to noise. An extension of the RUR test, called the forward–backward range unit‐root (FB‐RUR) improves the check in the presence of additive outliers. Finally, we illustrate the performances of both range tests and their discrepancies with the Dickey–Fuller unit‐root test on exchange rate series.     

An adhesion test method for spray‐applied fire‐resistive materials

Adhesion of spray‐applied fire‐resistive materials (SFRMs) to steel structures is critical in enabling a building to remain functional during a fire for a specific period of time for life safety and fire department access. Empirical tests such as ASTM E736 have been widely adopted by the industry in an effort to ensure sufficient bonding between SFRMs and steel structures. ASTM E736 assesses the adhesion of SFRMs by using tensile strength, a failure parameter that depends on the test geometry and has limited use for predicting failure in other geometries and conditions. These limitations have produced an urgent need for a scientifically based adhesion test method. In this paper, we propose a new test method that would provide more fundamental information that is independent of test geometry and has predictive capability. This paper utilizes a fracture energy‐based failure criterion (G_C) to characterize the adhesion between SFRMs and steel. The theoretical basis of this test method is validated by experimental compliance tests. The dependence of G_C on various test variables such as specimen width, substrate type, SFRM formulation, and test rate are examined. A comparison between this new test method, and the current widely used strength‐based test method is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

A Robbins–Monro Algorithm for Non‐Parametric Estimation of NAR Process with Markov Switching: Consistency

We approach the problem of non‐parametric estimation for autoregressive Markov switching processes. In this context, the Nadaraya–Watson‐type regression functions estimator is interpreted as a solution of a local weighted least‐square problem, which does not admit a closed‐form solution in the case of hidden Markov switching. We introduce a non‐parametric recursive algorithm to approximate the estimator. Our algorithm restores the missing data by means of a Monte Carlo step and estimates the regression function via a Robbins–Monro step. We prove that non‐parametric autoregressive models with Markov switching are identifiable when the hidden Markov process has a finite state space. Consistency of the estimator is proved using the strong α‐mixing property of the model. Finally, we present some simulations illustrating the performances of our non‐parametric estimation procedure.     

Modified carrageenan. 4. Synthesis and swelling behavior of crosslinked κC‐g‐AMPS superabsorbent hydrogel with antisalt and pH‐responsiveness properties

To synthesize a novel biopolymer‐based superabsorbent hydrogel, 2‐acrylamido‐2‐methylpropanesulfonic acid (AMPS) was grafted onto kappa‐carrageenan (κC) backbones. The graft copolymerization reaction was carried out in a homogeneous medium and in the presence of ammonium persulfate (APS) as an initiator, N,N,N′,N′‐tetramethyl ethylenediamine (TMEDA) as an accelerator, and N,N′‐methylene bisacrylamide (MBA) as a crosslinker. A proposed mechanism for κC‐g‐AMPS formation was suggested and the hydrogel structure was confirmed using FTIR spectroscopy. The affecting variables on swelling capacity, i.e., the initiator, the crosslinker, and the monomer concentration, as well as reaction temperature, were systematically optimized. The swelling measurements of the hydrogels were conducted in aqueous solutions of LiCl, NaCl, KCl, MgCl₂, CaCl₂, SrCl₂, BaCl₂, and AlCl₃. Due to the high swelling capacity in salt solutions, the hydrogels may be referred to as antisalt superabsorbents. The swelling of superabsorbing hydrogels was measured in solutions with pH ranging 1 to 13. The κC‐g‐AMPS hydrogel exhibited a pH‐responsiveness character so that a swelling–deswelling pulsatile behavior was recorded at pH 2 and 8. The overall activation energy for the graft copolymerization reaction was found to be 14.6 kJ/mol. The swelling kinetics of the hydrogels was preliminarily investigated as well. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 255–263, 2005     

A class of optimal tests for contemporaneous non‐causality in VAR models

The aim of this paper was to test for contemporaneous non‐causality defined by Granger (1969) between two groups of variables in a VAR(p) setting. Since contemporaneous correlation of the innovations is a necessary condition for contemporaneous causality (Pierce and Haugh, 1977), we focused on testing some restrictions on the covariance matrix of the noise. The class of the derived tests is locally asymptotically most stringent (in the Le Cam sense), invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone radial transformations. Those tests are based on multivariate ranks of distances and multivariate signs of the o bservations and are shown to be asymptotically distribution free under very mild assumptions on the noise.