Estimation and tests for power-transformed and threshold GARCH models

Consider a class of power transformed and threshold GARCH(p,q) (PTTGRACH(p,q)) model, which is a natural generalization of power-transformed and threshold GARCH(1,1) model in Hwang and Basawa (2004) and includes the standard GARCH model and many other models as special cases. We ¯rst establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has ¯nite fourth moment. For the case of heavy-tailed errors, we propose a least absolute deviations estimation (LADE) for PTTGARCH(p,q) model, and prove that the LADE is asymptotically normally distributed under very weak moment conditions. This paves the way for a statistical inference based on asymptotic normality for heavy-tailed PTTGARCH(p,q) models. As a consequence, we can construct the Wald test for GARCH structure and discuss the order selection problem in heavy-tailed cases. Numerical results show that LADE is more accurate than QMLE for heavy tailed errors. Furthermore the theory is applied to the daily returns of the Hong Kong Hang Seng Index, which suggests that asymmetry and nonlinearity could be present in the ¯nancial time series and the PTTGARCH model is capable of capturing these characteristics. As for the probabilistic structure of PTTGARCH(p,q), we give in the appendix a necessary and su±cient condition for the existence of a strictly stationary solution of the model, the existence of the moments and the tail behavior of the strictly stationary solution

Sudden jumps and plateaus in the quench dynamics of a Bloch state

We take a one-dimensional tight binding chain with periodic boundary condition and put a particle in an arbitrary Bloch state, then quench it by suddenly changing the potential of an arbitrary site. In the ensuing time evolution, the probability density of the wave function at an arbitrary site \emph{jumps indefinitely between plateaus}. This phenomenon adds to a former one in which the survival probability of the particle in the initial Bloch state shows \emph{cusps} periodically, which was found in the same scenario [Zhang J. M. and Yang H.-T., EPL, \textbf{114} (2016) 60001]. The plateaus support the scattering wave picture of the quench dynamics of the Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a Luttinger-like model, based on which, the locations of the jumps and the heights of the plateaus are accurately predicted.Comment: final versio

Measurements of the instantaneous velocity difference and local velocity with a fiber-optic coupler

New optical arrangements with two single-mode input fibers and a fiber-optic coupler are devised to measure the instantaneous velocity difference and local velocity. The fibers and the coupler are polarization-preserving to guarantee a high signal-to-noise ratio. When the two input fibers are used to collect the scattered light with the same momentum transfer vector but from two spatially separated regions in a flow, the obtained signals interfere when combined via the fiber-optic coupler. The resultant light received by a photomultiplier tube contains a cross-beat frequency proportional to the velocity difference between the two measuring points. If the two input fibers are used to collect the scattered light from a common scattering region but with two different momentum transfer vectors, the resultant light then contains a self-beat frequency proportional to the local velocity at the measuring point. The experiment shows that both the cross-beat and self-beat signals are large and the standard laser Doppler signal processor can be used to measure the velocity difference and local velocity in real time. The new technique will have various applications in the general area of fluid dynamics.Comment: Patent number: 67437 for associated information on the hardware, see http://karman.phyast.pitt.edu/horvath

Triclosan Adsorption Using Wastewater Biosolids-derived Biochar

Organic micropollutants are ubiquitous in the environment and stem from municipal wastewater treatment plant discharges. Adsorption can be used as a tertiary treatment to complement the conventional activated sludge process to remove micropollutants prior to discharge. This research evaluated the performance of wastewater biosolids-derived biochar as an adsorbent to remove triclosan from water. Pre-conditioning of the biochar using hydrochloric acid (HCl) was an essential step for triclosan adsorption. Using acid-conditioned biochar, maximum adsorption of 872 μg triclosan per g biochar was achieved with biochar produced at 800 °C. Biochar produced at higher pyrolysis temperatures tended to have higher triclosan sorption capacity using initial triclosan concentrations of 200 μg L−1 levels. However, pyrolysis temperature had less impact on triclosan sorption at lower, environmentally relevant concentrations. Low solution pH (3) enhanced adsorption and high pH (11) inhibited adsorption. Effective triclosan sorption was observed between pH 5 and 9, with little variation, which is positive for practical applications operated at near-neutral solution pH. In wastewater, acid-treated biochar also effectively sorbed triclosan, albeit at a decreased adsorption capacity and removal rate due to competition from other organic constituents. This study indicated that adsorption may occur mainly due to high surface area, hydrophobicity, and potential interaction between biochar and triclosan functional groups including hydrogen bonding and π-stacking. This work demonstrated that acid-conditioned biosolids-derived biochar could be a suitable sorbent to remove triclosan from wastewater as a final polishing treatment step