X-Ray Spectral Variability in Cygnus X-1

Spectral variability in different energy bands of X-rays from Cyg X-1 in different states is studied with RXTE observations and time domain approaches. In the hard tail of energy spectrum above $\sim 10$ keV, average peak aligned shots are softer than the average steady emission and the hardness ratio decreases when the flux increases during a shot for all states. In regard to a soft band lower $\sim 10$ keV, the hardness in the soft state varies in an opposite way: it peaks when the flux of the shot peaks. For the hard and transition states, the hardness ratio in respect to a soft band during a shot is in general lower than that of the steady component and a sharp rise is observed at about the shot peak. For the soft state, the correlation coefficient between the intensity and hardness ratio in the hard tail is negative and decreases monotonically as the timescale increases from 0.01 s to 50 s, which is opposite to that in regard to a soft band. For the hard and transition states, the correlation coefficients are in general negative and have a trend of decrease with increasing timescale.Comment: 14 pages, 3 figures, accepted by Ap

Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and kurtosis appear directly in the functional form of this density. In this setting VaR can be described as a function of the time-varying higher moments by applying the Cornish-Fisher expansion series of the first four moments. An evaluation of the predictive performance of the proposed model in the estimation of 1-day and 10-day VaR forecasts is performed in comparison with the historical simulation, filtered historical simulation and GARCH model. The adequacy of the VaR forecasts is evaluated under the unconditional, independence and conditional likelihood ratio tests as well as Basel II regulatory tests. The results presented have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives

Investigation of the energy dependence of the orbital light curve in LS 5039

LS 5039 is so far the best studied $\gamma$-ray binary system at multi-wavelength energies. A time resolved study of its spectral energy distribution (SED) shows that above 1 keV its power output is changing along its binary orbit as well as being a function of energy. To disentangle the energy dependence of the power output as a function of orbital phase, we investigated in detail the orbital light curves as derived with different telescopes at different energy bands. We analysed the data from all existing \textit{INTEGRAL}/IBIS/ISGRI observations of the source and generated the most up-to-date orbital light curves at hard X-ray energies. In the $\gamma$-ray band, we carried out orbital phase-resolved analysis of \textit{Fermi}-LAT data between 30 MeV and 10 GeV in 5 different energy bands. We found that, at $\lesssim$100 MeV and $\gtrsim$1 TeV the peak of the $\gamma$-ray emission is near orbital phase 0.7, while between $\sim$100 MeV and $\sim$1 GeV it moves close to orbital phase 1.0 in an orbital anti-clockwise manner. This result suggests that the transition region in the SED at soft $\gamma$-rays (below a hundred MeV) is related to the orbital phase interval of 0.5--1.0 but not to the one of 0.0--0.5, when the compact object is "behind" its companion. Another interesting result is that between 3 and 20 GeV no orbital modulation is found, although \textit{Fermi}-LAT significantly ($\sim$18$\sigma$) detects LS 5039. This is consistent with the fact that at these energies, the contributions to the overall emission from the inferior conjunction phase region (INFC, orbital phase 0.45 to 0.9) and from the superior conjunction phase region (SUPC, orbital phase 0.9 to 0.45) are equal in strength. At TeV energies the power output is again dominant in the INFC region and the flux peak occurs at phase $\sim$0.7.Comment: 7 pages, 6 figures, accepted for publication in MNRA