Testing for a break in persistence under long-range dependencies

Abstract.  We show that tests for a break in the persistence of a time series in the classical I (0)/ I (1) framework have serious size distortions when the actual data-generating process (DGP) exhibits long-range dependencies. We prove that the limiting distribution of a CUSUM of squares-based test depends on the true memory parameter if the DGP exhibits long memory. We propose adjusted critical values for the test and give finite sample response curves that allow easy implementation of the test by the practitioner and also ease in computing the relevant critical values. We furthermore prove the consistency of the test for a simple breakpoint estimator also under long memory. We show that the test has satisfying power properties when the correct critical values are used.     

A simple test of changes in mean in the possible presence of long‐range dependence

We propose a simple testing procedure to test for a change point in the mean of a possibly long‐range dependent time series. Under the null hypothesis, the series is stationary with long‐range dependence and our test statistic converges to a non‐degenerate distribution, whereas under the alternative, the series has a change point in the mean and the test statistic diverges to infinity. We demonstrate the good size and power properties of our test via simulations and illustrate its usefulness by analysing two real data sets.     

Testing for Change‐Points in Long‐Range Dependent Time Series by Means of a Self‐Normalized Wilcoxon Test

We propose a testing procedure based on the Wilcoxon two‐sample test statistic in order to test for change‐points in the mean of long‐range dependent data. We show that the corresponding self‐normalized test statistic converges in distribution to a non‐degenerate limit under the hypothesis that no change occurred and that it diverges to infinity under the alternative of a change‐point with constant height. Furthermore, we derive the asymptotic distribution of the self‐normalized Wilcoxon test statistic under local alternatives, that is, under the assumption that the height of the level shift decreases as the sample size increases. Regarding the finite sample performance, simulation results confirm that the self‐normalized Wilcoxon test yields a consistent discrimination between hypothesis and alternative and that its empirical size is already close to the significance level for moderate sample sizes.     

Simulating a class of stationary Gaussian processes using the Davies–Harte algorithm, with application to long memory processes

We demonstrate that the fast and exact Davies–Harte algorithm is valid for simulating a certain class of stationary Gaussian processes – those with a negative autocovariance sequence for all non-zero lags. The result applies to well known classes of long memory processes: Gaussian fractionally differenced (FD) processes, fractional Gaussian noise (fGn) and the nonstationary fractional Brownian Motion (fBm).     

On LM‐type tests for seasonal unit roots in the presence of a break in trend

This article proposes tests for seasonal unit roots allowing for the presence of a break in the trend slope occurring at an unknown date. In particular, new LM‐type tests are derived based on the framework introduced by Hylleberg et al. (1990). Null asymptotic distributions are derived for the no break case as well as when a break is present in the data‐generating process and a Monte Carlo investigation on the finite sample size and power performance of the new procedures is presented.     

Decolourisation of dyes and dyehouse effluent in a bubble‐column reactor by ozonation in the presence of H2O2, KMnO4 or Ferral

The decolourisation of aqueous solutions of dyes by ozonation in the presence of hydrogen peroxide, potassium permanganate or Ferral using a bubble column reactor was investigated. Addition of hydrogen peroxide in the ozonation reaction of dyes did not affect its decolourisation efficiency. The addition of potassium permanganate considerably increased the decolourisation efficiency during ozonation of all of the dyes studied. Ferral showed excellent catalytic activity under acidic conditions but in alkaline conditions its catalytic activity diminished. The effect of the ozonation on COD was also monitored and was found to be highly effective in reducing the COD of aqueous dye solutions. In addition to studying the effect of addition of hydrogen peroxide, potassium permanganate or Ferral on the ozonation of aqueous solutions of individual dyes, tests were carried out on effluent from a commercial dyeing unit. Copyright © 2005 Society of Chemical Industry     

The use of CO2 for reversible pH shifting,and the removal of succinic acid in a polymer‐based two‐phase partitioning bioreactor

BACKGROUND: Succinic acid (SA) is an intermediate in the production of commodity chemicals, but SA bioproduction has not yet been commercialized due to end product inhibition and high product separation costs. Two‐phase partitioning bioreactors (TPPBs) can increase volumetric productivity through in situ product removal, although SA uptake by polymers requires a pH below the pK_A2 of SA (4.2). It was proposed to reversibly reduce the pH with CO₂ sparging for absorption of SA, followed by nitrogen stripping to allow continued bioproduction after returning to metabolic pH levels. RESULTS: At 1 atm CO₂ sparging lowered the pH of RO water to 3.8 but only to 4.75 in medium, requiring acid/base pH adjustment in subsequent experiments. Actinobacillus succinogenes was temporarily exposed to pH 4.2 for between 5 min and 4 h to observe the effect on subsequent growth; cells could grow after up to 4 h of low pH exposure, sufficient time for SA uptake. Because atmospheric CO₂ could not adequately lower the pH of medium, a TPPB was operated with the pH being shifted using strong acid/base; SA was recovered in situ, however, the accumulation of salts hindered further cell growth. CONCLUSION: Several key elements of this novel processing strategy were successfully demonstrated, and work is continuing with high pressure CO₂ to achieve the desired pH adjustment levels. Copyright © 2011 Society of Chemical Industry     

Development of a tool, using CFD, for the assessment of the disinfection process by ozonation in industrial scale drinking water treatment plants

Foreseen standards regarding microorganism content for drinking water require assessment of the capability of existing plants to reach the upcoming requirements. This paper presents the development of a tool to assess this capability in a commonly encountered key step of water disinfection: ozonation. In this paper, this tool is applied to the test case of an ozonation channel of the Belgian drinking water producer Vivaqua. This tool is based on a mathematical model of the momentum and mass transport phenomena in an ozonation channel. The gas–liquid flow is coupled to ozone mass transfer and kinetics describing the ozone and microorganisms concentrations decay. The degradation of Bacillus subtilis spores, as a representative of resistant microorganisms, is implemented in the model. The model takes explicitly into account the bubble size variation and its impact on mass transfer. Bubbles sizes and kinetics parameters are estimated based on dedicated experiments. The model is partially validated by comparing simulations results, obtained using computational fluid dynamics, to experimental residence time distributions, residual ozone concentration and Bacillus subtilis spores degradation efficiency measurements obtained on the studied ozonation channel. It is shown that, at the industrial scale, bubble diameter variation has a significant impact on ozone concentration in the liquid at the reactor exit. Using the tool, it is also shown that, the ozonation channel of Vivaqua can be used to achieve degradation of resistant microorganisms but only with its maximal flow rate and concentration of ozone injection. Moreover, at low operating temperature, some microorganisms that present latency towards reaction with dissolved ozone might hardly be destroyed.     

Semi-empirical model of toluene transport in polyethylene membranes based on the data using a new type of apparatus for determining gas permeability, diffusivity and solubility

Solubility, diffusivity and permeability of toluene vapors in low-density polyethylene (LDPE) membranes of various thicknesses (approximately 48, 93, 138 and 187 μm) at different temperatures 30, 40 and 50 °C in the range of relative vapor pressure p/p⁰=(0.05; 0.95) were measured using new type of permeation apparatus. Moreover, special construction of the new cell enables determination of the permeant amount sorbed in the membrane in the steady state operation of vapor permeation.The simple semi-empirical model of toluene transport in a polyethylene membrane based on relation between experimentally obtained effective diffusion coefficients and concentration dependent diffusion coefficients evaluated from experiments on a new permeation apparatus was proposed. The model enables estimation of toluene fluxes, sorption in the steady state of vapor permeation and concentration profiles in a polyethylene membrane from equilibrium sorption isotherms and effective diffusion coefficients. Very good agreement between experimental and calculated values from the proposed model was obtained.     

Effect of pretreatment and regeneration conditions of Ru/γ-Al2O3 catalysts for N2O decomposition and/or reduction in O2-rich atmospheres and in the presence of NOX, SO2 and H2O

The effect of the pretreatment (inert, oxidative, and reducing) of Ru/γ-Al₂O₃ catalyst on its activity and stability in the decomposition of N₂O in the absence or presence of O₂, SO₂, H₂O and NO_X was studied in the present work. Decomposition of pure N₂O was slightly enhanced by the H₂-pretreated catalyst (metallic Ru) compared to the O₂- or He-pretreated ones, owing to a cyclic oxidation–reduction pathway of metallic Ru. The observed decrease of activity by O₂ or H₂O addition was reversible compared to SO₂ which caused a strong, irreversible deactivation of the catalyst, irrespective of the type of pretreatment. This was attributed to the formation of stable sulphates, mainly those on RuO₂ surface, which could only be removed by regeneration under reducing (H₂ in He) atmosphere at temperatures of ca. 500 °C. Oxidative or inert regeneration required very high temperatures (i.e. >700 °C) in order to decompose these sulphates. A method of retaining N₂O conversion activity very high (≥98%) for long reaction times is suggested and is based on frequent and short-time (ca. 10 min) regenerations of the catalyst under reducing atmosphere (ca. 5% H₂ in He). The effect of co-feeding various reducing agents, such as CO or C₃H₆, on the N₂O conversion activity in the presence of O₂, SO₂, H₂O and NO_X is negligible, mainly because they are oxidized at relatively low temperatures in the O₂-rich feeds used in this study.