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2010MNRAS.404..931E - Mon. Not. R. Astron. Soc., 404, 931-946 (2010/May-2)
On the use of structure functions to study blazar variability: caveats and problems.
EMMANOULOPOULOS D., McHARDY I.M. and UTTLEY P.
Abstract (from CDS):
The SF is often invoked in the framework of shot-noise models to determine the temporal properties of individual shots. We caution that although the SF may be fitted to infer the shot parameters, the resultant shot-noise model is usually inconsistent with the observed PSD. As any model should fit the data in both the time and the frequency domain, the shot-noise model, in these particular cases, cannot be valid.
Moreover, we show that the lack of statistical independence between adjacent SF points, in the standard SF formulation, means that it is not possible to perform robust statistical model fitting following the commonly used least-squares fitting methodology. The latter yields uncertainties in the fitting parameters (i.e. slopes, breaks) that are far too small with respect to their true statistical scatter. Finally, it is also commonly thought that SFs are immune to the sampling problems, such as data gaps, which affects the estimators of the PSDs. However, we show that SFs are also troubled by gaps which can induce artefacts.
Abstract Copyright: © 2010 The Authors. Journal compilation © 2010 RAS
Journal keyword(s): methods: data analysis - methods: numerical - methods: statistical - galaxies: active - BL Lacertae objects: general - galaxies: individual: Mrk501
Simbad objects: 4
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