Dynamic Density Forecasts for Multivariate Asset Returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time-varying) non-central co-moments of assets. We estimate the coefficients of the polynomial via the Method of Moments for a carefully selected set of co-moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed as well as standard techniques to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the “negative tail” of the joint distribution.

Joint measurements and Bell inequalities

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Cognitive Single Carrier Systems: Joint Impact of Multiple Licensed Transceivers

In this paper, the impact of interference from multiple licensed transceivers on cognitive underlay single carrier systems is examined. Specifically, the situation is considered in which the secondary network is limited by three key parameters: 1) maximum transmit power at the secondary transmitter, 2) peak interference power at the primary receivers, and 3) interference power from the primary transmitters. For this cognitive underlay single carrier system, the signal-to-interference ratio (SIR) of the secondary network is obtained for transmission over frequency selective fading channels. Based on this, a new closedform expression for the cumulative distribution function of the SIR is evaluated, from which the outage probability and the ergodic capacity are derived. Further insights are established by analyzing the asymptotic outage probability and the asymptotic ergodic capacity in the high transmission power regime. In particular, it is corroborated that the asymptotic outage diversity gain is equal to the multipath gain of the frequency selective channel in the secondary network. The asymptotic ergodic capacity also gives new insight into the additional power cost for different network parameters while maintaining a specified target ergodic capacity. Illustrative numerical examples are presented to validate the outage probability and ergodic capacity under different interference power profiles.

On the Multivariate Gamma-Gamma (ΓΓ) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.

The ejected mass distribution of Type Ia supernovae: a significant rate of non-Chandrasekhar-mass progenitors

The ejected mass distribution of Type Ia supernovae (SNe Ia) directly probes progenitor evolutionary history and explosion mechanisms, with implications for their use as cosmological probes. Although the Chandrasekhar mass is a natural mass scale for the explosion of white dwarfs as SNe Ia, models allowing SNe Ia to explode at other masses have attracted much recent attention. Using an empirical relation between the ejected mass and the light-curve width, we derive ejected masses Mej and 56Ni masses MNi for a sample of 337 SNe Ia with redshifts z <0.7 used in recent cosmological analyses. We use hierarchical Bayesian inference to reconstruct the joint Mej-MNi distribution, accounting for measurement errors. The inferred marginal distribution of Mej has a long tail towards sub-Chandrasekhar masses, but cuts off sharply above 1.4 M⊙. Our results imply that 25-50 per cent of normal SNe Ia are inconsistent with Chandrasekhar-mass explosions, with almost all of these being sub-Chandrasekhar mass; super-Chandrasekhar-mass explosions make up no more than 1 per cent of all spectroscopically normal SNe Ia. We interpret the SN Ia width-luminosity relation as an underlying relation between Mej and MNi, and show that the inferred relation is not naturally explained by the predictions of any single known explosion mechanism.