Extreme Value GARCH modelling with Bayesian Inference

RePEC Working Paper Series No: 05/2009Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised extreme value distribution. This study examines a conditional extreme value distribution with the added specification that the extreme values (maxima or minima) follows a conditional autoregressive heteroscedasticity process. The dependence has been modelled by allowing the location and scale parameters of the extreme distribution to vary with time. The resulting combined model, GEV-GARCH, is developed by implementing the GARCH volatility mechanism in these extreme value model parameters. Bayesian inference is used for the estimation of parameters and posterior inference is available through the Markov Chain Monte Carlo (MCMC) method. The model is firstly applied to relevant simulated data to verify model stability and reliability of the parameter estimation method. Then real stock returns are used to consider evidence for the appropriate application of the model. A comparison is made between the GEV-GARCH and traditional GARCH models. Both the GEV-GARCH and GARCH show similarity in the resulting conditional volatility estimates, however the GEV-GARCH model differs from GARCH in that it can capture and explain extreme quantiles better than the GARCH model because of more reliable extrapolation of the tail behaviour

X-ray flares in Orion young stars. I. Flare characteristics

Pre-main sequence (PMS) stars are known to produce powerful X-ray flares which resemble magnetic reconnection solar flares scaled by factors up to 10^4. However, numerous puzzles are present including the structure of X-ray emitting coronae and magnetospheres, effects of protoplanetary disks, and effects of stellar rotation. To investigate these issues in detail, we examine 216 of the brightest flares from 161 PMS stars observed in the Chandra Orion Ultradeep Project (COUP). These constitute the largest homogeneous dataset of PMS, or indeed stellar flares at any stellar age, ever acquired. Our effort is based on a new flare spectral analysis technique that avoids nonlinear parametric modeling. It can be applied to much weaker flares and is more sensitive than standard methods. We provide a catalog with >30 derived flare properties and an electronic atlas for this unique collection of stellar X-ray flares. The current study (Paper I) examines the flare morphologies, and provides general comparison of COUP flare characteristics with those of other active X-ray stars and the Sun. Paper II will concentrate on relationships between flare behavior, protoplanetary disks, and other stellar properties. Several results are obtained. First, the COUP flares studied here are among the most powerful, longest, and hottest stellar X-ray flares ever studied. Second, no significant statistical differences in peak flare luminosity or temperature distributions are found among different morphological flare classes, suggesting a common underlying mechanism for all flares. Third, comparison with the general solar-scaling laws indicates that COUP flares may not fit adequately proposed power-temperature and duration-temperature solar-stellar fits. Fourth, COUP super-hot flares are found to be brighter but shorter than ... ABRIDGEDComment: Accepted for publication in ApJ (07/11/08); 63 pages, 16 figures, 4 table

Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals

We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting data assimilation and compressive recovery of land surface-atmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the sparsity of the fields of temperature is relatively pressure-independent while atmospheric humidity and geopotential heights are typically sparser at lower and higher pressure levels, respectively. We provide evidence that these land-atmospheric states can be accurately estimated using a small set of measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl

Bioelectrochemical dechlorination of trichloroethene: From electron transfer mechanisms to process scale-up

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Radiative accretion shocks along nonuniform stellar magnetic fields in classical T Tauri stars

(abridged) AIMS. We investigate the dynamics and stability of post-shock plasma streaming along nonuniform stellar magnetic fields at the impact region of accretion columns. We study how the magnetic field configuration and strength determine the structure, geometry, and location of the shock-heated plasma. METHODS. We model the impact of an accretion stream onto the chromosphere of a CTTS by 2D axisymmetric magnetohydrodynamic simulations. Our model takes into account the gravity, the radiative cooling, and the magnetic-field-oriented thermal conduction. RESULTS. The structure, stability, and location of the shocked plasma strongly depend on the configuration and strength of the magnetic field. For weak magnetic fields, a large component of B may develop perpendicular to the stream at the base of the accretion column, limiting the sinking of the shocked plasma into the chromosphere. An envelope of dense and cold chromospheric material may also develop around the shocked column. For strong magnetic fields, the field configuration determines the position of the shock and its stand-off height. If the field is strongly tapered close to the chromosphere, an oblique shock may form well above the stellar surface. In general, a nonuniform magnetic field makes the distribution of emission measure vs. temperature of the shocked plasma lower than in the case of uniform magnetic field. CONCLUSIONS. The initial strength and configuration of the magnetic field in the impact region of the stream are expected to influence the chromospheric absorption and, therefore, the observability of the shock-heated plasma in the X-ray band. The field strength and configuration influence also the energy balance of the shocked plasma, its emission measure at T > 1 MK being lower than expected for a uniform field. The above effects contribute in underestimating the mass accretion rates derived in the X-ray band.Comment: 11 pages, 11 Figures; accepted for publication on A&A. Version with full resolution images can be found at http://www.astropa.unipa.it/~orlando/PREPRINTS/sorlando_accretion_shocks.pd