On infinitely cohomologous to zero observables

We show that for a large class of piecewise expanding maps T, the bounded p-variation observables u_0 that admits an infinite sequence of bounded p-variation observables u_i satisfying u_i(x)= u_{i+1}(Tx) -u_{i+1}(x) are constant. The method of the proof consists in to find a suitable Hilbert basis for L^2(hm), where hm is the unique absolutely continuous invariant probability of T. In terms of this basis, the action of the Perron-Frobenious and the Koopan operator on L^2(hm) can be easily understood. This result generalizes earlier results by Bamon, Kiwi, Rivera-Letelier and Urzua in the case T(x)= n x mod 1, n in N-{0,1} and Lipchitizian observables u_0.Comment: 24 pages. We included new results by A. Avila. He kindly agreed to include them in this new version. We also fixed some typo

On infinitely cohomologous to zero observables

We show that for a large class of piecewise expanding maps T, the bounded p-variation observables u_0 that admits an infinite sequence of bounded p-variation observables u_i satisfying u_i(x)= u_{i+1}(Tx) -u_{i+1}(x) are constant. The method of the proof consists in to find a suitable Hilbert basis for L^2(hm), where hm is the unique absolutely continuous invariant probability of T. In terms of this basis, the action of the Perron-Frobenious and the Koopan operator on L^2(hm) can be easily understood. This result generalizes earlier results by Bamon, Kiwi, Rivera-Letelier and Urzua in the case T(x)= n x mod 1, n in N-{0,1} and Lipchitizian observables u_0.Comment: 24 pages. We included new results by A. Avila. He kindly agreed to include them in this new version. We also fixed some typo

The entropy of elliptical galaxies in Coma: a clue for a distance indicator

We have fitted the surface brightness of a sample of 79 elliptical galaxies pertaining to the Coma cluster of galaxies using the Sersic profile. This model is defined through three primary parameters: scale length (a), intensity (\Sigma_0), and a shape parameter (\nu); physical and astrophysical quantities may be computed from these parameters. We show that correlations are stronger among primary parameters than the classical astrophysical ones. In particular, the galaxies follow a high correlation in \nu and a parameters. We show that the \nu and a correlation satisfies a constant specific entropy condition. We propose to use this entropy relation as distance indicator for clusters.Comment: 5 pages, 3 figures, submitted to MNRAS Letter

Evaluating Value-at-Risk models via Quantile Regression

This paper is concerned with evaluating value at risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Maganelli (2004) are based on such variables. In this paper we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series