On surface brightness fluctuations: probabilistic and statistical bases I: Stellar population and theoretical SBF

This work aims to provide a theoretical formulation of Surface Brightness Fluctuations (SBF) in the framework of probabilistic synthesis models, and to distinguish between the different distributions involved in the SBF definition. RESULTS: We propose three definitions of SBF: (i) stellar population SBF, which can be computed from synthesis models and provide an intrinsic metric of fit for stellar population studies; (ii) theoretical SBF, which include the stellar population SBF plus an additional term that takes into account the distribution of the number of stars per resolution element psi(N); theoretical SBF coincide with Tonry & Schneider (1998) definition in the very particular case that psi(N) is assumed to be a Poisson distribution. However, the Poisson contribution to theoretical SBF is around 0.1% of the contribution due to the stellar population SBF, so there is no justification to include any reference to Poisson statistics in the SBF definition; (iii) observational SBF, which are those obtained in observations that are distributed around the theoretical SBF. Finally, we show alternative ways to compute SBF and extend the application of stellar population SBF to defining a metric of fitting for standard stellar population studies. CONCLUSIONS: We demostrate that SBF are observational evidence of a probabilistic paradigm in population synthesis, where integrated luminosities have an intrinsic distributed nature, and they rule out the commonly assumed deterministic paradigm of stellar population modeling.Comment: A&A accepte

The fine-structure of volatility feedback I: multi-scale self-reflexivity

We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kernel is diagonal. The calibration of these models on US stock returns reveals several unexpected features. The off-diagonal (non ARCH) coefficients of the quadratic kernel are found to be highly significant both In-Sample and Out-of-Sample, but all these coefficients turn out to be one order of magnitude smaller than the diagonal elements. This confirms that daily returns play a special role in the volatility feedback mechanism, as postulated by ARCH models. The feedback kernel exhibits a surprisingly complex structure, incompatible with models proposed so far in the literature. Its spectral properties suggest the existence of volatility-neutral patterns of past returns. The diagonal part of the quadratic kernel is found to decay as a power-law of the lag, in line with the long-memory of volatility. Finally, QARCH models suggest some violations of Time Reversal Symmetry in financial time series, which are indeed observed empirically, although of much smaller amplitude than predicted. We speculate that a faithful volatility model should include both ARCH feedback effects and a stochastic component

The Long and Large Decline in U.S. Output Volatility

output volatility, macroeconomics, decline, U.S. output

Evaluating the impact of inequality constraints and parameter uncertainty on optimal portfolio choice

© 2015 Taylor & Francis. We present new analytical results for the impact of portfolio weight constraints on an investor’s optimal portfolio when parameter uncertainty is taken into account. While it is well known that parameter uncertainty and imposing weight constraints results in reduced certainty equivalent returns, in the general case, there are no analytical results. In a special case, commonly used in the funds management literature, we derive analytical expression for the certainty equivalent loss that does not depend on the risk aversion parameter. We illustrate our theoretical results using hedge fund data, from the perspective of a fund-of-fund manager. Our contribution is to formalize the framework to investigate this problem, as well as providing tractable analytical solutions that can be implemented using either simulated or asset manager returns

Detection and removal of eyeblink artifacts from EEG using wavelet analysis and independent component analysis

Electrical signals generated by brain activity that are measured by the electroencephalogram can be distorted by electrical activity originating from eyeblinks and eye movements. This thesis proposes a new technique to identify and remove eyeblink artifacts from EEG data. An algorithm using a combination of wavelet analysis and independent component analysis (ICA) is implemented to detect the temporal location of the eyeblink artifact and eliminate it without compromising the integrity of the primary EEG data. The discrete wavelet transform is performed on 10 second epochs of data to detect the occurrence of ocular artifact. ICA is used to separate out the independent components within the data and the temporal locations of the eyeblink are used to remove the artifact and reconstruct the EEG data without that source of distortion. The results obtained indicate that the technique implemented may be robust enough to effectively process EEG data and is capable of removing eyeblink artifacts successfully when they are prominent and the data does not contain a great deal of movement artifact. The results show an 88.68% detection rate, a false positive rate of 4.03%, and an 87.23% removal rate for all eyeblinks that were accurately detected. The statistics obtained compared favorably with work done by others in this field of investigation

Why do variance swaps exist?

This paper studies the determinants of the variance risk premium and concludes on the hedging possibilities offered by variance swaps. We start by showing that the variance risk premium responds to changes in higher order moments of the distribution of market returns. But the uncertainty that determines the variance risk premium –the fear by investors to deviations from Normality in returns- is also strongly related to a variety of risks: risk of default, employment growth risk, consumption growth risk, stock market risk and market illiquidity risk. Therefore, the variance risk premium could be interpreted as reflecting the market willingness to pay for hedging against financial and macroeconomic sources of risk. We provide additional evidence in support of that view.Variance risk premium, Non-normality, Economic risks, Hedging