Desperately Seeking Non-Gaussianity

Abstract

“Non-Gaussian” is the casual explanation often given for anything unexpected in an astronomical time series. What better place to look for non-Gaussianity, therefore, than in the light curve of 0957+561, the gravitational lens that, until recently, had yielded frustratingly inconsistent determinations of its lag. We discuss the difficulties in measuring deviations from Gaussianity in weakly nonstationary processes (such as 1/f noise or random walk) and define a restricted set of “well-behaved” three-point statistics. An important special case of such a well-behaved statistic is the skew of a linear combination of the data, with coefficients summing to zero. Analytic and Monte Carlo calculations evaluate the performance of such a statistic in the case of a non-Gaussian “wedge model” (shot noise, with each shot having a rapid rise and slow decay). We find that even for as well studied an object as 0957+561, the detectability of any deviation from Gaussian is problematical at best. At present, one can rule out a wedge model only if the individual shots are as infrequent as one in 10–20 days.