Properties of the sample autocorrelations of non-linear transformations in long memory stochastic volatility models

The autocorrelations of log-squared, squared, and absolute financial returns are often used to infer the dynamic properties of the underlying volatility. This article shows that, in the context of long-memory stochastic volatility models, these autocorrelations are smaller than the autocorrelations of the log volatility and so is the rate of decay for squared and absolute returns. Furthermore, the corresponding sample autocorrelations could have severe negative biases, making the identification of conditional heteroscedasticity and long memory a difficult task. Finally, we show that the power of some popular tests for homoscedasticity is larger when they are applied to absolute returns.Publicad

XMMPZCAT: A catalogue of photometric redshifts for X-ray sources

The third version of the XMM-Newton serendipitous catalogue (3XMM), containing almost half million sources, is now the largest X-ray catalogue. However, its full scientific potential remains untapped due to the lack of distance information (i.e. redshifts) for the majority of its sources. Here we present XMMPZCAT, a catalogue of photometric redshifts (photo-z) for 3XMM sources. We searched for optical counterparts of 3XMM-DR6 sources outside the Galactic plane in the SDSS and Pan-STARRS surveys, with the addition of near- (NIR) and mid-infrared (MIR) data whenever possible (2MASS, UKIDSS, VISTA-VHS, and AllWISE). We used this photometry data set in combination with a training sample of 5157 X-ray selected sources and the MLZ-TPZ package, a supervised machine learning algorithm based on decision trees and random forests for the calculation of photo-z. We have estimated photo-z for 100,178 X-ray sources, about 50% of the total number of 3XMM sources (205,380) in the XMM-Newton fields selected to build this catalogue (4208 out of 9159). The accuracy of our results highly depends on the available photometric data, with a rate of outliers ranging from 4% for sources with data in the optical+NIR+MIR, up to $\sim$40% for sources with only optical data. We also addressed the reliability level of our results by studying the shape of the photo-z probability density distributions.Comment: 16 pages, 14 figures, A&A accepte