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

Gravitational Lensing by Dark Matter Halos with Non-universal Density Profiles

The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe. By comparing predicted strong lensing probabilities with observations, we can test the mass distribution of dark matter halos, in particular, the inner density slope. In this letter, unlike previous work that directly models the density profiles of dark matter halos semi-analytically, we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, $\alpha$, of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively. This approach is an alternative and independent way to examine the slopes of mass density profiles of halos. We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant $\Lambda$. It is shown that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data. Together with the previous work on lensing probability, our results suggest that a singular isothermal sphere mass model of less than about 10^{13}h^{-1}M_{\sun} can predict strong lensing probabilities that are consistent with observations of small splitting angles.Comment: 11 pages, 2 figures, Accepted by ApJL for publication (February 10 issue 2004

Bayesian analysis of endogenous delay threshold models

We develop Bayesian methods of analysis for a new class of threshold autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions

Characteristics of noise complaints and the associations with urban morphology: A comparison across densities

This study aimed to characterise spatial-temporal distribution of noise complaints across urban areas with different densities and to analyse the associations between urban morphology and noise complaints. Taking New York City as the study area, crowdsourced noise complaints and urban morphology datasets from the city government's open data source were statistically analysed. The results suggest that between boroughs the characteristics of noise complaints are different, in terms of their spatial-temporal distribution, their relation to road transport network, land use, and building morphology. Noise complaints were clustered around the highest density area (Manhattan). The rate of noise complaints showed a year-on-year increase, peaking in autumn and spring. The rate of noise complaints is higher in areas with higher densities and roads that are 20-40m wide, closer to road crossings, and in enclosed blocks. The relationships between noise complaints and urban morphology are weaker in high-density boroughs than in other boroughs

Relationship between urban development patterns and noise complaints in England

The role of urban planning in sound environments has recently received increased research attention. This study aims to examine the relationship between the rate of noise complaints and urban development patterns concerning planning and landscape at city/region level. Open-source government data sets are used for statistical analysis across all district and unitary local authorities in England. The indicators for urban development patterns are categorised into six groups: population, industrial structure, built-up area, transport network, commuting, and natural landscape factors. Our research found that noise complaints tend to be higher in service-dominated cities/regions with high population densities; large and uneven cities/regions also tend to have more noise complaints, as do clustered cities/regions. However, dispersed, fragmented, and/or cities/regions having ragged boundaries are likely to have less noise complaints. These findings were confirmed by analysis of transport networks and commuting factors. Finally, cities/regions with more natural landscapes and greater separation of residences from workplaces also have fewer noise complaints

Electron Transfer in Donor-Acceptor Systems: Many-Particle Effects and Influence of Electronic Correlations

We investigate electron transfer processes in donor-acceptor systems with a coupling of the electronic degrees of freedom to a common bosonic bath. The model allows to study many-particle effects and the influence of the local Coulomb interaction U between electrons on donor and acceptor sites. Using the non-perturbative numerical renormalization group approach we find distinct differences between the electron transfer characteristics in the single- and two-particle subspaces. We calculate the critical electron-boson coupling alpha_c as a function of $U$ and show results for density-density correlation functions in the whole parameter space. The possibility of many-particle (bipolaronic) and Coulomb-assisted transfer is discussed.Comment: 4 pages, 4 figure