A hierarchical regime cascade versus the damped random walk on 21 years of GRS 1915+105 and Cyg X-1

Abstract

The damped random walk (an Ornstein–Uhlenbeck process) is the default stochastic description of accreting-source light curves. We race it, fairly, against an exact 2^k-state Markov-switching multifractal cascade on the public Swift/BAT transient-monitor products for the bright pair, with per-point measurement errors folded into the emission model so the noise model cannot decide the contest, and with stronger linear rivals (CARMA(2,1), OU mixtures) entered beside the DRW. On GRS 1915+105 the cascade wins decisively and out of sample; on Cyg X-1 it does not, and the paper reports the split rather than the win. A parametric bootstrap under DRW truth places the observed statistic beyond every replicate at the ensemble resolution floor, a cadence sweep over a factor of sixteen shows the verdict is not an artifact of daily binning, and a population sweep places the two-source result in the Swift/BAT catalog: the wins scale with multi-stateness rather than with brightness.